
    UNITED STATES of America, Appellant, v. Corey REINGOLD, Defendant-Appellee.
    
    Docket No. 11-2826-CR.
    United States Court of Appeals, Second Circuit.
    Argued: May 4, 2012.
    Decided: Sept. 26, 2013.
    
      Ali Kazemi (Amy Busa, on the brief), Assistant United States Attorneys, for Loretta E. Lynch, United States Attorney for the Eastern District of New York, Brooklyn, NY, for Appellant.
    Colleen P. Cassidy, Appeals Bureau, Federal Defenders of New York, Inc., New York, NY, for Defendanb-Appellee.
    Before: SACK, RAGGI, and LOHIER, Circuit Judges.
    
      
       The Clerk of Court is directed to amend the official caption as shown above.
    
   REENA RAGGI, Circuit Judge:

Corey Reingold pleaded guilty in the United States District Court for the Eastern District of New York (Jack B. Wein-stein, Judge) to one count of distributing child pornography. See 18 U.S.C. § 2252(a)(2). The United States now appeals from that part of the June 21, 2011 judgment of conviction as sentenced Rein-gold to 30 months’ incarceration. The government contends that the district court erred in refusing to impose the minimum five-year prison term mandated by 18 U.S.C. § 2252(b)(1) on the ground that applying such a punishment to this immature 19-year-old defendant would violate the Cruel and Unusual Punishment Clause. See U.S. Const, amend. VIII. The government further disputes the district court’s Sentencing Guidelines calculations. The district court explained its sentencing decisions both on the record and in a 401-page opinion accompanied by 55 pages of appendices. See United States v. C.R., 792 F.Supp.2d 343 (E.D.N.Y.2011). Having carefully reviewed that opinion, the applicable law, and the record as a whole, we conclude that the district court erred in both respects identified by the government. We therefore remand the case to the district court with directions that it vacate the sentence and resentence the defendant consistent with this opinion.

I. Background

A. Events Leading to Reingold’s Prosecution

On November 16, 2008, an agent of the Federal Bureau of Investigation (“FBI”), investigating child pornography in an undercover capacity, accessed a computer program called “GigaTribe,” which allows users to download material onto their computers and then to place some in folders designated for sharing with others. For GigaTribe users to access each other’s designated sharing folders, they must be on the same “closed network of buddies,” which is accomplished by invitation.' Id. at 352 (internal quotation marks omitted) (citing United States v. Ladeau, No. 09-CR-40021-FDS, 2010 WL 1427523, at *1 (D.Mass. Apr. 7, 2010) (describing operation of GigaTribe)).

When the undercover agent accessed Gi-gaTribe on November 16, he observed child pornography in the mini-profile of a person with the username “Boysuek0416.” The agent also noted that this user’s full profile contained the terms “Boy Love KDV PJK BCP,” which the agent identified as child pornography search terms. The agent invited the user to share files, and after the user agreed, the agent downloaded ten videos and one still image of child pornography from the user’s designated share folder. See United States v. Ladeau, 2010 WL 1427523, at *1 (“A user can also join the networks of other Giga-Tribe users, but only with the permission of the user who created the network.”). He then proceeded to trace the user’s Internet Protocol address to a residence at 3-14 Beach 147th Street in Queens, New York, which turned out to be the home of Jamie and Brian McLeod, the mother and stepfather of defendant Corey Reingold.

On January 15, 2009, FBI agents executed a search warrant at the McLeod home and seized two computers used exclusively by Reingold, each of which contained child pornography. Reingold, who was present at the time of the search, admitted that he was “Boysuck0416”; that he had opened a GigaTribe account in November 2008 and used it and another file sharing program, LimeWire, to download “a ton” of child pornography onto the seized computers; and that he had shared child pornography files in designated folders with between 10 and 20 other Giga-Tribe users. Pre-Sentence Report (“PSR”) ¶ 9; see United States v. C.R., 792 F.Supp.2d at 353. Subsequent forensic analysis would confirm that the seized Reingold computer linked to GigaTribe contained more than 100 video files and at least 208 digital images of child pornography, while the seized computer linked to LimeWire contained 10 videos of child pornography.

B. Reingold’s Admissions to Sexual Conduct with Minors

As part of initial plea negotiations with federal prosecutors, Reingold agreed to take a polygraph examination -with the understanding that he would be allowed to plead guilty to simple possession of child pornography, see 18 U.S.C. § 2252(a)(4)(B), if he could truthfully state that he had not had any sexual contact with minors. Even before the polygraph examination, however, Reingold admitted to federal authorities that he had engaged his minor half-sister in sexual activities on three occasions over a course of three years. Specifically, Reingold stated that (1) when he was 15 and his sister eight, he had the child manually stimulate his penis; (2) when Reingold was 16 and his sister nine, he again had the girl manually stimulate his penis while he rubbed his hand over her vagina through her underwear; and (3) when Reingold was 18 and his sister 11, he had the girl manually stimulate his penis while he rubbed her vagina both over and beneath her underwear. Reingold subsequently admitted that during this third sexual encounter, he also coached the child to perform oral sex on him and, in turn, performed oral sex on her.

C. Plea and Sentencing

1. Entry and Acceptance of Reingold’s Guilty Plea

On March 18, 2009, Reingold was indicted by a grand jury sitting in the Eastern District of New York on four counts of distributing child pornography based on the GigaTribe “sharing” of four specified video files to the undercover agent on November 17, 2008, see 18 U.S.C. § 2252(a)(2), (b)(1); and one count of possessing child pornography, see id. § 2252(a)(4)(B), (b)(2). On September 16, 2009, Reingold pleaded guilty before a magistrate judge to the first distribution count.

Before formally accepting Reingold’s guilty plea and in anticipation of sentencing, the district court conducted hearings between September 2009 and May 2011 where it heard from “a dozen expert witnesses in the fields of child sexual abuse; online child pornography; risk assessment; treatment of sex offenders; and neuropsy-chology and adolescent brain development.” United States v. C.R., 792 F.Supp.2d at 349. Together with prosecutors, defense counsel, and two of his law clerks, the district judge also traveled to Massachusetts and personally toured FMC Devens, the Bureau of Prisons facility that offers inmates sex offender treatment. See id. at 520-24.

On May 10, 2011, the initial sentencing date, the district court declined to accept Reingold’s guilty plea before the magistrate judge, questioning whether the undercover agent’s retrieval of child pornography from Reingold’s designated shared folder on GigaTribe was enough to make the defendant guilty of distribution under 18 U.S.C. § 2252(a)(2). Although the government and defense counsel both urged acceptance of the plea, the district court adjourned the case to May 16, 2011, to allow it to consider the matter further.

On May 16, 2011, the district court accepted Reingold’s guilty plea. On the record, it explained that its acceptance was “based on the allocution and all other information now known to me.” May 16, 2011 Sentencing Tr. 5:21-22. In its published opinion filed the same day, however, the district court expressed continued reservations as to whether the defendant had adequately admitted knowing and intentional distribution of child pornography as proscribed by 18 U.S.C. § 2252(a)(2). See United States v. C.R., 792 F.Supp.2d at 353-55 (construing statute to require proof of both “active intent[ ]” to transfer child pornography to another person and “active participation” in delivery of such pornography). In the end, however, the district court accepted the guilty plea, explaining that the statute’s distribution element might be construed to reach Reingold’s conduct; that “a jury could reasonably find that [Reingold] was not truthful when he testified that he did not intend to distribute his files to another individual”; that a court can accept a guilty plea even when a defendant maintains his innocence, “as long as there is a strong factual basis for the plea”; and that the record showed Reingold to have thoroughly considered his decision to plead guilty with the support of close relatives and able counsel, and to have demonstrated a wish to accept responsibility for his conduct. Id. at 356-57 (citing North Carolina v. Alford, 400 U.S. 25, 37-38, 91 S.Ct. 160, 27 L.Ed.2d 162 (1970)).

2. Reingold’s Sentencing

In its PSR to the district court, the Probation Department advised that Rein-gold’s crime of conviction was subject to a mandatory minimum prison sentence of five years pursuant to 18 U.S.C. § 2252(b)(1).. Further, based on Sentencing Guidelines calculations yielding a total offense level of 35 and a criminal history category of I, the PSR reported that Rein-gold’s recommended sentencing range was 168 to 210 months’ imprisonment.

The district court viewed the case quite differently. Rejecting the Probation Department’s application of various enhancements to Reingold’s Guidelines calculation, the district court concluded that the applicable Sentencing Guidelines range in Reingold’s case was 63 to 78 months’ imprisonment. The district court further determined that Reingold should not be sentenced even within that reduced Guidelines range because such a term of imprisonment was greater than necessary to achieve the objectives of 18 U.S.C. § 3553(a). Insofar as Congress had statutorily mandated a prison sentence of at least five years for any defendant guilty of distributing child pornography, the district court concluded that such a sentence would constitute cruel and unusual punishment in Reingold’s case given his particular immaturity and the relative passivity of his crime. See United States v. C.R., 792 F.Supp.2d at 509-10. Accordingly, the district court sentenced Reingold to 30 months’ imprisonment, five years’ supervised release, and a $100 special assessment. It recommended that Reingold serve his term in the FMC Devens Sex Offender Treatment Program and allowed him to self-surrender.

II. Discussion

A. Eighth Amendment Challenge to Five-Year Mandatory Minimum

The government argues that the district court was legally obligated to sentence Reingold to the minimum five-year prison term mandated by 18 U.S.C. § 2252(b)(1) for any distribution of child pornography. It submits that the district court erred as a matter of law in holding that the application of that mandated minimum sentence to Reingold would violate the Eighth Amendment. We review de novo a district court’s “[e]onclusions of law, including those involving constitutional questions,” United States v. Fell, 531 F.3d 197, 209 (2d Cir.2008), and here conclude that the district court erred in holding the mandatory minimum sentence unconstitutional.

B. Standards Applicable to Eighth Amendment Analysis

The Eighth Amendment states that “[e]xcessive bail shall not be required, nor excessive fines imposed, nor cruel and unusual punishments inflicted.” U.S. Const, amend. VIII. In identifying cruel and unusual punishments, the Supreme Court has not limited itself to “historical conceptions” of impermissible sanctions, Graham v. Florida, 560 U.S. 48, 130 S.Ct. 2011, 2021, 176 L.Ed.2d 825 (2010), but has looked to “ ‘the evolving standards of decency that mark the progress of a maturing society,’ ” Kennedy v. Louisiana, 554 U.S. 407, 419, 128 S.Ct. 2641, 171 L.Ed.2d 525 (2008) (quoting Trop v. Dulles, 356 U.S. 86, 101, 78 S.Ct. 590, 2 L.Ed.2d 630 (1958) (plurality opinion)). A punishment will be deemed “cruel and unusual” not only when it is “inherently barbaric,” but also when it is “disproportionate to the crime.” Graham v. Florida, 130 S.Ct. at 2021; see Harmelin v. Michigan, 501 U.S. 957, 997-98, 111 S.Ct. 2680, 115 L.Ed.2d 836 (1991) (Kennedy, J., concurring in part and concurring in the judgment) (tracing history of proportionality principle).

