
663 F.3d 224 (2011)
UNITED STATES of America, Plaintiff-Appellee,
v.
John Charles WELLMAN, Defendant-Appellant.
No. 10-4689.
United States Court of Appeals, Fourth Circuit.
Argued: October 28, 2011.
Decided: December 7, 2011.
*225 ARGUED: Jonathan D. Byrne, Office of the Federal Public Defender, Charleston, West Virginia, for Appellant. J. Christopher Krivonyak, Office of the United States Attorney, Charleston, West Virginia, for Appellee. ON BRIEF: Mary Lou Newberger, Federal Public Defender, David R. Bungard, Assistant Federal Public Defender, Office of The Federal Public Defender, Charleston, West Virginia, for Appellant. R. Booth Goodwin II, United States Attorney, Charleston, West Virginia, for Appellee.
Before KEENAN and WYNN, Circuit Judges, and HAMILTON, Senior Circuit Judge.
Affirmed by published opinion. Judge KEENAN wrote the opinion, in which Judge WYNN and Senior Judge HAMILTON joined.

OPINION
BARBARA MILANO KEENAN, Circuit Judge:
John Charles Wellman was convicted in a jury trial of three offenses related to his possession of child pornography. He raises three challenges in this appeal. Wellman argues that the search warrant that led to his arrest was invalid, that a jury instruction involving the term "obscene" was erroneous because it lacked a knowledge requirement, and that his sentence was imposed in violation of the Eighth Amendment prohibition against cruel and unusual punishment. Upon our review of these issues, we affirm Wellman's convictions and sentences.

I.
On March 14, 2007, Corporal D.C. Eldridge, a member of the West Virginia State Police assigned to the Internet Crimes Against Children Task Force (the Task Force), received a spreadsheet generated by the Wyoming Division of Criminal *226 Investigation Task Force. This spreadsheet contained a list of entries purporting to identify instances in which child pornography had been transmitted over the Gnutella computer file sharing network.[1] The allegedly pornographic files were not identified by name, type, or description, but by hash value.[2] Each entry on the spreadsheet contained a hash value for a digital file, the Internet Protocol (IP) address[3] of the computer offering the file for download, the locality in which that computer operated, the time and date the file was observed, and the officer from the Task Force who identified the file, as well as his or her law enforcement agency.
Corporal Eldridge focused on one IP address from Bluefield, West Virginia on the spreadsheet that was alleged to have hosted five different digital files of suspected child pornography. Using the American Registry of Internet Numbers web site, Eldridge determined that the IP address was assigned to Comcast Corporation (Comcast) and secured an order from a West Virginia state court to obtain the subscriber information associated with that IP address. Comcast identified the subscriber as John Wellman, whose address was located on Walters Avenue in Bluefield, West Virginia.
Using this information, Eldridge conducted a driver's license inquiry and confirmed that a John Wellman was listed at the address provided by Comcast. Wellman's name, address, and telephone number also were corroborated by a background report from the West Virginia Intelligence Exchange database. That database further indicated that Wellman previously had been convicted of first degree sexual abuse in 1987 (the abuse conviction), a felony.
Upon receipt of this information, Eldridge contacted the West Virginia Criminal Identification Bureau and confirmed Wellman's abuse conviction. Eldridge also confirmed with the West Virginia State Police Sex Offender Registration Section that Wellman had not registered with the West Virginia State Police as a sex offender, as required by state law.
Eldridge next obtained and reviewed an abstract of the indictment that led to Wellman's abuse conviction. That abstract indicated that Wellman's victim was a seven-year-old male child, and that Wellman had used physical force to compel the child to submit to sexual intercourse.
Using all this information, Eldridge assembled a 24-page application for a search warrant of the Walters Avenue residence. In the warrant application, Eldridge acknowledged that neither he nor the investigators who conducted the peer-to-peer searches over the Gnutella network possessed supporting documentation regarding the content of the digital files suspected of being child pornography. As *227 paragraph 21(c) of attachment D of the application explained:
The information in [the spreadsheet] is believed to be accurate, but no supporting documentation (i.e. downloads of child pornographic files from the suspect computers) was collected by the investigating officers during these searches of the Gnutella networks.
