
544 F.3d 110 (2008)
UNITED STATES of America, Appellee,
v.
David J. FALSO, also known as Sealed Premise, Defendant-Appellant.
Docket No. 06-2721-cr.
United States Court of Appeals, Second Circuit.
Argued: September 24, 2007.
Decided: September 25, 2008.
*112 Brenda K. Sannes, Assistant United States Attorney (Glenn T. Suddaby, United States Attorney for the Northern District of New York; Miroslav Lovric, Assistant United States Attorney, on the brief), Syracuse, NY, for Appellee.
Bruce R. Bryan (Vincent L. Briccetti, Briccetti, Calhoun & Lawrence, LLP, White Plains, NY, on the brief), Syracuse, NY, for Defendant-Appellant.
Before: JACOBS, Chief Judge, SOTOMAYOR and LIVINGSTON, Circuit Judges.
Chief Judge JACOBS joins Part I of the discussion and has filed a dissent.
Judge LIVINGSTON joins Part II of the discussion and has filed a concurring opinion.
SOTOMAYOR, Circuit Judge.
Defendant-appellant David J. Falso ("Falso") appeals from the June 6, 2006 judgment of the United States District Court for the Northern District of New York (McAvoy, J.). Falso was convicted, upon his conditional guilty plea to a 242-count indictment, of crimes relating to child pornography and traveling with the intent to engage in illicit sexual conduct with minors. Prior to Falso's guilty plea, the district court denied his motion to suppress evidence seized from his home on the grounds that probable cause for the search existed and that, in any event, the "good-faith" exception to the exclusionary rule applied.[1]
The threshold issue presented on appeal is whether a substantial basis for the district court's finding of probable cause exists where the law enforcement affidavit supporting the search warrant alleged that Falso "appears" to have "gained or attempted to gain" access to a website that distributed child pornography and had been convicted eighteen years earlier of a misdemeanor based on sexual abuse of a minor. In a divided opinion in United States v. Martin, 426 F.3d 68 (2d Cir. 2005), this Court held that probable cause to search the defendant's home existed, largely based on his membership to a website whose principal purpose was sharing of child pornography (hereafter, a "child-pornography website"). Id. at 75-76. In *113 United States v. Coreas, 419 F.3d 151 (2d Cir.2005), a different panel expressed its belief that Martin "was wrongly decided," but adhered to Martin's holding because the cases were indistinguishable and Martin was binding precedent. Id. at 159 (2d Cir.2005).
Falso's case tests the limits of these precedents, insofar as it presents the following distinguishing factor: Falso was not alleged to be a member or subscriber to a child-pornography website; it was alleged only that Falso "appeared" to "have gained or attempted to gain" access to a site that contained approximately eleven images of child pornography. Absent any allegation that Falso in fact accessed the website at issue, the question is whether Falso's eighteen-year old conviction involving the sexual abuse of a minor (or some other factor) provides a sufficient basis to believe that evidence of child pornography crimes would be found in Falso's home. A majority of this panel (Jacobs, C.J. & Sotomayor, J.) holds that probable cause was lacking. A differently aligned majority of this panel (Sotomayor & Livingston, J.J.), however, holds that the good-faith exception to the exclusionary rule applies. See United States v. Leon, 468 U.S. 897, 923-25, 104 S.Ct. 3405, 82 L.Ed.2d 677 (1984). Thus, notwithstanding the absence of probable cause to sustain issuance of the search warrant, a majority of this panel affirms the district court's denial of Falso's motion to suppress the physical evidence seized from his home.[2]

BACKGROUND

A. The Search Warrant Affidavit
On or about June 1, 2005, the Federal Bureau of Investigation ("FBI") submitted an application for a warrant to search for and seize evidence of child pornography in Falso's home. The application was supported by, inter alia, a twenty-six page affidavit by FBI Agent James Lyons ("Agent Lyons"). Among other things, the affidavit provided information about (1) the use of computers and the internet to view and collect child pornography; (2) the characteristics of child-pornography collectors; and (3) the investigation that implicated Falso.