1. General Principles of Constitutional Proportionality

This appeal focuses on the proportionality aspect of Eighth Amendment jurispru-denee. The Supreme Court first interpreted the Eighth Amendment to prohibit “ ‘greatly disproportioned’ ” sentences in Weems v. United States, 217 U.S. 349, 371, 30 S.Ct. 544, 54 L.Ed. 793 (1910) (quoting O’Neil v. Vermont, 144 U.S. 323, 340, 12 S.Ct. 693, 36 L.Ed. 450 (1892) (Field, J., dissenting)). Since then, the Court has emphasized that constitutional proportionality is a “narrow” principle in that it “does not require strict proportionality,” and it “forbids only extreme sentences that are ‘grossly disproportionate’ to the crime.” Harmelin v. Michigan, 501 U.S. at 997, 1001, 111 S.Ct. 2680 (Kennedy, J., concurring) (quoting Solem v. Helm, 463 U.S. 277, 288, 103 S.Ct. 3001, 77 L.Ed.2d 637 (1983)); accord Graham v. Florida, 130 S.Ct. at 2021.

A number of principles inform this narrow view of the constitutional mandate of proportionality: (1) the “substantial deference” generally owed by reviewing courts “to the broad authority that legislatures necessarily possess in determining the types and limits of punishments for crimes”; (2) a recognition that the Eighth Amendment does not mandate “any one penological theory” and that “competing theories of mandatory and discretionary sentencing have been in varying degrees of ascendancy or decline since the beginning of the Republic”; (3) respect for the “marked divergences both in underlying theories of sentencing and in the length of prescribed prison terms” that “are the inevitable, often beneficial, result of the federal structure”; and (4) prudential understanding that proportionality review “should be informed by objective factors to the maximum possible extent,” that the “most prominent objective factor is the type of punishment imposed,” and that while the Supreme Court has frequently referenced “the objective line between capital punishment and imprisonment for a term of years,” it has itself acknowledged a “lack [of] clear objective standards to distinguish between sentences for different terms of years.” Harmelin v. Michigan, 501 U.S. at 998-1001, 111 S.Ct. 2680 (Kennedy, J., concurring) (internal quotation marks omitted).

2. Reviewing the Proportionality of a Punishment in a Particular Case

The Supreme Court’s proportionality cases fall into two classifications. “The first involves challenges to the length of term-of-years sentences given all the circumstances in a particular case.” Graham v. Florida, 130 S.Ct. at 2021 (emphasis added). In making a case-particular assessment of proportionality, the Court has employed a two-step analysis, first “comparing the gravity of the offense and the severity of the sentence.” Id. at 2022. Given the principles already discussed, the Court has observed that it will be “ ‘the rare ease in which this threshold comparison ... leads to an inference of gross disproportionality.’ ” Id. (quoting Harmelin v. Michigan, 501 U.S. at 1005, 111 S.Ct. 2680 (Kennedy, J., concurring) (first alteration in Graham omitted)). Should such an inference arise, however, the second step of the analysis requires a court to “compare the defendant’s sentence with the sentences received by other offenders in the same jurisdiction and with the sentences imposed for the same crime in other jurisdictions.” Id. Only “[i]f this comparative analysis ‘validate^] an initial judgment that [the] sentence is grossly disproportionate’ ” will the sentence be deemed “cruel and unusual.” Id. (quoting Harmelin v. Michigan, 501 U.S. at 1005, 111 S.Ct. 2680 (Kennedy, J., concurring) (alterations in original)).

In this case-particular review, the Supreme Court has thus far identified a term-of-years sentence as grossly disproportionate on only one occasion. In Solem v. Helm, a South Dakota court sentenced a defendant with a prior record of six nonviolent felony convictions to a non-mandatory term of life imprisonment without parole for passing a bad check in the amount of $100. See 463 U.S. at 279, 281-82, 103 S.Ct. 3001. The Supreme Court drew a threshold inference of gross disproportion-ality from the fact that the crime of conviction was “one of the most passive felonies a person could commit,” involving “neither violence nor threat of violence to any person,” id. at 296, 103 S.Ct. 3001 (internal quotation marks omitted), while the punishment was “the most severe” non-capital sentence “that the State could have imposed on any criminal for any crime,” id. at 297, 103 S.Ct. 3001. That inference of disproportionality was then validated by the fact that “Helm was treated more severely than he would have been in any other State.” Id. at 300, 103 S.Ct. 3001.

Since Solem, the Supreme Court has consistently rejected proportionality challenges to prison sentences in particular cases. In Harmelin v. Michigan, the Court upheld a statutorily mandated term of life imprisonment without parole in the Michigan case of a recidivist defendant convicted of possessing 672 grams of cocaine. See 601 U.S. at 1009, 111 S.Ct. 2680 (Kennedy, J., concurring). Declining to draw a threshold inference of gross dispro-portionality, Justice Kennedy observed that Harmelin’s crime was distinguishable from the “relatively minor, nonviolent crime at issue in Solem,” because the “[possession, use, and distribution of illegal drugs represent one of the greatest problems affecting the health and welfare of our population.” Id. at 1002, 111 S.Ct. 2680 (internal quotation marks omitted) (recognizing range of criminal activity associated with drug possession). In such circumstances, “the Michigan Legislature could with reason conclude that the threat posed to the individual and society by possession of this large an amount of cocaine — in terms of violence, crime, and social displacement — is momentous enough to warrant the deterrence and retribution of a life sentence without parole.” Id. at 1003, 111 S.Ct. 2680.

Thereafter, in Ewing v. California, 538 U.S. 11, 123 S.Ct. 1179, 155 L.Ed.2d 108 (2003), the Supreme Court rejected a proportionality challenge to a prison sentence of 25 years to life imposed pursuant to California’s Three Strikes Law on a recidivist felon convicted of stealing $1,200 worth of golf clubs, see id. at 16-18, 123 S.Ct. 1179 (plurality) (referencing Cal.Penal Code Ann. § 667(e)(2)(A)). Declining to draw an inference of gross dispropor-tionality, the Court plurality reasoned that defendant’s grand theft felony was not one of the most passive crimes a person could commit, that the California legislature “made a judgment that protecting the public safety requires incapacitating criminals who have already been convicted of at least one serious or violent crime[, and that njothing in the Eighth Amendment prohibits California from making that choice.” Id. at 25, 28, 123 S.Ct. 1179; see Lockyer v. Andrade, 538 U.S. 63, 77, 123 S.Ct. 1166, 155 L.Ed.2d 144 (2003) (rejecting prisoner’s Eighth Amendment habeas challenge to sentence of 25 years to life under California’s Three Strikes law for stealing approximately $150 worth of videotapes).

As these cases make plain, at the same time that the Eighth Amendment prohibits grossly disproportionate sentences, it is rare that a sentence falling within a legislatively prescribed term of years will be deemed grossly disproportionate. See Harmelin v. Michigan, 501 U.S. at 1001, 111 S.Ct. 2680 (Kennedy, J., concurring) (noting that “outside the context of capital punishment, successful challenges to the proportionality of particular sentences are exceedingly rare” (alterations and internal quotation marks omitted; emphasis in original)); accord United States v. Polk, 546 F.3d 74, 76 (1st Cir.2008) (observing that “instances of gross disproportionality” are “hen’s-teeth rare”).

3. Ensuring Proportionality Through Categorical Rules

“The second classification of [proportionality] cases has used categorical rules to define Eighth Amendment standards.” Graham v. Florida, 130 S.Ct. at 2022. Until Graham, such categorical pronouncements were made with respect to a single punishment — the death penalty — and fell into “two subsets, one considering the nature of the offense” for which death was ordered, “the other considering the characteristics of the offender” sentenced to death. Id. Thus, the Supreme Court has categorically prohibited death sentences for “nonhomicide crimes against individuals,” id., such as rape, see Kennedy v. Louisiana, 554 U.S. at 413, 128 S.Ct. 2641, or felony murder where'the defendant participated in the felony but did not kill or intend to kill anyone, see Enmund v. Florida, 458 U.S. 782, 801, 102 S.Ct. 3368, 73 L.Ed.2d 1140 (1982). The Court has also categorically prohibited death sentences for juvenile defendants, see Roper v. Simmons, 543 U.S. 551, 578, 125 S.Ct. 1183, 161 L.Ed.2d 1 (2005), and persons who are mentally retarded, see Atkins v. Virginia, 536 U.S. 304, 321, 122 S.Ct. 2242, 153 L.Ed.2d 335 (2002).

In identifying types of crimes or types of defendants for whom capital punishment is categorically disproportionate, the Supreme Court has prescribed a two-step analysis. It “first considers objective in-dicia of society’s standards, as expressed in legislative enactments and state practice to determine whether there is a national consensus against the sentencing practice at issue.” Graham v. Florida, 130 S.Ct. at 2022 (internal quotation marks omitted). But because “[c]ommunity consensus, while entitled to great weight, is not itself determinative of whether a punishment is cruel and unusual,” it then proceeds to a second step. Id. at 2026 (internal quotation marks omitted). “[GJuided by the standards elaborated by controlling precedents and by the Court’s own understanding and interpretation of the Eighth Amendment’s text, history, meaning, and purpose, the Court must determine in the exercise of its own independent judgment whether the punishment in question violates the Constitution.” Id. at 2022 (internal quotation marks omitted). In this inquiry, a court properly considers “the culpability of the [class of] offenders at issue in light of their crimes and characteristics, along with the severity of the punishment in question.” Id. at 2026. It “also considers whether the challenged sentencing practice serves legitimate penological goals.” Id.

In Graham v. Florida, the Supreme Court for the first time applied this analysis to pronounce a categorical rule for a non-capital sentencing practice: the imposition of life imprisonment without parole on juvenile offenders for nonhomicide crimes. The Court concluded that just as the Eighth Amendment categorically prohibits capital punishment for juvenile offenders, so too does it categorically prohibit life without parole for those same offenders when they stand convicted of nonhomicide crimes. See 130 S.Ct. at 2030. In reaching this conclusion, the Court identified a kinship between sentences of death and of life imprisonment without parole that warranted certain categorical rules to ensure proportionality. See id. at 2027, 2033 (observing that although “[t]he State does not execute the offender sentenced to life without parole,” “Graham’s sentence guarantees he will die in prison”). Nevertheless, the Court did not construe the Eighth Amendment to require that juvenile defendants be released at some time during their natural life. See id. at 2030 (“A State is not required to guarantee eventual freedom to a juvenile offender convicted of a non-homicide crime.”). It required only that juveniles be given “some meaningful opportunity to obtain release based on demonstrated maturity and rehabilitation.” Id.

Last term, the Court pronounced another categorical rule for a sentence of life without parole, barring its mandatory application to juvenile offenders convicted of homicide crimes. See Miller v. Alabama, — U.S. -, 132 S.Ct. 2455, 183 L.Ed.2d 407 (2012). Here, the Supreme Court identified no categorical constitutional requirement that juveniles sentenced to life imprisonment for murder be afforded some opportunity for release. It ruled only that life without parole for such juvenile offenders could not be mandatory and had to reflect an individualized sentencing determination. See id. at 2460.