Therefore, the warrant application contained neither an exemplar of an allegedly offending image nor any description of such an image. Ultimately, a state circuit court judge signed each page of the application, concluded that there was probable cause to conduct a search of Wellman's home, and issued the search warrant.
The West Virginia State Police executed the warrant and conducted a search of Wellman's home. Wellman, who was present during the search, voluntarily produced a DVD containing images of child pornography and admitted that other such images were stored in his home on computer "hard drives" and in other electronic formats.
Following his arrest, Wellman was indicted in the United States District Court for the Southern District of West Virginia on three counts relevant to this appeal: (1) receiving a visual depiction of a minor engaging in sexually explicit conduct that is obscene and had been transported in interstate commerce, in violation of 18 U.S.C. § 1466A(a); (2) receiving obscene visual representations of the sexual abuse of children while being required by federal and state law to register as a sex offender, in violation of 18 U.S.C. § 2260A; and (3) knowingly possessing images and videos of child pornography that had been transported in interstate commerce, in violation of 18 U.S.C. § 2252A(a)(5)(B).
Wellman moved to suppress the evidence obtained from the search of his home, arguing that the warrant application was insufficient, and that the issuing judge acted merely as a "rubber stamp." After the district court denied the motion, Wellman was tried by a jury and convicted on all three counts.
The district court sentenced Wellman to a total term of 300 months' imprisonment. He received concurrent sentences of 180 months on Counts One and Three, and a sentence of 120 months on Count Two, to be served consecutively with the other two sentences, as mandated by 18 U.S.C. § 2260A. Wellman later filed a motion challenging his sentence with respect to Count Two, arguing that it violated the Eighth Amendment's prohibition on cruel and unusual punishment. The district court denied his motion, and Wellman now appeals.

II.
Wellman raises three issues on appeal. First, he contends that the district court erred in denying his motion to suppress evidence seized in the search of his home. Second, Wellman asserts that the district court gave the jury an erroneous instruction that failed to include a knowledge requirement regarding the obscene nature of the sexually explicit material at issue in Count One. Third, Wellman argues that the district court's imposition of a 10-year sentence with respect to Count Two violates the Eighth Amendment. We address these arguments in turn.

A.
Wellman asserts that the search warrant authorizing the search of his home was defective, because the warrant application failed to include either an exemplar or a description of an image alleged to be child pornography. He contends that in the absence of such information, the application merely contained the officers' conclusions *228 that the material sought constituted child pornography. According to Wellman, this defect in the warrant application precluded the reviewing judge from making an independent probable cause determination.
We review de novo the district court's denial of Wellman's motion to suppress. United States v. Rusher, 966 F.2d 868, 873 (4th Cir.1992). However, we reach our determination mindful of the principle that a judicial officer's determination of probable cause customarily is accorded "great deference" by reviewing courts. Illinois v. Gates, 462 U.S. 213, 236, 103 S.Ct. 2317, 76 L.Ed.2d 527 (1983).
In determining whether there was probable cause to believe that Wellman's house contained images of child pornography at the time the warrant was issued, the relevant question is whether the known facts and circumstances were sufficient such that a person of reasonable prudence could conclude that the described evidence would be found in that particular place. United States v. Perez, 393 F.3d 457, 461 (4th Cir.2004). The probable cause standard "is not defined by bright lines and rigid boundaries" but "allows a [judicial officer] to review the facts and circumstances as a whole and make a common sense determination" whether there is a fair probability that evidence of a crime will be found. United States v. Grossman, 400 F.3d 212, 217 (4th Cir.2005).
We decline to impose a requirement that a search warrant application involving child pornography must include an image of the alleged pornography. See United States v. Battershell, 457 F.3d 1048, 1052 (9th Cir.2006) (citing New York v. P.J. Video, Inc., 475 U.S. 868, 874 n. 5, 106 S.Ct. 1610, 89 L.Ed.2d 871 (1986)). While the inclusion of such material certainly would aid in the probable cause determination, we do not impose a fixed requirement or a bright-line rule, because law enforcement officers legitimately may choose to include a variety of information when submitting a search warrant application. Instead, when considering the merits of a judicial officer's probable cause determination, we will review a search warrant application in its entirety to determine whether the application provided sufficient information to support the issuance of the warrant. See Grossman, 400 F.3d at 217.