Of the affidavit's generalized information, Agent Lyons explained that individuals who exploit children, including collectors of child pornography, commonly use computers to: communicate with like-minded individuals, store their child pornography collections, and locate, view, download, collect and organize images of child pornography found on the internet. The affidavit further explained that collectors and distributors of child pornography sometime use online resources to retrieve and store child pornography, including services offered by internet portals such as Yahoo! Inc. ("Yahoo"). The affidavit also contained information gathered by a member of the FBI's Behavioral Analysis Unit, including his observations that "[t]he majority of individuals who collect child pornography are persons who have a sexual attraction to children," and that those who collect images of child pornography generally store their collections at home.
Specific to the investigation of Falso, the affidavit explained that the FBI obtained the Internet Protocol address of a website, www.cpfreedom.com, which contained approximately *114 eleven images of child pornography, and which advertised additional child pornography at an internet address that was hidden until a membership was purchased. The affidavit further stated that an undercover FBI agent paid $99 for a one-month membership and received an e-mail from CP Freedom Group, which provided the internet address, login number, and password for its membership website, www.cp-members.com. The affidavit then explained that an FBI forensic examination of "the website hosting www. cpfreedom.com" revealed "several possible subscribers along with e-mail addresses and other information." According to the affidavit, the FBI subpoenaed subscriber information for these e-mail addresses, which included cousy1731@yahoo.com. Records obtained from Yahoo revealed that Falso had an active Yahoo account, with a login name of "cousy1731" and the Yahoo e-mail address referenced above. The affidavit also stated that the residential address associated with Falso's Yahoo account had active internet service during the period immediately preceding the warrant request. The affidavit further stated that, based upon the FBI investigation and the forensic examination, "it appear[ed]" that Falso "either gained access or attempted to gain access to the [non-member] website www.cpfreedom.com."
The affidavit also revealed that on February 18, 1987approximately eighteen years earlierFalso was arrested by the New York State Police for sexually abusing a seven-year old girl and was charged with Sexual Abuse and Endangering the Welfare of a Child. According to the affidavit, the police report relating to this incident stated that Falso placed his hands inside the girl's underwear and digitally penetrated her, and acknowledged to police that he may need counseling for latent problems. The affidavit also stated that, on or about September 21, 1987, Falso pled guilty to Acting in a Manner Injurious to a Child Less than Sixteen, a misdemeanor for which Falso received a sentence of three years probation.[3]
Based on the foregoing, Agent Lyons opined that "there [was] probable cause to believe that the individual utilizing the Yahoo ID `cousy 1731' [i.e. Falso] ... is a collector of child pornography." Judge McAvoy agreed and issued a search warrant on June 1, 2005, permitting the FBI to search Falso's home for, inter alia, evidence of child-pornography related crimes.

B. The Search and Seizure
Five law enforcement officers, including Agent Lyons, executed the search warrant at Falso's home on June 8, 2005. The officers seized Falso's computer and a box containing child pornography in Falso's bedroom. Agent Lyons and another officer also interviewed Falso for approximately ninety minutes during the search. Agent Lyons's report from the interview stated that Falso admitted to, among other things, obtaining child pornography from the internet; engaging in sexual activity with females in other countries whom he believed to be between the ages of sixteen and eighteen; and having been convicted for sexually abusing a seven-year old girl. Falso was placed under arrest at the conclusion of the search. A later search of Falso's computer revealed additional images of child pornography.