In reaching this conclusion, the Court not only reiterated the analogy Graham drew between a death sentence and life without parole, but also clarified that the kinship between these two harshest possible sentences explained Graham’s pronouncement of a categorical rule “in a way unprecedented for a term of imprisonment.” Id. at 2466. Relying on that kinship, and on precedent categorically barring both capital punishment for juveniles and mandatory capital punishment for adults, Miller held that the Eighth Amendment’s “principle of proportionality” categorically prohibited mandatory life without parole for juveniles. Id. at 2475. Thus, “a judge or jury must have the opportunity to consider mitigating circumstances before imposing the harshest possible penalty for juveniles.” Id.

C. Proportionality Review of the Mandatory Five-Year Minimum Sentence as Applied to Reingold

1. The District Court’s Mistaken Reliance on “Categorical Rule” Analysis To Assess the Proportionality of a Mandatory Five-Year Sentence in This Particular Case

The district court appears to have construed Graham to invite categorical rule analysis of any term-of-years sentence, including the mandatory five-year sentence at issue here. See United States v. C.R., 792 F.Supp.2d at 507. This misconstrues Graham.

First, as Miller recognized, Graham’s “unprecedented” imposition of a categorical ban outside the context of capital sentencing derives from the Court’s recognition that life without parole for juveniles was “akin to the death penalty.” Miller v. Alabama, 132 S.Ct. at 2466. Nothing in Gmham or Miller suggests that a five-year prison term is the sort of inherently harsh sentence that — like the death penalty or its deferred equivalent, life imprisonment without parole — requires categorical rules to ensure constitutional proportionality as applied to particular felony crimes or classes of defendants. Certainly, a five-year sentence does not deprive a defendant of all hope of release, the only categorical limitation the Supreme Court thought constitutionally necessary for mandatory life sentences imposed on juvenile defendants imprisoned for nonhomi-cide crimes. See Graham v. Florida, 130 S.Ct. at 2030. Much less does a five-year sentence equate to one of “the law’s most serious punishments” so as to raise the constitutional concerns identified in Miller v. Alabama about the mandatory application of life without parole to all juveniles. 132 S.Ct. at 2467, 2471; see also Harmelin v. Michigan, 501 U.S. at 995, 111 S.Ct. 2680 (“[A] sentence which is not otherwise cruel and unusual” does not “become[ ] so simply because it is mandatory.” (internal quotation marks omitted)). Accordingly, a mandatory minimum five-year sentence is not the sort of sentencing practice that the Supreme Court has ever signaled requires categorical rules to ensure constitutional proportionality.

Second, insofar as the district court purported to identify a consensus against five-year prison terms for juveniles convicted of child pornography crimes, we are by no means persuaded by its analysis. We need not discuss the point, however, because any such consensus is not relevant here. Reingold was already 19 when he committed the crime of conviction. In short, he was an adult, not a juvenile. The district court tries to blur the distinction between juvenile and adult offenders by finding that, “at the time of the crime,” Reingold was “a developmentally immature young adult.” United States v. C.R., 792 F.Supp.2d at 506. Even if we accept this assessment, however, it hardly supports categorical rule analysis in this case. Nowhere does the record reveal any consensus about how immature adults should be sentenced for child pornography crimes. Moreover, immaturity, unlike age, is a subjective criterion, ill suited to the pronouncement of categorical rules. See generally Harmelin v. Michigan, 501 U.S. at 1000, 111 S.Ct. 2680 (Kennedy, J., concurring) (emphasizing that proportionality review “should be informed by objective factors to the maximum possible extent” (internal quotation marks omitted)). The Supreme Court recognized as much when, in “[djrawing the line at 18 years of age” for death eligibility in Roper v. Simmons, it acknowledged that “[t]he qualities that distinguish juveniles from adults do not disappear when an individual turns 18.” 543 U.S. at 574, 125 S.Ct. 1183. Nevertheless, “a line must be drawn” to pronounce a categorical rule, and because “[t]he age of 18 is the point where society draws the line for many purposes between childhood and adulthood,” the Court used that age to distinguish the class of offenders that categorically could not be sentenced to death from others to whom no such categorical prohibition would apply. Id. This is not to suggest that an adult defendant’s immaturity is irrelevant to sentencing. To the contrary, that circumstance is appropriately considered by a judge in making a case-specific choice of sentence within a statutorily prescribed range. See generally 18 U.S.C. §§ 3553(a), 3661. We here conclude only that the district court could not substitute the defendant’s relative immaturity for the actual age of minority in applying categorical-rule analysis to the mandated five-year minimum sentence at issue.

Third, the district court did not, in any event, employ Graham’s analytic approach to pronounce a categorical rule. Rather, it employed such analysis to find a five-year minimum sentence “disproportionate to the offense” of conviction “as applied to this defendant.” United States v. C.R., 792 F.Supp.2d at 510 (emphasis added and internal quotation marks omitted). The Supreme Court’s proportionality jurisprudence does not support such a substitution of Graham’s categorical-rule approach for Harmelin’s particular-case approach to assess the proportionality of an otherwise permissible term-of-years sentence as applied to a particular case. As the Court explained in Graham, where the proportionality of a term-of-years sentence is challenged as applied to a particular defendant convicted for a specific crime, the proper analytic approach is that employed in Harmelin and Ewing, which requires “a threshold comparison between the severity of the penalty and the gravity of the crime.” Graham v. Florida, 130 S.Ct. at 2028. It is where a “type of sentence” is challenged “as it applies to an entire class of offenders who have committed a range of crimes” that such “a threshold comparison ... does not advance the analysis” and “the categorical approach” is properly employed. Id. at 2022-23. Thus, in Graham, a categorical approach was required to assess a proportionality challenge to a sentence of life imprisonment without parole as applied to the class of persons under the age of 18 convicted of a range of nonhomicide crimes. By contrast, here, a mandatory minimum sentence of five years is challenged as applied to Reingold because of his particular immaturity and the circumstances under which he distributed child pornography. That proportionality inquiry is properly conducted by reference to Harmelin’s case-specific rather than Graham’s categorical-rule analysis.

When we conduct particular-case analysis here, as we do in the next section of this opinion, we conclude that the statutorily mandated five-year minimum sentence does not constitute cruel and unusual punishment as applied to Reingold.

2. The Mandatory Five-Year Minimum Sentence Is Not Grossly Disproportionate as Applied to Reingold

In reviewing the proportionality of a challenged sentence as applied to a particular case, a court must first consider whether the “gravity of the offense and the severity of the sentence” give rise to an “inference of gross disproportionality.” Graham v. Florida, 130 S.Ct. at 2022 (internal quotation marks omitted). The district court failed to make this comparative assessment. We do so here and conclude that the comparison supports no inference of gross disproportionality in applying the minimum five-year sentence mandated by 18 U.S.C. § 2252(b)(1) to Reingold.

a. The Gravity of the Offense

Starting with the gravity of the offense at issue, there can be no question that the dissemination of child pornography is a serious crime that causes real injury to particularly vulnerable victims. As Congress, courts, and scholars all recognize, child pornography crimes at their core demand the sexual exploitation and abuse of children. Not only are children seriously harmed — physically, emotionally, and mentally — in the process of producing such pornography, but that harm is then exacerbated by the circulation, often for years after the fact, of a graphic record of the child’s exploitation and abuse. See New York v. Ferber, 458 U.S. 747, 757-59 & nn.9-10, 102 S.Ct. 3348, 73 L.Ed.2d 1113 (1982) (citing congressional and scholarly reports, and court cases).

The circumstances of this case do not mitigate the general severity of such criminal conduct. The pornography that is the subject of Reingold’s distribution count of conviction is a video depicting a female child, approximately eight years old, unclothed, as an adult male penetrates her mouth with his erect penis and then places his mouth on her vagina. It is not necessary for us to detail similar depictions of the sexual exploitation of children in the materials that Reingold designated for sharing with — i.e., distribution to — other GigaTribe users, to confirm the seriousness of the criminal conduct at issue.

Nor can any mitigation be located in the fact that Reingold’s crimes were facilitated by a recent “digital revolution” that has “enormously increased the ways that child pornography can be created, accessed, and distributed.” United States v. C.R., 792 F.Supp.2d at 367. The ease with which a person can access and distribute child pornography from his home — -often with no more effort than a few clicks on a computer — may make it easier for perpetrators to delude themselves that their conduct is not deviant or harmful. But technological advances that facilitate child pornography crimes no more mitigate the real harm caused by these crimes than do technological advances making it easier to perpetrate fraud, traffic drugs, or even engage in acts of terrorism—all at a distance from victims — mitigate those crimes. If anything, the noted digital revolution may actually aggravate child pornography crimes insofar as an expanding market for child pornography fuels greater demand for perverse sexual depictions of children, making it more difficult for authorities to prevent their sexual exploitation and abuse. See generally United States v. Lewis, 605 F.3d 395, 403 (6th Cir.2010) (noting that distribution through computers “is particularly harmful because it can reach an almost limitless audience” (internal quotation marks omitted) (citing H.R.Rep. No. 104-90, at 3-4 (1995), reprinted in 1995 U.S.C.C.A.N. 759, 760-61)). But precisely because the prevention of such exploitation and abuse is “a government objective of surpassing importance,” New York v. Ferber, 458 U.S. at 757, 102 S.Ct. 3348; see id. at 756-57, 102 S.Ct. 3348 (“It is evident beyond the need for elaboration that a State’s interest in safeguarding the physical and psychological well-being of a minor is compelling.” (internal quotation marks omitted)), we cannot view the distribution of child pornography, however accomplished, as anything but a serious crime that threatens real, and frequently violent, harm to vulnerable victims, cf. Hamelin v. Michigan, 501 U.S. at 1002-03, 111 S.Ct. 2680 (Kennedy, J., concurring) (observing that characterization of drug possession with intent to distribute as “nonviolent and victimless” crime “is false to the point of absurdity” given “pernicious effects” of drug use).

No different conclusion is warranted because Reingold professed a principal interest in receiving rather than distributing child pornography. See United States v. C.R., 792 F.Supp.2d at 354. Reingold acknowledged that when he joined GigaTribe he knew that in order to secure child pornography from others, he would have to share child pornography with them in return. In short, Reingold understood from the start that, in this barter-like market, distribution was integral to receipt. To the extent such arrangements only expand the market in which child pornography is disseminated, Reingold’s interest in augmenting his own collection of child pornography does not render his distribution of such pornography any less serious a crime.