Based on the present record, however, we need not reach the merits of the question whether the warrant application before us sufficiently supported the judge's probable cause determination. Instead, we will assume, without deciding, that the content of the warrant was insufficient to support a finding of probable cause. Upon our review, we conclude that the evidence seized from Wellman's home pursuant to the search warrant was not subject to suppression, because the record shows that the West Virginia State Police relied in good faith on the issued search warrant. United States v. Leon, 468 U.S. 897, 926, 104 S.Ct. 3405, 82 L.Ed.2d 677 (1984).
In its decision in Leon, the Supreme Court instructed that a reviewing court should not suppress evidence discovered "under the authority of a warrant, even a subsequently invalidated warrant, unless a reasonably well trained officer would have known that the search was illegal despite the [judicial officer's] authorization." United States v. Bynum, 293 F.3d 192, 195 (4th Cir.2002) (citing Leon, 468 U.S. at 922 n. 23, 104 S.Ct. 3405) (quotation marks omitted). This "good faith" exception will be applied except in four limited situations: (1) when the affiant based his application on knowing or reckless falsity; (2) when the judicial officer wholly abandoned his role as a neutral *229 and detached decision maker and served merely as a "rubber stamp" for the police; (3) when the affidavit supporting the warrant was so lacking in indicia of probable cause as to render official belief in its existence entirely unreasonable; and (4) when the warrant was so facially deficient that the executing officers could not reasonably have presumed that the warrant was valid. United States v. Doyle, 650 F.3d 460, 467 (4th Cir.2011) (quoting United States v. DeQuasie, 373 F.3d 509, 519-20 (4th Cir.2004)).
According to Wellman, the state circuit court judge reviewing the warrant application acted as a "rubber stamp" by issuing a search warrant without sufficient information and, therefore, the Leon good faith exception is inapplicable. We find no merit in this argument.
The record before us shows that when the judge approved the search warrant, he did not act as a "rubber stamp" or abandon his role as a neutral and detached decision maker. Moreover, as we explained in Doyle, an allegation that a search warrant application contained grossly insufficient information is best analyzed under the third Leon exclusion. Doyle, 650 F.3d at 470 (distinguishing United States v. Wilhelm, 80 F.3d 116, 121-23 (4th Cir.1996)). We therefore review the evidence under the third Leon exclusion to determine whether the warrant application was so lacking in indicia of probable cause as to render official belief in its existence entirely unreasonable. See Doyle, 650 F.3d at 467.
In conducting this review, we observe that Corporal Eldridge's affidavit bears many of the indicia of a strong search warrant application. Eldridge provided information in the application regarding his background as an investigator, which established his experience in dealing with crimes involving child pornography. He set forth a thorough explanation of the technology employed by the Task Force and how that technology was used to identify Wellman. Rather than relying exclusively on the information provided by the spreadsheet and Comcast, Eldridge performed additional research into Wellman's background to provide corroboration and to minimize the possibility of mistake or confusion. Further, the dates provided in the search warrant application demonstrate that the affidavit was not a hastily-assembled document based on a single tip, but was the product of a six-week investigation. Upon examining the totality of this information before the issuing judge, we conclude that the affidavit supporting the warrant was not so lacking in indicia of probable cause as to render official belief in its existence entirely unreasonable. Therefore, upon application of the Leon analysis, we hold that the district court did not err in denying Wellman's motion to suppress.

B.
Wellman next argues that the district court's instruction regarding Count One was erroneous because the instruction did not contain a knowledge requirement. He asserts that the jury should have been instructed that the government was required to prove beyond a reasonable doubt that Wellman knew that the images of the minors engaged in sexually explicit conduct were obscene. We disagree with this argument.