*115 C. Falso's Criminal Proceedings
Falso was indicted on June 16, 2005 for traveling with the intent to engage in illicit sexual conduct with minors in violation of 18 U.S.C. §§ 2423(b), (f) & 2246 (Counts 1-2); production of child pornography in violation of 18 U.S.C. § 2251(a) (Counts 3-10); receiving child pornography via the internet in violation of 18 U.S.C. §§ 2252A(a)(2)(A), (B) & 2256 (Counts 11-233); transporting and shipping child pornography in violation of 18 U.S.C. §§ 2252A(a)(1) & 2256 (Counts 234-241); and possession of child pornography in violation of 18 U.S.C. § 2252A(a)(5)(B) (Count 242). The indictment also alleged that Falso had a prior conviction relating to the sexual exploitation of children, and sexual abuse involving a minor, which invoked the penalty provisions of 18 U.S.C. §§ 2252A(b)(1), (b)(2) and 2251.
Falso subsequently moved to suppress the evidence seized from his home and computer on the ground that probable cause for the search was lacking. Specifically, Falso claimed that the presence of his e-mail address on the cpfreedom.com website was an insufficient basis for probable cause in the absence of any allegations in the affidavit that Falso was a member or subscriber to the website, or that the overriding purpose of the website was the trading of child pornography.
Falso also sought a Franks hearing,[4] claiming that certain of the information in the affidavit was designed to mislead the court into believing that Falso was actually a member of or subscriber to the cpfreedom website, and that the government misleadingly failed to disclose that Falso's e-mail address could have appeared on the cpfreedom.com website for innocent reasons, such as being part of a spam mailing list. In support, Falso submitted an affidavit from a data forensics expert, Robert DeCicco ("DeCicco"). That affidavit explained that "there is a difference between visiting a website, and become [sic] a member and/or subscriber to the site"; the latter normally "involves the assignment of a password and user name conditioned on the payment of a fee or the provision of specific personal information." DeCicco's affidavit further explained that internet service providers [such as Yahoo] do not maintain records identifying the websites visited by their customers and, thus, a review of service provider records "would not disclose whether a customer was a subscriber or member of a particular website." Moreover, his affidavit stated that "[i]t is common practice for websites to obtain lists of e-mail addresses from other sources ... and to send unsolicited e-mail to such addresses." Thus, DeCicco concluded, "the fact that [Falso's] e-mail address appeared on the [cpfreedom.com] website does not mean that he contacted or attempted to contact that site."
On February 24, 2006, the district court issued an oral ruling denying Falso's motions, holding that: (1) Falso was not entitled to a Franks hearing; (2) probable cause for the search existed; and (3) even if there was an insufficient basis for probable cause, suppression of the evidence was not warranted because the good-faith exception to the exclusionary rule applied.
More specifically, in response to Falso's Franks claim, the court found that Agent Lyons did not make any false or misleading statements, and explained that, "[s]ignificantly, the court was not misled by Agent Lyons." The court explained that it *116 had never understood Agent Lyons "to be saying that defendant had actually subscribed to the CP Freedom website;" rather, it understood the affidavit to say that there was reason to believe Falso had either gained or attempted to gain access to the site.
The district court then explained its basis for concluding that probable cause existed:
First, there was the information concerning the background of persons dealing in child pornography, including the fact that persons who collect child pornography have a sexual attraction to children. Second, there was information that the web site, CP Freedom, advertised that it contained child pornography, actually had some images of child pornography available on it free of charge and advertised that it had additional images of child pornography upon payment of a fee. Third, the FBI determined that the material associated with the website is hardcore child pornography. Fourth, there was evidence that [Falso] had access or attempted to access the CP Freedom web site. Fifth, there was information [that Falso] actually engaged in inappropriate sexual contact with a minor in the past.
Thus, the court found:
Together, this information set forth a reasonable probability that [Falso] had a sexual attraction to minors and that he was undertaking efforts to appeal to his sexual attraction to minors by viewing pictures of child pornography via the internet. In light of the proclivity of such persons to store images of child pornography on their computer and otherwise maintain images of child pornography, there was a reasonable probability that child pornography would be found in the defendant's home, including on his computer.