Nor is Reingold’s crime mitigated by the fact that, once he established his Giga-Tribe share folder, users on the same “closed network of buddies,” id. at 352 (internal quotation marks omitted), could access its content without further action by Reingold. Reingold was obliged in the first instance to create a share folder and had to designate materials to be included therein. The materials he elected to share were child pornography, and among the child pornography he designated for sharing was the described video depicting the sexual exploitation of an eight-year-old girl. From the totality of affirmative actions that Reingold took to allow others to gain access to his share file, we cannot conclude that his was among the “most passive” felony crimes. Solem v. Helm, 463 U.S. at 296, 103 S.Ct. 3001 (internal quotation marks omitted). Nor, for reasons already discussed, can we conclude that the distribution of child pornography is a victimless crime or one posing no threat of violence or physical harm. Cf. id. (noting that passing bad check posed no threat of violence); Harmelin v. Michigan, 501 U.S. at 1002, 111 S.Ct. 2680 (Kennedy, J., concurring) (declining to view drug possession with intent to distribute as “nonviolent and victimless” crime).

Such a conclusion seems particularly unwarranted here, where Reingold admitted that in addition to viewing and distributing child pornography, he repeatedly engaged his pre-pubescent sister in sexual activity. Indeed, his last reported sexual interaction with the child, when he was 18 and she was 11, was disturbingly similar to the conduct depicted on the video that is the subject of the distribution count of conviction. The district court concluded that Reingold’s sexual conduct with his sister was mitigated by the lack of adequate parental supervision, Reingold’s minority during the first two encounters, and his continued immaturity as an adult. See United States v. C.R., 792 F.Supp.2d at 511; May 16, 2011 Sentencing Tr. 15:24-16:1. Even if correct, such excuses cannot transform the admitted three encounters into something benign, or deny their scarring effect on the girl. Much less do these excuses mitigate the exacerbating harm caused to children by Reingold’s distribution of pornography in which they are depicted.

For all these reasons, the distribution crime of conviction is appropriately viewed as a serious offense.

b. The Seventy of the Sentence at Issue

With the gravity of Reingold’s offense thus weighing heavily in the balance, we consider whether a congressionally mandated five-year minimum sentence is grossly disproportionate to the crime. The question requires no extended discussion.

As has long been recognized, “it is difficult, if not impossible to halt” the sexual exploitation and abuse of minors by pursuing only the producers of child pornography. New York v. Ferber, 458 U.S. at 759-60, 102 S.Ct. 3348. Thus, the Supreme Court has acknowledged that “[t]he most expeditious if not the only practical method of law enforcement may be to dry up the market for this material by imposing severe criminal penalties ” on all persons in the distribution chain. Id. at 760, 102 S.Ct. 3348 (emphasis added). With precisely this objective in mind, see H.R. Conf. Rep. 108-66, at *28 (2003), reprinted in 2003 U.S.C.C.A.N. 683 (quoting New York v. Ferber, 458 U.S. at 760, 102 S.Ct. 3348), Congress, in 2003, established a graduated sentencing regime for crimes involving child pornography, with any knowing receipt or distribution of child pornography transmitted in interstate or foreign commerce punishable by a prison term of “not less than five years and not more than 20 years” in prison. 18 U.S.C. § 2252(b)(1). The question on this appeal is not whether we would ourselves have made that precise policy decision if charged with legislative responsibility. In our judicial capacity, we conclude simply that no inference of “gross disproportionality” can be drawn from Congress’s enactment of a five-year minimum sentence for as serious a felony crime as the distribution of child pornography. See Harmelin v. Michigan, 501 U.S. at 999, 111 S.Ct. 2680 (Kennedy, J., concurring) (emphasizing “substantial deference” that reviewing courts owe legislature’s “broad authority ... in determining the types and limits of punishments for crimes” (internal quotation marks omitted)).

In making that determination, we need not look beyond the depicted sexual exploitation of an eight-year old on the distributed video to conclude that the crime of conviction here is a more serious offense than the golf club and videotape thefts in Ewing and Lockyer, for which the Supreme Court upheld prison sentences of 25 years to life. To be sure, those sentences were informed by the defendants’ prior criminal records. Nevertheless, a large number of federal felony crimes carry the possibility of five-year prison terms for first time offenders. In such circumstances, we can hardly infer gross dispro-portionality from Congress’s decision to apply such a punishment to a felony crime presenting the serious harms associated with the distribution of child pornography.

No different conclusion is warranted because Congress mandated a minimum five-year sentence rather than leaving the possibility of such a punishment to the discretion of the sentencing judge. As the Supreme Court observed in Harmelin v. Michigan, the legislature’s “ ‘power to define criminal punishments without giving the courts any sentencing discretion’ ” is “beyond question.” 501 U.S. at 1006, 111 S.Ct. 2680 (Kennedy, J., concurring) (quoting Chapman v. United States, 500 U.S. 453, 467, 111 S.Ct. 1919, 114 L.Ed.2d 524 (1991)); see id. at 999, 111 S.Ct. 2680 (recognizing that “competing theories of mandatory and discretionary sentencing have been in varying degrees of ascendancy or decline since the beginning of the Republic”). Precisely because statutorily mandated sentences represent not the judgment of a single judge but “the collective wisdom of the ... Legislature and, as a consequence, the ... citizenry,” in Harmelin the Court accorded great deference to a state legislature’s policy decision to mandate life sentences for persons who possessed more than 650 grams (approximately a pound and a half) of cocaine. Id. at 1006, 111 S.Ct. 2680. Indeed, the Court there noted that it had “never invalidated a penalty mandated by a legislature based only on the length of sentence, and, especially with a crime as severe as [drug possession], we should do so only in the most extreme circumstance.” Id.

This case does not present that extreme circumstance. The crime here at issue is as harmful as that in Harmelin, while the challenged five-year minimum is far less “severe and unforgiving” than the life sentence upheld in that ease. Id. at 1008, 111 S.Ct. 2680. Indeed, here Congress did not mandate a single sentence for all persons who distribute child pornography, nor set a maximum sentence that was the harshest term of incarceration permitted by law. See generally Miller v. Alabama, 132 S.Ct. at 2467-68. Rather, it provided a sentencing range of “not less than 5 years and not more than 20 years” for the distribution of child pornography. 18 U.S.C. § 2252(b)(1). To the extent every sentence is a function of both the crime committed and the character of the defendant who committed it, Congress decided only that the distribution of child pornography was a sufficiently serious crime as to require at least a five-year sentence even for the most sympathetic defendant. But having set this floor, Congress then left it entirely to district courts to assess the particulars of the crime and the character of the defendant to determine whether some other sentence, between the five-year minimum and twenty-year maximum, might be warranted to serve the interests of justice. In this respect it afforded more “mechanisms for consideration of individual circumstances” in child pornography distribution cases than were available for drug trafficking in Harmelin. Harmelin v. Michigan, 501 U.S. at 1008, 111 S.Ct. 2680 (Kennedy, J., concurring); see id. (noting that “[p]rosecutorial discretion before sentence and executive or legislative clemency afterwards provide means for the State to avert or correct unjust sentences”).

Nor does Reingold’s immaturity give rise to an inference of gross disproportionality. An adult defendant’s immaturity may mitigate his moral culpability, but it does not reduce the harmful effects of his crime, which, as we have explained, are properly viewed as quite serious in cases of distribution of child pornography. Indeed, where the sentence at issue for such a serious crime is a minimum prison term of five years, the punishment is not so severe as to permit us to infer gross dis-proportionality from Congress’s decision to mandate its imposition on all adult defendants, without regard to their relative maturity. See generally Miller v. Alabama, 132 S.Ct. at 2460 (prohibiting mandatory life imprisonment without parole only for juvenile, not adult, offenders); United States v. Merchant, No. 12-12957, 2013 WL 461218, at *1 (11th Cir. Feb. 7, 2013) (rejecting argument that 25-year-old defendant’s lack of sophistication, limited life experience, and amenability to treatment rendered 17.5-year sentence for distribution of large quantity of child pornography grossly disproportionate); cf United States v. Moore, 643 F.3d 451, 454 (6th Cir.2011) (rejecting claim that imposition of 15-year mandatory minimum sentence on four-time felon convicted of carrying firearm was grossly disproportionate in light of defendant’s diminished mental capacity). We nevertheless reiterate the point we made earlier: the district court may, of course, take the defendant’s immaturity into account in deciding where within the prescribed statutory range to sentence Rein-gold. See 18 U.S.C. §§ 3553(a), 3661; see also United States v. Moore, 643 F.3d at 455 (noting district court’s consideration of defendant’s reduced mental capacity in imposing sentence at very bottom of Guidelines range); United States v. Stern, 590 F.Supp.2d 945, 953 (N.D.Ohio 2008) (concluding that fact that defendant began downloading child pornography at 14 “weighted] heavily in favor of a deviation [from Guidelines range] under § 3553(a)”); cf. United States v. Wachowiak, 412 F.Supp.2d 958, 964 (E.D.Wis.2006) (imposing 70-month sentence on defendant subject to mandatory minimum sentence of five years with applicable Guidelines range of 121 to 151 months’ imprisonment in light of various mitigating factors). But it cannot rely on Reingold’s relative immaturity to hold a five-year minimum sentence for the distribution of child pornography to be cruel and unusual punishment.

Our conclusion that imposition of the five-year mandatory minimum sentence in this case does not give rise to an inference of gross disproportionality finds further support in our own precedent. In United States v. Ramos, 685 F.3d 120 (2d Cir.2012), a case in which a recidivist defendant convicted of receiving and possessing child pornography faced a 15-year minimum sentence, we easily rejected an Eighth Amendment challenge to that higher minimum, noting that it was well below the defendant’s Guidelines range and that “ ‘[l]engthy prison sentences ... do not violate the Eighth Amendment’s prohibition against cruel and unusual punishment when based on proper application of the Sentencing Guidelines or statutorily mandated ... terms,’ ” id. at 134 n. 11 (quoting United States v. Yousef, 327 F.3d 56, 163 (2d Cir.2003)) (second and third alterations in Ramos).

Our sister circuits have similarly rejected Eighth Amendment challenges to mandatory minimum sentences in child pornography or exploitation cases. See United States v. Hart, 635 F.3d 850, 859 (6th Cir.2011) (upholding 15-year mandatory minimum under 18 U.S.C. § 2251 for persuading minor to engage in sexually explicit conduct for purpose of producing visual depictions, and noting same ruling with respect to 10-year mandatory minimum for enticing minor into sexual relations in violation of 18 U.S.C. §§ 2422(b) and 2251); United States v. Nagel, 559 F.3d 756, 762 (7th Cir.2009) (holding 10-year mandatory minimum sentence under 18 U.S.C. § 2422(b) not grossly disproportionate to crime of attempting to entice minor to engage in criminal sexual act); United States v. Malloy, 568 F.3d 166, 180 & n. 14 (4th Cir.2009) (upholding 15-year mandatory minimum sentence under 18 U.S.C. § 2251); United States v. Gross, 437 F.3d 691, 695 (7th Cir.2006) (concluding that 15-year mandatory minimum sentence under 18 U.S.C. § 2252A(b)(l) for distribution of child pornography by defendant who was former victim and perpetrator of child sexual abuse was not grossly disproportionate to crime in light of high bar Supreme Court has set for such claims, seriousness of crime, and defendant’s prior record); United States v. MacEwan, 445 F.3d 237, 250 (3d Cir.2006) (rejecting gross dispro-portionality challenge to 15-year minimum sentence mandated by 18 U.S.C. § 2252(a)(2)(B), (b)(1) for repeat offender convicted of receipt of child pornography); see also United States v. Dwinells, 508 F.3d 63, 69 (1st Cir.2007) (rejecting Eighth Amendment challenge to mandatory minimum sentence for attempting to persuade, induce, entice, or coerce minor to engage in criminal sexual activity in violation of 18 U.S.C. § 2242(b), noting that “it is not the proper function of the courts to act as super-legislatures, passing judgment upon Congress’s penological determinations”).