The fatal flaw in Wellman's argument is his attempt to graft a subjective, fact-based knowledge requirement onto an objective legal standard. The statute under which Wellman was convicted provides, in relevant part:
Any person who . . . knowingly produces, distributes, receives, or possesses *230 with intent to distribute, a visual depiction of any kind, including a drawing, cartoon, sculpture, or painting, that
(A) depicts a minor engaging in sexually explicit conduct; and
(B) is obscene . . .
shall be subject to the penalties provided in section 2252A(b)(1), including the penalties provided for cases involving a prior conviction.
18 U.S.C. § 1466A(a).
The term "obscene," as used in statutes of this type, refers to an objective, legal standard, not to an issue of fact. The Supreme Court explained this distinction in Hamling v. United States, 418 U.S. 87, 94 S.Ct. 2887, 41 L.Ed.2d 590 (1974), a case involving a prosecution under 18 U.S.C. § 1461 for the mailing of, and conspiring to mail, an obscene brochure containing sexually explicit photographs. The Court explicitly rejected the defendants' argument that the government was required to prove that the defendants knew that the mailed materials were obscene. The Court emphasized that:
It is constitutionally sufficient that the prosecution show that a defendant had knowledge of the contents of the materials he distributed, and that he knew the character and nature of the materials. To require proof of a defendant's knowledge of the legal status of the materials would permit the defendant to avoid prosecution by simply claiming that he had not brushed up on the law. Such a formulation of the scienter requirement is required neither by the language of [the statute] nor by the Constitution.
418 U.S. at 123-24, 94 S.Ct. 2887.
Contrary to Wellman's suggestion, the Hamling analysis is not affected by the Supreme Court's later decision in United States v. X-Citement Video, Inc., 513 U.S. 64, 115 S.Ct. 464, 130 L.Ed.2d 372 (1994). There, the Supreme Court considered a prosecution brought under 18 U.S.C. § 2252(a), which alleged the transportation or shipment of materials containing depictions of minors engaging in sexually explicit conduct. That statute provided, in relevant part:
Any person who
(1) knowingly transports or ships in interstate or foreign commerce by any means including by computer or mails, any visual depiction, if
(A) the producing of such visual depiction involves the use of a minor engaging in sexually explicit conduct; and
(B) such visual depiction is of such conduct;
(2) knowingly receives, or distributes, any visual depiction that has been mailed, or has been shipped or transported in interstate or foreign commerce, or which contains materials which have been mailed or so shipped or transported, by any means including by computer, or knowingly reproduces any visual depiction for distribution in interstate or foreign commerce or through the mails, if
(A) the producing of such visual depiction involves the use of a minor engaging in sexually explicit conduct; and
(B) such visual depiction is of such conduct;
. . .
shall be punished as provided in subsection (b) of this section.
18 U.S.C. § 2252(a) (1988 & Supp. V).
The Supreme Court concluded that, among other things, the term "knowingly" imposed a scienter requirement with regard to factual issues involving the age of the persons depicted and whether the material at issue was sexually explicit. 513 *231 U.S. at 78, 115 S.Ct. 464. Thus, the Court held that under the statute, the government was required to prove that the defendants knew that persons appearing in the materials at issue were "minor[s]," and that the conduct depicted was "sexually explicit." See id.
Notably, however, the Court in X-Citement Video did not apply a knowledge requirement to any legal standard. This distinction is critical, as the Court's analysis in Hamling illustrates. Under that analysis, a defendant's knowledge of the law is not a relevant consideration in a prosecution involving the distribution of allegedly obscene materials. 418 U.S. at 123-24, 94 S.Ct. 2887. Thus, we conclude that the district court did not give the jury an erroneous instruction on this issue, because the jury was not required to find that Wellman knew that the images at issue were obscene.

C.
Finally, we consider Wellman's argument addressing the length of his sentence. He asserts that the length and consecutive nature of his ten-year sentence with respect to Count Two constitute a de facto life sentence given his age of 68 years. He contends that, therefore, his sentence on Count Two is unconstitutionally disproportionate. We disagree with Wellman's argument.