The district court also considered and rejected Falso's claim that the presence of his email address on the website might simply have been the product of a spam mailing list. While recognizing the proliferation of spam, the court explained that Agent Lyons's affidavit suggested "something more"namely, that "it appear[ed] that someone with [Falso's] e-mail address... either gained access or attempted to gain access to the website."
Additionally, the district court measured Falso's case against our precedents in Martin and Coreas (discussed infra). After identifying what it perceived to be similarities between those cases and Falso's case,[5] the court recognized that, unlike in Martin and Coreas, there was no evidence that Falso was a member of a child-pornography website. The court explained, however, that there "is information... that [Falso] accessed or attempted to access the site and that free child pornography was available to anyone who accessed the site." Also contributing to probable cause, the court continued, was:
[I]nformation in this case that was not available in Martin or [Coreas]. That information is defendant's prior criminal history involving sexual contact with a seven year old  conduct that is highly relevant to the criminal activity at issue here. The character provided by the FBI indicates that the majority of individuals who collect child pornography have a sexual attraction to them. [sic] In *117 light of [Falso's] known sexual attraction to minors and his having accessed or gained access to a site offering child pornography, there's a reasonable probability that he would collect child pornography.
Finally, the district court held that even if there had been an insufficient basis for finding probable cause, suppression of the evidence was not warranted because the good-faith exception to the exclusionary rule applied. In this regard, the court explained that it found no statements in the affidavit to be false or in reckless disregard for the truth, and that "the warrant was not so lacking in indicia of probable cause as to render [the executing officers'] belief in the existence of probable cause entirely unreasonable."
After the district court denied Falso's motions, he pled guilty to all 242 counts in the indictment. Falso specifically reserved the right to appeal from the district court's denial of his motions to suppress. Falso also objected to the district court's use of his prior state conviction for Endangering the Welfare of a Child as a basis for enhancing the statutory minimum and maximum penalties. On June 2, 2006, the district court sentenced Falso principally to 30 years' imprisonment.

DISCUSSION

I. Probable Cause

A. Standards for Probable Cause
The Fourth Amendment prohibits "unreasonable searches and seizures," and requires that "no warrants shall issue, but upon probable cause, supported by Oath." U.S. Const. amend. IV. The Supreme Court has explained that "probable cause is a fluid conceptturning on the assessment of probabilities in particular factual contextsnot readily, or even usefully, reduced to a neat set of legal rules." Illinois v. Gates, 462 U.S. 213, 232, 103 S.Ct. 2317, 76 L.Ed.2d 527 (1983). "The task of the issuing magistrate [or judge[6]]is simply to make a practical, common-sense decision whether, given all the circumstances set forth in the affidavit before him, ... there is a fair probability that contraband or evidence of a crime will be found in a particular place." Id. at 238, 103 S.Ct. 2317.
This Court must afford "great deference" to the district court's probable cause determination. Gates, 462 U.S. at 236, 103 S.Ct. 2317 (internal quotation marks omitted). Our "duty" on review, therefore, "is simply to ensure that the [district court] had a substantial basis for... concluding that probable cause existed." Id. at 238, 103 S.Ct. 2317 (internal marks omitted). Nevertheless, under this standard, we "may properly conclude that... [a] warrant was invalid because the [district court's] probable-cause determination reflected an improper analysis of the totality of circumstances." Leon, 468 U.S. at 915, 104 S.Ct. 3405 (citing Gates, 462 U.S. at 238-39, 103 S.Ct. 2317).