In sum, the application of a mandatory five-year sentence to the distribution crime of conviction in this particular case does not give rise to an inference of gross disproportionality suggestive of cruel and unusual punishment. Thus, we need not engage in any sentencing comparison to determine, as we do here, that the district court erred in concluding that the Eighth Amendment barred the application of a five-year mandatory minimum sentence in this case. Accordingly, we remand the case for the district court to vacate its original sentence and to resentence Rein-gold consistent with the statutory mandate.

D. Calculation of the Applicable Guidelines Range

The United States submits that the district court erred in failing to apply certain Sentencing Guidelines enhancements to the calculation of Reingold’s applicable Guidelines range. Specifically, it contends that enhancements were warranted for (1) Reingold’s engagement in a pattern of sexual abuse or exploitation of a minor, see U.S.S.G. § 2G2.2(b)(5); (2) the use of a computer to commit the crime of conviction, see id. § 2G2.2(b)(6); and (3) the distribution of child pornography, see id. § 2G2.2(b)(3)(F). Reingold responds that the district court correctly declined to apply these enhancements, but asserts that, if there was error, it was necessarily harmless because “the record is abundantly clear that Judge Weinstein would have imposed the same sentence regardless of the recommended guideline range.” Ap-pellee’s Br. 43.

Our identification of a Guidelines calculation error as “harmless” allows us to uphold an otherwise valid sentence and to avoid vacatur and remand where it is clear that the district court would impose the same sentence in any event. See United States v. Jass, 569 F.3d 47, 68 (2d Cir.2009). In this case, however, we cannot avoid remand and resentencing because we have identified a non-Guidelines sentencing error, i.e., the district court’s refusal to impose a mandatory five-year minimum sentence based on an erroneous Eighth Amendment determination. Thus, on remand, the district court will not be able to impose the same sentence. We recognize that the district court may well choose on remand to impose a non-Guidelines sentence. Nevertheless, “we have indicated that a correct Guidelines calculation must normally precede [such a] decision.” United States v. Rodriguez, 587 F.3d 573, 584 (2d Cir.2009). Accordingly, we proceed to consider the government’s Guidelines calculation challenge.

In doing so, we interpret relevant Guidelines provisions de novo, but we defer to the district court’s findings of facts pertinent to the Guidelines absent clear error. See United States v. Broxmeyer, 699 F.3d 265, 281 (2d Cir.2012).

1. Pattern of Abuse Enhancement

Guideline § 2G2.2, which applies to defendants convicted of child pornography crimes pursuant to 18 U.S.C. § 2252, provides for a five-level enhancement in offense level “[i]f the defendant engaged in a pattern of activity involving the sexual abuse or exploitation of a minor.” U.S.S.G. § 2G2.2(b)(5). This Guideline attempts to assess both a defendant’s risk of recidivism and the potential harm to others that such recidivism could present. See United States v. Laraneta, 700 F.3d 983, 987 (7th Cir.2012) (observing that, with respect to § 2G2.2(b)(5), defendant’s “[ojther acts of sexual predation ... have predictive significance with regard to the likelihood of recidivism, ... [a] relevant consideration in deciding how long a defendant should be incapacitated (by being imprisoned) from committing further crimes”). The Probation Department initially recommended, and the government urged, that this five-level enhancement be applied to Reingold based on his admitted three sexual contacts with his half-sister. The district court disagreed, finding § 2G2.2(b)(5) inapplicable because Rein-gold was a minor when the first two contacts with his sister occurred. Further, it observed that the acts were attributable largely to a lack of “proper parental supervision,” and were so lacking in temporal proximity as to appear “aberrant.” May 16, 2011 Sentencing Tr. 15:24-16:1. These circumstances do not, in fact, make § 2G2.2(b)(5) inapplicable here.

The “pattern of activity involving the sexual abuse or exploitation of a minor” required to warrant a § 2G2.2(b)(5) enhancement is specifically defined in the Guideline’s application notes to mean “any combination of two or more separate instances of the sexual abuse or sexual exploitation of a minor by the defendant, whether or not the abuse or exploitation (A) occurred during the course of the offense; (B) involved the same minor; or (C) resulted in a conviction for such conduct.” U.S.S.G. § 2G2.2 cmt. n.l. The same application note defines “sexual abuse or exploitation” to mean

(A) conduct described in 18 U.S.C. § 2241, § 2242, § 2243, § 2251(a)-(c), § 2251(d)(1)(B), § 2251A, § 2260(b), § 2421, § 2422, or § 2423; (B) an offense under state law, that would have been an offense under any such section if the offense had occurred within the special maritime or territorial jurisdiction of the United States; or (C) an attempt or conspiracy to commit any of the offenses under subdivisions (A) or (B).

Id. The note also specifically excludes from the definition of “sexual abuse or exploitation” the “possession, accessing with intent to view, receipt, or trafficking in material relating to the sexual abuse or exploitation of a minor.” Id.

Read together, these definitions signal that § 2G2.2(b)(5) is narrow in one respect and expansive in another. The specifically referenced federal statutes cabin the conduct that qualifies as “sexual abuse or exploitation” for purposes of a § 2G2.2(b)(5) enhancement. At the same time, the expansive word “any” in the phrase “any combination of two or more separate instances of the sexual abuse or sexual exploitation of a minor by the defendant” signals that any conduct described within one of the specified statutes is properly considered in making a § 2G2.2(b)(5) assessment and that nothing more than two separate instances of such conduct is required to demonstrate the requisite pattern.

Thus, the lack of temporal proximity in Reingold’s sexual contacts with his sister was not a permissible ground for refusing to apply a § 2G2.2(b)(5) enhancement. See generally United States v. Salim, 549 F.3d 67, 79 (2d Cir.2008) (holding it legal error to impose additional requirement beyond plain language of Guideline). In so holding, we join our sister circuits, which have uniformly concluded that no temporal proximity among acts of sexual abuse or exploitation is required to satisfy the pattern requirement of § 2G2.2(b)(5). See, e.g., United States v. Woodard, 694 F.3d 950, 953-54 (8th Cir.2012); United States v. Clark, 685 F.3d 72, 79 (1st Cir.2012); United States v. McGarity, 669 F.3d 1218, 1260 (11th Cir.2012); United States v. Bacon, 646 F.3d 218, 221 (5th Cir.2011); United States v. Olfano, 503 F.3d 240, 243 (3d Cir.2007); United States v. Garner, 490 F.3d 739, 743 (9th Cir.2007); United States v. Gawthrop, 310 F.3d 405, 414 (6th Cir.2002); United States v. Lovaas, 241 F.3d 900, 904 (7th Cir.2001).

Nor can § 2G2.2(b)(5) and its application notes be construed to exclude conduct satisfying its definition of sexual abuse and exploitation from pattern consideration based on mitigating circumstances. As noted, the Guideline strictly limits the activities qualifying as sexual abuse and exploitation, but where conduct falls within that narrowly defined sphere, “any combination of two or more instances” of such abuse or exploitation — not any combination unexplained by mitigating circumstances — qualifies as a “pattern” warranting an enhancement. That mitigating circumstances are not relevant to a particular Guideline’s applicability does not, however, mean that a district court may not properly rely on such circumstances either in deciding where within the applicable Guidelines range to sentence a defendant or in deciding to sentence a defendant to a non-Guidelines sentence.

We further conclude that the district court erred in excluding from § 2G2.2(b)(5) consideration of Reingold’s first two sexual contacts with his half-sister on the ground that defendant was then himself a minor. This court has not previously had occasion to consider whether acts of sexual abuse or exploitation of a minor by a minor can support a § 2G2.2(b)(5) enhancement. We have however, considered that question in similar circumstances and held that they can. See United States v. Phillips, 431 F.3d 86, 90-93 (2d Cir.2005).

In Phillips, a defendant convicted of sexually exploiting a minor in violation of 18 U.S.C. § 2251(a) and (b) argued that the “ § 4B1.5(b) enhancement for a pattern of prohibited sexual behavior does not apply to unadjudicated conduct perpetrated by an adolescent because neither the Guidelines nor the Application Notes explicitly say that it does.” Id. at 90. In rejecting this argument, we noted that one of the statutes defining conduct supporting the enhancement, 18 U.S.C. § 2243, does not “limit[ ] its coverage to violators over the age of eighteen,” thus making “sexual abuse of a minor by a minor ... prohibited conduct constituting an offense under federal law.” Id. at 91. We further observed that, by contrast to other Guidelines, which condition enhancements on whether relevant offenses were adult convictions, § 4B1.5(b) contained no comparable language “placing constraints on the use of a conviction based on the defendant’s age.” Id. at 93; see U.S.S.G. §§ 4A1.1, 4B1.1. Accordingly, we concluded that, under § 4B1.5(b), “the district court [was] permitted to take into account sexually exploi-tive conduct that occurred when the defendant was himself a juvenile.” United States v. Phillips, 431 F.3d at 93.

The same reasoning applies to § 2G2.2(b)(5). Among the statutes whose conduct describes the sexual abuse or exploitation of a minor relevant to this Guideline is 18 U.S.C. § 2241(c), which makes it a crime knowingly to engage “in a sexual act with another person who has not attained the age of 12” within the jurisdiction of the United States. Like § 2243, § 2241(c) does not limit its coverage to offenders over the age of 18. Nor does any language in § 2G2.2(b)(5) or its application notes require consideration of a defendant’s age at the time of past instances of sexual abuse or exploitation. In the absence of such language, and consistent with our decision in Phillips, we here conclude that sexual abuse or exploitation of a minor undertaken by a defendant who was a juvenile at the time of the incident is properly considered in applying the § 2G2.2(b)(5) pattern enhancement. The two of our sister circuits to have considered this question have reached the same conclusion. See United States v. Woodard, 694 F.3d at 953 [8th Cir.]; United States v. Olfano, 503 F.3d at 243 [3d Cir.].

We therefore conclude that the district court erred in relying on Reingold’s minority, lack of temporal proximity, and inadequate supervision as grounds not to consider his contacts with his sister as a basis for a § 2G2.2(b)(5) enhancement in this case. In rejecting these grounds for decision, we do not, however, conclude that Reingold warrants a § 2G2.2(b)(5) enhancement. That depends on whether his sexual contacts with his sister qualify as “sexual abuse or exploitation,” a factual finding that the district court never made.