The Eighth Amendment to the Constitution of the United States bans, among other things, "cruel and unusual punishments." U.S. Const. amend. VIII. In applying the Eighth Amendment to such a claim, an appellate court decides only whether the sentence under review is within constitutional limits. Solem v. Helm, 463 U.S. 277, 290 n. 16, 103 S.Ct. 3001, 77 L.Ed.2d 637 (1983).
In Solem, the Supreme Court instructed that reviewing courts should "grant substantial deference to the broad authority that legislatures necessarily possess in determining the types and limits of punishments for crimes. . . ." Id. at 290, 103 S.Ct. 3001. Thus, appellate courts only "rarely will be required to engage in extended analysis to determine that a sentence is not constitutionally disproportionate." Id. at 290 n. 16, 103 S.Ct. 3001; see also Hutto v. Davis, 454 U.S. 370, 374, 102 S.Ct. 703, 70 L.Ed.2d 556 (1982) (stating that "successful challenges to the proportionality of particular sentences should be exceedingly rare") (quotation marks omitted). As one of our sister circuits colorfully stated, the instances of disproportionate sentences resulting in an Eighth Amendment violation will be "hen's-teeth rare." United States v. Polk, 546 F.3d 74, 76 (1st Cir.2008).
We are not confronted here with a disproportionate sentence of constitutional magnitude. And, as we observed in United States v. Rhodes, 779 F.2d 1019, 1028 (4th Cir. 1985), extensive proportionality analyses are only required in those cases involving life sentences without the possibility of parole. In contrast, other lesser sentences that are clearly within the prerogative of Congress and subject to imposition by a district court may be disposed of swiftly. Id.
In Solem, the Supreme Court employed a three-part test using objective factors to gauge the proportionality of sentences for purposes of Eighth Amendment compliance: (1) the gravity of the offense and the harshness of the penalty; (2) the sentences imposed on other criminals in the same jurisdiction; and (3) the sentences imposed for commission of the same crime in other jurisdictions. 463 U.S. at 292, 103 S.Ct. 3001. Because the crime in this case, like the crime reviewed in Rhodes, involves the violation of a federal statute, the last two elements collapse into a single element. See Rhodes, 779 F.2d at 1029.
*232 The harshness of Wellman's penalty reflects the gravity of his crimes. Wellman received and possessed images depicting the sexual abuse of some of the most vulnerable members of our society. Children, as the subject of these images, undeniably suffer serious harm when they are used to create this type of material. Additionally, Wellman's failure to obey the statutory requirement that he register as a sex offender demonstrated an attempt to evade the law and the protections Congress established for the communities in which such offenders reside.
Ultimately, however, as the district court correctly noted, the severity of Wellman's sentence was based on his recidivism. See Ewing v. California, 538 U.S. 11, 25, 123 S.Ct. 1179, 155 L.Ed.2d 108 (2003) ("Recidivism has long been recognized as a legitimate basis for increased punishment.") In 1987, Wellman was convicted of sexual abuse in the first degree for his use of force in coercing a seven-year-old child to engage in sexual intercourse with him. In recidivist situations like the one before us, Congress is well within its authority to provide for enhanced sentences.
The ten-year sentence for Count Two also is proportional to other sentences for violations of 18 U.S.C. § 2260A, because this sentence is mandated by statute. Thus, we conclude that Wellman's consecutive sentence for his conviction on Count Two does not violate the Eighth Amendment.

III.
For these reasons, we affirm the district court's judgment.
AFFIRMED
NOTES
[1]  The Gnutella computer file sharing network allows users who have installed certain client applications on their personal computers to download a copy of each others' digital files. This "peer-to-peer" (computer to computer) system allows individuals to transfer files over the Internet without the use of a centralized server.
[2]  A "hash value" is an alphanumeric string that serves to identify an individual digital file as a kind of "digital fingerprint." Although it may be possible for two digital files to have hash values that "collide," or overlap, it is unlikely that the values of two dissimilar images will do so. United States v. Cartier, 543 F.3d 442, 446 (8th Cir.2008). In the present case, the district court found that files with the same hash value have a 99.99 percent probability of being identical.
[3]  An IP address is a numerical label that is assigned to each device (e.g., computer, printer) participating in a computer network that uses the Internet Protocol for communication.