B. Martin and Like Cases
In Martin, this Court considered the sufficiency of an affidavit filed in support of a search warrant of Martin's residence based on information obtained from an FBI investigation into child pornography e-groups. See Martin, 426 F.3d at 73-77. The majority opinion affirmed the district *118 court's finding of probable cause based on the following factors: (1) the e-group's welcome page and title, "girls 12-16," made plain "its essential purpose to trade child pornography" of minor girls;[7] (2) the affidavit's discussion of the "modus operandi of those who use computers to collect and distribute child pornography"; (3) the affidavit's description of the "characteristics and proclivities of child-pornography collectors," including their tendency to collect pornographic images; (4) the fact that the e-group's "illicit purpose could be inferred from the website's technological features" that facilitated trading in child pornography; (5) the affiant's confirmation that the e-group contained child pornography available to all members; (6) the fact that the defendant lived at the house to be searched; and (7) the fact that the defendant was an e-group member who joined voluntarily and never cancelled his membership. Id. at 75-76. The majority deemed it "common sense" that "an individual who joins such a site would more than likely download and possess such material," and concluded that the affidavit, as corrected to eliminate statements determined to be false, established probable cause for the search warrant. Id.[8]
Judge Pooler dissented, expressing her concern that "the majority announces a dangerous precedent." Id. at 78 (Pooler, J., dissenting). Under the majority's decision, she explained, the government could obtain a warrant simply where an individual subscribes to an internet e-group that has an illegal purpose, notwithstanding the absence of particularized evidence indicating that the individual visited the e-group after joining or participated in the e-group's functions. Id. But this result, she *119 opined, cannot be squared with the general proscription against finding probable cause based solely on an individual's "`mere propinquity to others' suspected of criminal activity." Id. at 81 (quoting Ybarra v. Illinois, 444 U.S. 85, 91, 100 S.Ct. 338, 62 L.Ed.2d 238 (1979)). In Judge Pooler's opinion, the affidavit provided insufficient particularized facts as to Martin's involvement in illegal activity, and the inferences drawn by the majority were ill-supported. For instance, she believed, the affidavit at issue did not support the inferential leaps that: (1) Martin participated in the functions of the e-group simply because he was a member of the group; (2) the overriding purpose of the e-group was illegal, because the group also fostered discussion that did not necessarily include the sharing of pornographic images of children; and (3) all members collect pornographic images of children simply because some do. Id. at 79-82. Finally, she challenged the majority's "attempts to create the required nexus between Martin and illegal activity by appealing to `common sense.'" Id. at 83. In this regard, Judge Pooler explained that "[w]hile the majority is correct that a magistrate [judge] presented with a warrant may `make a practical, common-sense decision,' that decision must be based on the circumstances set forth in the affidavit.'" Id. (quoting Gates, 462 U.S. at 238, 103 S.Ct. 2317).
Two weeks after Martin was decided, the panel in Coreas expressed its view that "Martin itself was wrongly decided," but "under established rules of this circuit" adhered to Martin's holding because that case was heard first. Coreas, 419 F.3d at 159. The affidavit at issue in Coreas was substantively identical to the one considered by this Court in Martin, except that it pertained to a member of a different e-group, titled "Candyman." Id. at 157 (finding the distinction immaterial for purposes of the case).[9] The Coreas panel concurred with Judge Pooler's minority position in Martin, and detailed how easy it was to become a member of the e-group, including by the innocent or inadvertent single click of a button. Id. at 156, 158. Coreas also explained that Martinto the extent it focused on the overriding illegal purpose of the group rather than on the activities of the person targeted for the search"might tend to dilute the First Amendment's protection against guilt by association and diminish the Fourth Amendment's focus on particularity and on protection of the privacy of the individual to be searched." Id. at 158.[10]
*120 Our sister circuits have addressed this issue consistently with the majority's holding in Martin, although the facts and considerations of the decisions vary. United States v. Shields, 458 F.3d 269 (3d Cir. 2006); United States v. Wagers, 452 F.3d 534 (6th Cir.2006); United States v. Gourde, 440 F.3d 1065 (9th Cir.2006) (en banc); United States v. Froman, 355 F.3d 882 (5th Cir.2004); United States v. Hutto, 84 Fed.Appx. 6 (10th Cir.2003) (unpublished). The common thread among these cases is the defendants' membership in or subscription to websites whose principal purpose was the collection and/or sharing of child pornography. See Shields, 458 F.3d at 272-73, 278; Gourde, 440 F.3d at 1070; Froman, 355 F.3d at 890-91; Hutto, 84 Fed.Appx. at * 8; see also Wagers, 452 F.3d at 543.[11] Additional factors weighing in favor of probable cause in some of these cases included: (1) acts of the defendant that tended to negate the possibility that his membership or subscription was unintended, see, e.g., Shields, 458 F.3d at 278-79 (defendant's membership in multiple sites undermined suggestion that his membership may have been unwitting or innocent); Wagers, 452 F.3d at 536-37 (same); Gourde, 440 F.3d at 1070 (defendant's subscription required him to provide his credit card information, home address, and e-mail address); (2) e-mail addresses or screen names suggestive of an interest in collecting child pornography, see Shields, 458 F.3d at 279-80 ("LittleLolitaLove@ aol.com e-mail"); Froman, 355 F.3d at 890-91 ("Littlebuttsue" and "Littletitgirly" screen names); and (3) defendant's criminal history relating to child pornography, Wagers, 452 F.3d at 541.