As we have already observed, “sexual abuse or exploitation,” as used in § 2G2.2(b)(5), means only such conduct as is described in certain criminal statutes. The definition of a “sexual act” for purposes of § 2241(c), which appears to be the relevant statute here, derives from 18 U.S.C. § 2246(2)(D), which defines the phrase to mean, inter alia, “the intentional touching, not through the clothing, of the genitalia of another person who has not attained the age of 16 years with an intent to abuse, humiliate, harass, degrade, or arouse or gratify the sexual desire of any person.”

Of Reingold’s three sexual contacts with his sister, the last — -when he was 18 and she was 11 — appears plainly to qualify. Reingold admitted that on that occasion, he had his sister “manually stimulate his penis, while he rubbed her breasts and manually stimulated her vagina, both over and under her panties,” PSR ¶ 11, and “coached her on how to perform oral sex on him” and performed oral sex on her, id. ¶ 3. The siblings’ first encounter might also qualify in that Reingold admitted that on that first occasion, when he was 15 and his sister eight, he had her sister manually stimulate his penis while he touched the girl’s “privates, under her clothing.” Id. Less clear is whether the second encounter qualifies as a sexual act. On that occasion, when Reingold was 16 and his sister nine, he again had his sister manually stimulate his penis, but Reingold admitted rubbing her vagina only over her underpants. We leave it to the district court to resolve these open factual questions as to which of Reingold’s contacts involved “a sexual act.”

If, however, the facts show that on two or more occasions Reingold engaged his sister, a girl then younger than twelve, in sexual acts as defined by federal law, those two separate instances of sexual abuse or exploitation would warrant a five-level enhancement to his Guidelines offense level calculation pursuant to U.S.S.G. § 2G2.2(b)(5).

2. Use of a Computer Enhancement

Guideline § 2G2.2(b)(6) provides for a two-level enhancement “[i]f the offense involved the use of a computer.” The district court declined to apply the enhancement in this case, finding it to constitute impermissible “double counting.” United States v. C.R., 792 F.Supp.2d at 512. That conclusion was unwarranted in light of United States v. Johnson, 221 F.3d 83, 99 (2d Cir.2000), in which we specifically rejected a double-counting challenge to the application of a § 2G2.2(b)(6) enhancement. As Johnson observed, the use of a computer is not essential to the act of distributing child pornography. A person “can traffic in child pornography without using a computer much like one could commit a robbery without the use of a gun.” Id. (internal quotation marks omitted). Thus, the enhancement does not result in double counting because it does not “increase a defendant’s sentence to reflect the kind of harm that has already been fully accounted for” by the base offense level. United States v. Volpe, 224 F.3d 72, 76 (2d Cir.2000) (internal quotation marks omitted).

This conclusion is reinforced by our earlier observation that the digital revolution, which may be responsible for more child pornography crimes’ being committed by computer, has aggravated rather than mitigated the harms associated with such crime. See supra at Part II.C.2.a. By making it easier to retrieve and distribute child pornography, computers have expanded the market for child pornography, which in turn fuels a greater demand for a product that can only be produced by abusing and exploiting children. See generally United States v. Lewis, 605 F.3d at 403. Moreover, once child pornography is circulated by computer, it becomes almost impossible to remove or destroy. In such circumstances, it was hardly unreasonable, much less double counting, for the Sentencing Commission to conclude that the base offense level applicable to all distributors of child pornography — even those who share items non-electronically — should be enhanced for persons who commit the crime by using a computer.

Reingold submits that since Johnson this court has expressed reservations about the § 2G2.2(b)(6) enhancement because, now that so many child pornography crimes are committed by computer, the enhancement applies “in virtually every case” so as to have “the flavor” of double counting. United States v. Tutty, 612 F.3d 128, 132 (2d Cir.2010); see United States v. Dorvee, 616 F.3d 174, 186 (2d Cir.2010). In neither case, however, did we reverse Johnson or hold that it would be impermissible double counting to apply a § 2G2.2(b)(6) enhancement when the distribution of child pornography is effected by computer. Rather, the noted reservations informed the observation that substantive reasonableness concerns could arise where courts imposed sentences near the statutory maximum as a result of Guidelines enhancements that now seemed to apply “in virtually every case.” United States v. Tutty, 612 F.3d at 132.

Here, we do not review the substantive reasonableness of a sentence at the top of the statutory range. We consider only whether the district court erred in concluding that it would be impermissible double counting to apply a computer use enhancement to the calculation of Reingold’s Guidelines. In light of Johnson, we conclude that the district court did so err. On remand, the district court should apply this enhancement to its calculation of Rein-gold’s recommended Guidelines range.

3. Distribution Enhancement

In calculating Reingold’s Guidelines range, the district court further declined to apply the two-level enhancement for distribution provided in U.S.S.G. § 2G2.2(b)(3)(F). The district court found that the base offense level for § 2G2.2(a)(2) already accounted for the harms attributable to distribution, making any enhancement “a form of double counting.” May 16,2011 Sentencing Tr. 13:8-10. Moreover, it found that Reingold’s primary objective in using the GigaTribe file sharing program was to receive child pornography rather than to distribute it to others. Neither ground makes the distribution enhancement inapplicable to this ease.

a. A § 2G2.2 Distribution Enhancement Does Not Constitute Double Counting in This Case

The district court concluded that because distribution was a necessary element of Reingold’s crime of conviction, any harm associated with distribution was necessarily fully accounted for in the base offense level of his Guideline. See United States v. Watkins, 667 F.3d 254, 261 (2d Cir.2012) (stating that impermissible double counting occurs when Guidelines enhancement is applied to reflect harm already “fully accounted for by another part of the guidelines” (alterations and internal quotation marks omitted)). The conclusion is unwarranted.

First, distribution need not be present in every conviction under the statute at issue. Section 2252(a)(2) proscribes the knowing receipt or distribution of child pornography. See United States v. Salim, 549 F.3d at 76 (holding that no double counting concern arises where Guidelines enhance for “additional factor that will not be present in every conviction under the statute” (internal quotation marks omitted)).

Second, neither the applicable Guideline, U.S.S.G. § 2G2.2, nor the base offense level dictated by that Guideline for this case, is limited to distribution crimes. Guideline § 2G2.2 sweeps broadly to address a wide range of criminal conduct occurring after child pornography has been produced. As that Guideline’s title indicates, such conduct includes (1) “Trafficking,” (2) “Receiving,” (3) “Transporting,” (4) “Shipping,” (5) “Soliciting,” and (6) “Advertising Material Involving the Sexual Exploitation of a Minor,” as well as (7) “Possessing” such material, both with and without intent to distribute.

To assist sentencing judges in distinguishing among such varied crimes and assessing their severity in particular cases, § 2G2.2 draws various distinctions. To begin, the Guideline draws a gross distinction between crimes of conviction implicating only simple possession of child pornography and all other covered crimes, assigning a base offense level of 18 to the former, see U.S.S.G. § 2G2.2(a)(l), and a base offense level of 22 to the latter, see id. § 2G2.2(a)(2). Within the latter set— which includes the receipt, solicitation, transportation, and advertisement of child pornography, as well as its sale or distribution — the Guideline provides for the base offense level to be reduced two levels in cases where “the defendant’s conduct was limited to the receipt or solicitation” of child pornography, and “the defendant did not intend to traffic, or distribute, in such material.” Id. § 2G2.2(b)(l). At the same time, however, the Guideline provides for an enhancement to the base offense level for offenses that involved the distribution of child pornography. See id. § 2G2.2(b)(3). Specifically, it dictates a two-level enhancement whenever an offense involved distribution, see id. § 2G2.2(b)(3)(F), with the possibility of greater enhancements if the distribution was for pecuniary or other tangible gain, see id. § 2G2.2(b)(3)(A)-(B), or to a minor, see id. § 2G2.2(b)(3)(C)-(E).

This structure cannot be understood to address the harm associated with the distribution of child pornography in a base offense level of 22 that applies equally to a variety of offenses, some involving distribution and others not. Rather, § 2G2.2 is structured so that the range of harms associated with distribution can be addressed through various enhancements. Indeed, that conclusion has been so obvious to those of our sister circuits to have considered the question that they have employed little discussion to reject double counting challenges to the application of a § 2G2.2(b)(3)(F) enhancement to defendants convicted of distribution offenses. See United States v. Chiaradio, 684 F.3d 265, 283 (1st Cir.2012) (identifying “absolutely no basis” for inferring that distribution enhancement did not apply to defendant convicted of distribution crime); United States v. Frakes, 402 Fed.Appx. 332, 335-36 (10th Cir.2010) (“Rather than forbidding double-counting, § 2G2.2 expressly allows a two-level enhancement for distribution,” such that a minimum two-point enhancement “will always apply” to defendants convicted of distribution offenses (emphasis in original)).

We agree that a minimum two-level enhancement for distribution applies to the calculation of Reingold’s Guidelines, and we conclude that the district court erred as a matter of law in holding that such an enhancement constituted impermissible double counting.

b. Reingold’s Offense Involved Distribution

No different conclusion is warranted because the district court concluded that Reingold’s primary purpose in committing the distribution offense of conviction was to receive rather than to distribute child pornography.

The application notes to § 2G2.2 define “distribution” to mean

any act, including possession with intent to distribute, production, transmission, advertisement, and transportation, related to the transfer of material involving the sexual exploitation of a minor. Accordingly, distribution includes posting material involving the sexual exploitation of a minor on a website for public viewing but does not include the mere solicitation of such material by a defendant.

U.S.S.G. § 2G2.2 cmt. n.l (emphasis added). Use of the word “any” to modify “act” signals that the phrase should be construed broadly. Similarly, use of the word “including” in the first sentence and “includes” in the second sentence signals that the cited acts of distribution are illustrative rather than exhaustive. See United States v. Ramos, 695 F.3d 1035, 1040 (10th Cir.2012) (construing “including” in § 2G2.2 application note’s definition of distribution as “non-exhaustive”). Nothing in the definition suggests that application of a § 2G2.2(b)(3) enhancement depends on distribution being a defendant’s primary-intent in committing the offense of conviction. Indeed, a number of our sister circuits have construed the enhancement to apply without regard to a defendant’s intent as long as the offense of conviction involved distribution. See United States v. Hayden, No. 12-11346, 2013 WL 781804, at *5 (11th Cir. Mar. 4, 2013) (observing that “neither § 2G2.2(b)(3)(F) nor the application notes impose an intent requirement” in upholding district court’s application of enhancement); United States v. Ramos, 695 F.3d at 1041 [10th Cir.] (holding that “intent to distribute is not required for act to qualify as ‘distribution’ under § 2G2.2(b)” (emphasis in original)).