C. No Probable Cause
Falso's case stands apart from those preceding it insofar as he was not alleged to have actually accessed or subscribed to any child-pornography website. Rather, Agent Lyons's affidavit alleged only that Falso was perhaps one of several hundred possible subscribers to the cpfreedom.com website, who appeared either to have gained or attempted to gain access to the site. For this reason, Martin and Coreas are not controlling.

1. Member of or Subscriber to a Child-Pornography Website
Falso asks us to interpret Martin rigidly as requiring, for a finding of probable cause, that a defendant in these types of cases be a member of or subscriber to a child-pornography website. His approach to the issue, however, is antithetical to the "fluid" concept of probable cause espoused by the Supreme Court. See Gates, 462 U.S. at 232, 103 S.Ct. 2317; see also Martin, 426 F.3d at 74. While the probable cause finding in Martin depended heavily on the fact that the defendant was a member of a principally illicit website, nothing in that decision should be read to require these conditions in all similar cases. For example, the absence of membership would not be dispositive if other factors such as evidence that the defendant otherwise downloaded illegal imageswere present.
*121 That said, membership in or subscription to a child-pornography website[12] is an important consideration in these types of cases because it supports the ultimate inference, drawn in Martin, that illegal activity is afoot. As the majority opinion explained in Martin, "membership in the e-group reasonably implied use of the website," and it is "common sense that an individual who joins such a site would more than likely download and possess such material." 426 F.3d at 75. Putting aside whether those inferences are reasonable, see id. at 79-81 (Pooler, J., dissenting) (explaining why they are not); Coreas, 419 F.3d at 156-58 (same), it is the fact of membership to a child-pornography website that largely supports the inferences drawn in Martin that the defendant more likely than not used the website and downloaded images from it.
In Falso's case, there is no allegation that he subscribed to CP Freedom's paying-membership site; only that it "appear[ed]" that he "gained access or attempted to gain access" to the non-member cpfreedom.com website. Even if one assumes (or infers) that Falso accessed the cpfreedom.com site, there is no specific allegation that Falso accessed, viewed or downloaded child pornography. While the non-member site contained approximately eleven images of child pornography, the affidavit lacks any information about whether the images were prominently displayed or required an additional click of the mouse; whether the images were downloadable; or what other types of services and images were available on the site.[13]
Falso's case is thus quite unlike Martin, where the supporting affidavits provided at least some of this information about the features of the sites at issue. For example, the supporting affidavit in Martin asserted that members of the e-group had access to, among other features, a "Files" section that enabled users to post images and video clips for other members "to access and download." Martin, 426 F.3d at 70. Indeed, the affidavit in Martin explained that an FBI agent had downloaded approximately 100 pictures and movies of child pornography from the Files section. Id. at 70. In addition, the affidavits in Martin and Coreas contained information about each site's "welcome pages," which the majority in Martin found to be highly relevant to the probable cause determination, insofar as the messages announced the e-groups' central purpose to trade child pornography. See Martin, 426 F.3d at 75; see also Coreas, 419 F.3d at 157. By contrast, Agent Lyons's affidavit contains no such information about the cpfreedom.com site.