Here, even if Reingold’s primary intent in joining GigaTribe was “not to distribute but more to just receive” child pornography, May 10, 2011 Sentencing Tr. 16:10-11, the record makes plain that he both knew from the start that distribution was a necessary condition of receipt, see id. at 16:9, 19-22 (admitting that “in order to receive” materials, GigaTribe “requires you to share with other people”), and, with that knowledge, took deliberate and purposeful actions to effect that distribution, see generally United States v. Kelly, 147 F.3d 172, 177 (2d Cir.1998) (approving definition of “intentionally” that requires defendant to have “acted deliberately and purposefully”). A federal agent, discussing how GigaTribe worked, explained that Reingold had to “specifically pick which folders or files he wantfed] to share”; persons on Reingold’s “buddy list” could then share “not his whole computer, [but] just the [files] that he selected.” May 10, 2011 Sentencing Tr. 12:24-25, 14:13-14. Indeed, Reingold “admitted that he shared his child pornography folders with an estimated 10 to 20 GigaTribe users on his invited buddy list.” PSR ¶ 9. Such conduct plainly supports defendant’s conviction for distributing child pornography as well as application of the § 2G2.2(b)(3)(F) enhancement.

As we recently stated in a summary order upholding such an enhancement, “knowingly placing child pornography files in a shared folder on a peer-to-peer file-sharing network constitutes distribution under U.S.S.G. § 2G2.2, even if no one actually obtains an image from the folder.” United States v. Farney, 513 Fed.Appx. 114, 116 (2d Cir.2013). Our sister circuits agree. See United States v. Conner, No. 12-3210, 2013 WL 1490109, at *6 (6th Cir. Apr. 11, 2013) (holding that “knowing use of [file-sharing service], much like the posting of a file on a website, is sufficient to trigger section 2B2.2(b)(3)(F)’s two-level enhancement”); United States v. Ramos, 695 F.3d at 1041 [10th Cir.] (concluding that when “individual uses a peer-to-peer network file-sharing program with knowledge that the program will deposit downloaded child-pornography files into a shared folder accessible to other users— e.g., rendering files only a mouse-click away — then that person has engaged in an act related to the transfer of child pornography” warranting § 2G2.2(b)(3)(F) enhancement); United States v. Glassgow, 682 F.3d 1107, 1110 (8th Cir.2012) (holding § 2G2.2(b)(3)(F) enhancement warranted where, inter alia, defendant “knowingly made files available for distribution”); United States v. Spriggs, 666 F.3d 1284, 1287 (11th Cir.2012) (stating that “[w]hen the user knowingly makes the files accessible to others, the distribution is complete”); United States v. Layton, 564 F.3d 330, 335 (4th Cir.2009) (holding that defendant who “knowingly us[es] a file-sharing program that allows others to access child pornography files” commits the transfer act necessary to warrant § 2G2.2(b)(3)(F) enhancement); United States v. Carani, 492 F.3d 867, 876 (7th Cir.2007) (concluding that “notion” that defendant “could knowingly make his child pornography available for others to access and download without this qualifying as ‘distribution’ does not square with the plain meaning of the word”).

We here reiterate as controlling our summary conclusion in Famey, and we clarify that it applies without regard to whether the defendant’s primary purpose in placing child pornography files in a file-sharing program was to receive or to distribute child pornography.

Thus, on remand, the district court should recalculate Reingold’s Guidelines before resentencing, applying enhancements under U.S.S.G. § 2G2.2(b)(3)(F), (b)(5), and (b)(6), as warranted consistent with this opinion. While the district court is required correctly to calculate and fairly to consider the Guidelines, see 18 U.S.C. § 3553(a)(4), nothing in this opinion is intended to limit the district court’s discretion to consider a non-Guidelines sentence pursuant to United States v. Booker, 543 U.S. 220, 245, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005).

III. Conclusion

To summarize, we conclude as follows:

1. The application of the five-year minimum sentence mandated by 18 U.S.C. § 2252(b)(1) is not so grossly disproportionate to the crime of distributing child pornography as to be precluded in this case by the Cruel and Unusual Punishment Clause of the Eighth Amendment. Accordingly, in exercising its sentencing discretion in this case, the district court cannot impose a lesser prison sentence than the statutorily mandated minimum.

2. In calculating a defendant’s Sentencing Guidelines range for distributing child pornography:

a. A pattern enhancement pursuant to U.S.S.G. § 2G2.2(b)(5) applies to a defendant who commits any two acts fitting the Guidelines definition of “sexual abuse or exploitation of a minor,” without regard to the temporal proximity of those acts, the defendant’s own minority at the time of such acts, or mitigating circumstances. Such circumstances may inform a district court’s exercise of discretion in selecting a within-Guidelines sentence or in imposing a non-Guidelines sentence, but they do not permit the court to refrain from applying an otherwise warranted § 2G2.2(b)(5) enhancement to the calculation of a defendant’s Guidelines range.

b. Because a computer is not essential to the crime of distributing child pornography, the computer-use enhancement provided in U.S.S.G. § 2G2.2(b)(6) does not constitute impermissible double counting simply because an ever larger number of child pornography distribution crimes are committed with computers.

c. Because neither the statute of conviction, 18 U.S.C. § 2252(a)(2), nor the applicable Guideline, § 2G2.2, is limited to distribution crimes, the distribution enhancement provided in § 2G2.2(b)(3)(F) does not constitute impermissible double counting.

Accordingly, we remand this ease to the district court with direction that it vacate Reingold’s sentence and Resentence him consistent with this opinion, specifically recalculating his Sentencing Guidelines range as indicated herein, and adhering to the statutorily mandated minimum sentence of five years’ imprisonment.

Judge SACK concurs in a separate opinion.

SACK, Circuit Judge,

concurring.

I am in full agreement with the judgment of the Court. I write only to express my concern about parts of section 2.A of the majority opinion.

I would have much preferred that the majority confine itself to a more narrow and straightforward analysis of the gravity-of-the-offense aspect of the Eighth Amendment inquiry. That analysis is already fully included as part of the section with which I take issue, as follows:

Starting with the gravity of the offense at issue, there can be no question that the dissemination of child pornography is a serious crime that causes real injury to particularly vulnerable victims. As Congress, courts and scholars all[] recognize, child pornography crimes at them core demand the sexual exploitation and abuse of children. Not only are children seriously harmed — physically, emotionally, and mentally — in the process of producing such pornography, but that harm is then exacerbated by the circulation, often for years after the fact, of a graphic record of the child’s exploitation and abuse. See New York v. Ferber, 458 U.S. 747, 757-59 & nn. 9-10 [102 S.Ct. 3348, 73 L.Ed.2d 1113] (1982) (citing congressional and scholarly reports, and court cases).[]
[Precisely because the prevention of such exploitation and abuse is “a government objective of surpassing importance,” New York v. Ferber, 458 U.S. at 757 [102 S.Ct. 3348]; see id., at 756-57 [102 S.Ct. 3348] (“It is evident beyond the need for elaboration that a State’s interest in safeguarding the physical and psychological well-being of a minor is compelling.” (internal quotation marks omitted)), we cannot view the distribution of child pornography, however accomplished, as anything but a serious crime that threatens real, and frequently violent, harm to vulnerable victims, cf. Harmelin v. Michigan, 501 U.S. [957] at 1002-03 [111 S.Ct. 2680, 115 L.Ed.2d 836] (1991) (Kennedy, J., concurring) (observing that characterization of drug possession with internet to distribute as a “nonviolent and victimless” crime “is false to the point of absurdity” given “pernicious effects” of drug use).

Maj. op. at 216-18.

Perhaps we cannot conclude from that excerpt alone that the sentence in this case was “fair” — but that issue is simply not posed by this Eighth Amendment inquiry. It seems to me, though, that the language does answer clearly and completely the legal question that is before the Court: Whether this is the “rare case” in which the comparison between crime and punishment leads “to an inference of gross dis-proportionality.” See Graham v. Florida, 560 U.S. 48, 130 S.Ct. 2011, 2022, 176 L.Ed.2d 825 (2010) (quoting Harmelin v. Michigan, 501 U.S. 957, 1005, 111 S.Ct. 2680, 115 L.Ed.2d 836 (1991) (Kennedy, J., concurring in part and concurring in the judgment in part)). It is not. And, that question having been answered, I think the majority should have stopped there, and proceeded to the other legal issues that have been raised.

Instead, the majority’s opinion includes graphic descriptions of one of the pornographic images in evidence, id. at 216-17, and discusses the effect on child pornography of the “recent digital revolution,” id. at 217-18; explains what it views as the irrelevance of “Reingold’s professed ... principal interest in receiving rather than distributing child pornography,” id. at 217; describes the nature of “GigaTribe” and the defendant’s interaction with it, id. at 218; and makes reference to the defendant’s sexual molestation of his minor half-sister, id. at 218-19.

These may be interesting observations, but are they necessary to the resolution of this appeal? I hardly think so. Suppose the facts were to the contrary. Suppose the pornographic images were somewhat less graphic than the one described; that they were received and distributed as photographs (as pornographic material was in Ferber) and not electronically through file sharing on the Internet; that Reingold did not allege that his principal interest was in receiving and not distributing the pornographic images; and that he never ever so much as touched a female human being other than his mother. Are we to believe that on any such or vaguely similar facts and in light of the law reflected in the two paragraphs of its opinion set forth in haec verba above, the majority could or would have decided that a five year sentence here did constitute “cruel and unusual punishment”?

I don’t think so. And, assuming I am correct, the verbiage to which I take exception is unnecessary to the consideration and resolution of this case. I would therefore have omitted it.

The omission would not be based on any general view on my part that a judge must be averse to saying more in an opinion than is strictly necessary. I do not think so. But to borrow a phrase from death-penalty cases and twist it, child pornography is different. Focusing on subjects that are associated with our most powerful taboos, these cases evoke uniquely strong, if differing, emotional, moral, and cultural reactions from judges, necessarily based on the differing beliefs, values, sensitivities, and life experiences of those judges.

I have no doubt that there are appeals in such cases that require the reviewing court to engage in a carefully, even painfully, detailed analysis of the child pornography and abuse at issue. This is not one of them. And when we go beyond what is necessary to resolve this sort of case, by setting forth in unnecessary or irrelevant detail the circumstances or other aspects of the crime, we risk the appearance of explicitly or implicitly voicing our moral indignation rather than exercising our legal judgment, which is of course our only charge.

I would have preferred then, as I have said, for the majority opinion to have hewed more rigorously to the line of legal inquiry in the matter before us.

I also concur with the majority as to the use of Reingold’s name in the caption of this case. Whether I would do so were his name not already on the record, I am not quite sure. Although I am of the general view that the more about an appeal that is public the better, including of course the names of the parties, the dissection of Reingold’s mental condition and the nature of his behavior is set forth in such unusually meticulous detail in the district court’s lengthy opinion that I can understand that court’s decision to identify him by his initials only. But the fact that his name is not only available in the files of the district court and this court, it can also be found on-line using Google — attributed on the website to Reuters — seems to me to make the decision much easier. See http://www. caringforourchildrenfoundation.org/?p= 8932 (last visited Sept. 20, 2013). 
      
      . In its opinion, as well as in various filings, the district court referred to Reingold by his initials "C.R." We note that, at the same time, Reingold was identified by his full name in certain documents that remain electronically available from the files of the Eastern District of New York.
      We identify no basis in law for shielding the identity of an adult criminal defendant. Cf. Fed.R.Crim.P. 49.1 (providing privacy protections in limited circumstances). No different conclusion obtains from United States v. Amodeo, 71 F.3d 1044 (2d Cir.1995), cited by Reingold. At issue in that case was the propriety of unsealing an investigative report that, among other things, would have identified confidential informants in an ongoing criminal investigation and circulated anonymous and unverified accusations of doubtful veracity against uncharged persons. See id. at 1047-48. By contrast, as the named adult defendant in a criminal case in which he has been adjudicated guilty, Reingold has no expectation of privacy in his identity. See id. at 1048 (noting public’s presumptive right of access to information pertaining to judicial adjudications); cf. id. at 1050-51 (recognizing that privacy interests of "innocent third parties” may warrant exception to presumption of public access). We therefore refer to Rein-gold by his name on our docket and in this opinion. Nevertheless, because the district court's published opinion is reported as United States v. C.R., we cite it as such.
     
      
      . A violation of 18 U.S.C. § 2252(a)(4)(B) carries no mandatory minimum penalty but is punishable by a prison term of "not more than 10 years.” 18 U.S.C. § 2252(b)(2).
     
      
      .Reingold further admitted that, at times when he was either 18 or 19, he had engaged three friends who were minors in sexual activity: (1) a 15-year-old boy whose penis Reingold had stimulated to the point of ejaculation; (2) a 15-year-old girl with whom Reingold had performed mutual genital stimulation and oral sex; and (3) a 16-year-old girl- whose vagina Reingold had touched through her sweat pants. Because the government focuses on Reingold’s sexual activity with his sister rather than these other encounters in making certain arguments on appeal, we do not discuss this additional conduct further.
     
      
      . Defense counsel submitted that a guilty plea to a distribution count carrying a five-year minimum was in Reingold's interest because the government was considering superseding the indictment to add an advertising charge carrying a 15-year mandatory minimum sentence. See 18 U.S.C. § 2251(d)(2), (e).
     
      
      . In hearings conducted by the district court, Reingold stated that his goal in participating in the GigaTribe website was "to receive child pornography.” United States v. C.R., 792 F.Supp.2d at 354. Nevertheless, "in achieving that goal he knew that he had to make his child pornography files available to others.” Id.
      
     
      
      . Because no party challenges the sufficiency of Reingold’s plea allocution or of these findings by the district court in support of its decision to accept the plea, we deem any challenge to the plea itself forfeited and do not discuss it further in this opinion.
     
      
      . The Probation Department arrived at offense level 35 by starting with a base offense level of 22, see U.S.S.G. § 2G2.2(a)(2), to which it added two points for the presence of pre-pubescent images, see id. § 2G2.2(b)(2); two points for distribution in a manner not otherwise described in the Guidelines, see id. § 2G2.2(b)(3)(F); five points for a pattern of abuse, based on Reingold's molestation of his half-sister, see id. § 2G2.2(b)(5); two points for use of a computer, see id. § 2G2.2(b)(6); and five points for possession of 600 or more images of child pornography, see id. § 2G2.2(b)(7)(D); after which it subtracted three points for timely acceptance of responsibility, see id. § 3E1.1.
     
      
      . The district court agreed that Reingold’s base offense level was 22, that enhancements were warranted for the presence of pre-pu-bescent images and for the possession of 600 or more images of child pornography, and that a reduction was warranted for timely acceptance of responsibility. See United States v. C.R., 792 F.Supp.2d at 511-12. But it declined to impose any distribution enhancement, concluding that Reingold’s “actions did not constitute] distribution under the statute.” Id. at 511. The district court also rejected application of the pattern of abuse enhancement because two of the incidents with Reingold’s half-sister had occurred while Reingold was a minor, see id., and the trio of activities "were aberrant acts separated by long periods, in large measure, due to the failure of proper parental supervision,” May 16, 2011 Sentencing Tr. 15:24-16:1. Finally, the district court concluded that application of the computer-use enhancement would "result[] in double counting and is not sufficiently particularized to the facts of the case.” United States v. C.R., 792 F.Supp.2d at 512. Accordingly, the district court calculated Reingold’s total offense level at 26, which with a criminal history category of I, yielded an advisory Guidelines imprisonment range of 63 to 78 months.
     
      
      . The government argues that self-surrender was precluded by 18 U.S.C. § 3143(c)(1). Because Reingold did surrender and is now imprisoned, the point is moot, which the government concedes, and we do not discuss it further on this appeal.
     
      
      . In Graham, the Supreme Court recognized Justice Kennedy’s concurring opinion in Harmelin. joined in by Justices O'Connor and Souter, as ''controlling” in its discussion of constitutional proportionality. Graham v. Florida, 130 S.Ct. at 2022; see also Marks v. United States, 430 U.S. 188, 193, 97 S.Ct. 990, 51 L.Ed.2d 260 (1977) ("When a fragmented court decides a case and no single rationale explaining the result enjoys the assent of five Justices, the holding of the Court may be viewed as that position taken by those members who concurred in the judgments on the narrowest grounds.” (internal quotation marks omitted)).
     
      
      . Reingold’s "immaturity” did not have its origins in any organic brain damage or cognitive limitations. To the contrary, at least one doctor who interviewed Reingold found that his "level of intellectual functioning is in the high-average range.” United States v. C.R., 792 F.Supp.2d at 412 (internal quotation marks omitted).
     
      
      . In doing so, we make no categorical pronouncement that a prescribed five-year mandatory minimum sentence can never ran afoul of the Eighth Amendment's guarantee of proportionality in noncapital criminal sentencing. We therefore leave open the possibility that the Eighth Amendment may pre-elude a congressionally-mandated five-year minimum sentence for much less serious conduct.
     
      
      . It is necessary to discuss these case-specific circumstances to explain why the district court's characterization of them as mitigating is not persuasive and, therefore, does not permit a conclusion favorable to Reingold at the first step of proportionality analysis.
     
      
      . Pursuant to this graduated scheme, simple possession of child pornography carries no mandatory minimum sentence and a possible maximum of “not more than 10 years.” 18 U.S.C. § 2252(b)(2). Meanwhile, the production of child pornography in interstate commerce or the publication of an "advertisement seeking or offering ... to receive, exchange, buy, produce, display, distribute, or reproduce” such child pornography is punishable by a prison term of “not less than 15 years nor more than 30 years.” Id. § 2251(d), (e). The penalties for each of these proscribed activities are increased for defendants with prior child pornography convictions. See id. §§ 2251(e), 2252(b)(2)-(2).
     
      
      . See, e.g., 18 U.S.C. § 81 (providing for sentence up to 25 years for arson); id. § 115 (b) (1) (B) (ii)-(iv) (providing for sentence up to 10 years for physical assault on federal official, with possible higher sentences depending on degree of injury); id. § 201 (providing for sentence up to 15 years for bribery); id. § 371 (providing for sentence up to five years for conspiracy); id. § 471 (providing for sentence up to 20 years for forgery of United States securities); id. § 545 (providing for sentence up to 20 years for smuggling); id. § 659 (providing for sentence up to 10 years for theft of goods in interstate commerce); id § 892 (providing for sentence up to 20 years for making an extortionate extension of credit); id. § 924(c)(1) (providing for mandatory consecutive sentence of five years for carrying firearm during crime of violence or drug trafficking, with possible enhancements for how gun was used, type of firearm, and criminal record); id. § 1001 (providing for sentence up to five years for making false statement to federal official); id. § 1341 (providing for sentence up to 20 years for mail fraud); id. § 1542 (providing for sentence up to 10 years for passport fraud); id. § 1621 (providing for sentence up to five years for perjury); id. § 1956 (providing for sentence up to 20 years for money laundering).
     
      
      . Even if inadequate parental supervision might somehow have contributed to Rein-gold's first sexual contact with his sister, when the 15-year-old boy and his eight-year-old sister shared a bed on a family vacation, it is not apparent how it mitigates the second and third contacts absent a conclusion that no responsible parent would leave a teenage boy alone with his pre-pubescent sister, which hardly seems warranted. We need not pursue this essentially factual question further, however, in light of our legal conclusion that the language of § 2G2.2(b)(5) provides for any conduct satisfying its limited definition of sexual abuse and exploitation to be considered, with any two separate instances of such conducl satisfying the pattern requirement for an enhancement.
     
      
      . 18 U.S.C. § 2243 makes it a felony for any person:
      in the special maritime and territorial jurisdiction of the United States or in a Federal prison, ... knowingly [to] engage[ ] in a sexual act with another person who—
      (1) has attained the age of 12 years but has not attained the age of 16 years; and
      (2) is at least four years younger than the person so engaging; or attempts to do so....
      
        Id. § 2243(a).
     
      
      . Neither case had occasion to consider whether the reason so many of the same enhancements apply in the child pornography cases we review is that the government, confronting an epidemic of such crimes with limited resources, has focused its prosecutorial efforts on those cases presenting these aggravating factors.
     
      
      . Guideline § 2G2.2 applies to defendants convicted of the myriad offenses proscribed by 18 U.S.C. §§ 1466A, 2251(d)(1)(A), 2252, 2252A(a) and (b), and 2260(b). See United States Sentencing Commission, Guidelines Manual, Appendix A.
     
      
      . This first set also includes production and distribution crimes involving adapted or modified depictions of a minor. See 18 U.S.C. § 2252A(a)(7).
     
      
      . I might have said “many scholars” on the theory that one is likely to find a scholar who disagrees with nearly any point of view.
     
      
      . The victims’ statements in this case, which are set forth at length in the district court's opinion, powerfully illustrate the nature and severity of their injuries resulting from the receipt and dissemination of the material at issue. See United States v. C.R., 792 F.Supp.2d 343, 378-404 (E.D.N.Y.2011).
     
      
      . That is the characterization used by the government. Gov. Br. at 6.
     
      
      . Even if we were to characterize these additional statements as dicta, our colleague Judge Leval was surely right when he wrote: "[DJictum can serve useful purposes. We have no need to purge dictum from our opinions and we shouldn't be embarrassed by its presence." Pierre N. Leval, Judging Under the Constitution: Dicta About Dicta, 81 N.Y.U. L.Rev. 1249, 1282 (2006).
     
      
      . Cf. Harmelin, 501 U.S. at 994, 111 S.Ct. 2680 (Kennedy, J., concurring in part and concurring in the judgment in part) ("Proportionality review is one of several respects in which we have held that 'death is different’. ...”)
     
      
      . See generally, e.g. Amy Adler, The Perverse Law of Child Pornography, 101 Colum. L.Rev. 209 (2001); see also id. at 211 (referring to "child pornography law ... [as] caught up in a cultural maelstrom”).
     
      
      . This not a criticism; it is an observation. And the issues I perceive are hardly unique to the legal arena, as illustrated by a recent film review in The New York Times, which begins: "Violence against children strikes most people as a uniquely terrible phenomenon, which may be why filmmakers are so fond of it.” A.O. Scott, After Two Children Vanish, Agony Begets Recklessness, N.Y. Times, September 20, 2013, p. C 12. It should be obvious in any event that I am not suggesting that the majority's judgment was compromised by the nature of the case or any personal reaction to it — after all, I agree with the judgment of the Court.
     