Agent Lyons's inconclusive statements about whether Falso even accessed the cpfreedom.com website, coupled with the absence of details about the features and nature of the non-member site, falls short of establishing probable cause. The question, then, is whether other allegations in the affidavit, considered as a whole, provide a basis to support the district court's finding of probable cause.

2. Falso's Criminal History
The most obvious other factor that might support a finding of probable cause is Falso's eighteen-year-old misdemeanor *122 conviction for Endangering the Welfare of a Child. The district court found Falso's conviction "[i]mportant[ ]" and "highly relevant" to the probable cause calculus in light of the affidavit's representation that "the majority of individuals who collect child pornography are persons who have a sexual attraction to [children]." But this reasoning falls victim to logic.
"It is an inferential fallacy of ancient standing to conclude that, because members of group A" (those who collect child pornography) "are likely to be members of group B" (those attracted to children), "then group B is entirely, or even largely composed of, members of group A." See Martin, 426 F.3d at 82 (Pooler, J., dissenting) (pointing out the fallacy in a different context).[14] Although offenses relating to child pornography and sexual abuse of minors both involve the exploitation of children, that does not compel, or even suggest, the correlation drawn by the district court.[15] Perhaps it is true that all or most people who are attracted to minors collect child pornography. But that association is nowhere stated or supported in the affidavit. See Gates, 462 U.S. at 238, 103 S.Ct. 2317 (probable cause assessments are to be made from "all the circumstances set forth in the affidavit"); Gourde, 440 F.3d at 1067 ("All data necessary to show probable cause for the issuance of a search warrant must be contained within the four corners of a written affidavit given under oath" (internal marks and citation omitted)). While the district court undoubtedly had the safety of the public in mind, an individual's Fourth Amendment right cannot be vitiated based on fallacious inferences drawn from facts not supported by the affidavit.
Nor is the district court's reasoning saved by the affidavit's general statement, relied upon by the government at oral argument, that "computers are utilized by individuals who exploit children (which includes collectors of child pornography) to... locate, view, download, collect and organize images of child pornography found through the internet."[16] There simply is nothing in this statement indicating that it is more (or less) likely that Falso's computer might contain images of child pornography. That is, the affidavit's sweeping representation that computers are used by those who exploit children to, inter alia, view and download child pornography, would be equally true if 1% or 100% of those who exploit children used computers to do those things.
Furthermore, we agree with Falso that even if his prior conviction were relevant to the analysis, it should have only been marginally relevant because the conviction was stale. This Court has explained that "[t]wo critical factors in determining whether facts supporting a search warrant are stale are `the age of those facts and the nature of the conduct alleged to have violated the law.'" United States v. Ortiz, 143 F.3d 728, 732 (2d Cir.1998) (quoting United States v. Martino, 664 F.2d 860, 867 (2d Cir.1981)). Here, both factors combine to undermine the probity of Falso's prior conviction.
*123 First, the sheer length of time that had elapsed renders Falso's prior sex crime only marginally relevant, if at all. Certainly there are cases where it may be appropriate for a district court to consider a dated sex crime; for example, where there is evidence of ongoing impropriety, because in such cases the prior offense would tend to be less aberrational. See, e.g., United States v. Irving, 452 F.3d 110, 124-25 (2d Cir.2006) (finding no error in the district court's consideration of defendant's twenty-year-old conviction for attempted sexual abuse of a minor when denying defendant's motion to suppress, where there was evidence of two-year-old letters written by defendant discussing the exploitation of children, evidence that he sexually abused boys in Mexico five years earlier, and the statement of a friend that had used his computer to receive child pornography). But no such evidence was provided in this case to bridge the temporal gap between Falso's eighteen-year old sex offense and the suspected child-pornography offense.
Second, although Falso's crime allegedly involved the sexual abuse of a minor,[17] it did not relate to child pornography. Cf. Wagers, 452 F.3d at 537, 541 (finding no error in the district court's reliance on defendant's seven-year-old conviction of possession of child pornography in upholding search warrant directed at same illegal activity). That the law criminalizes both child pornography and the sexual abuse (or endangerment) of children cannot be enough. They are separate offenses and, as explained above, nothing in the affidavit draws a correlation between a person's propensity to commit both types of crimes.[18]


*124 3. Other Factors
Absent any allegation that Falso accessed the cpfreedom.com website, and with little or no weight attaching to his prior conviction, the question remains whether other allegations in the affidavit, considered as a whole, support a finding of probable cause. Generalized allegations about: (1) the propensity of collectors of child pornography to intentionally maintain illegal images; (2) law enforcement's ability to retrieve such images from a computer; and (3) the ability to view child pornography on the cpfreedom.com website, fail to establish the requisite nexus of illegal activity to Falso. Although Falso might hoard images of child pornography if he viewed and downloaded them, there is no allegation in the affidavit that he was in a position, or was otherwise inclined, to do so.

* * *
In the end, the district court's finding of probable cause in Falso's case required it to make at least two significant additional inferential leaps not required in Martin and like cases. First, in Falso's case there is no allegation that he in fact gained access to the cpfreedom.com website, much less that he was a member or subscriber of any child-pornography site. Second, there are no allegations to support an inference that the sole or principal purpose of the cpfreedom.com website was the viewing and sharing of child pornography, much less that images of child pornography were downloadable from the site. Thus, it is only after making the inferences that (1) Falso in fact accessed a website[19] (2) whose principal purpose was the viewing and sharing of child pornography, that the district court could draw the ultimate inference, upheld in Martin, that those who become members of a child-pornography website are likely to collect such images. Putting aside the dangers of Martin's ultimate inference, see Martin, 426 F.3d at 81-83 (Pooler, J., dissenting); Coreas, 419 F.3d at 156-58, the dangers of coupling it with the inferences drawn in Falso's case are exponential.
We are not insensitive to "the need for law enforcement to have a certain amount of latitude in conducting criminal investigations." Martin, 426 F.3d at 76. But, as we explained in Coreas, requiring the government to gather "evidence particularized to the target of the search" before the warrant application is made "will simply focus law enforcement efforts on those who can reasonably be suspected of possessing child pornography." Id. at 158 (emphasis added).[20] If this proves to be a hindrance, it is one the Fourth Amendment demands.
Accordingly, we find no substantial basis for probable cause and reverse the district court's conclusion in this regard.


*125 II. Good-Faith Exception
Our determination that the district court erred in finding probable cause does not end the analysis of whether the evidence seized from Falso's home should be suppressed. In United States v. Leon, the Supreme Court held that the exclusionary rule barring illegally obtained evidence from the courtroom does not apply to evidence seized "in objectively reasonable reliance on" a warrant issued by a detached and neutral magistrate judge, even where the warrant is subsequently deemed invalid. 468 U.S. 897, 922, 104 S.Ct. 3405, 82 L.Ed.2d 677 (1984). The Court reasoned that, "even assuming that the [exclusionary] rule effectively deters some police misconduct and provides incentives for the law enforcement profession as a whole to conduct itself in accord with the Fourth Amendment, it cannot be expected, and should not be applied, to deter objectively reasonable law enforcement activity." Id. at 918-19, 104 S.Ct. 3405.
Consistent with this rationale, there are four circumstances in which the good-faith exception does not apply: "(1) where the issuing [judge] has been knowingly misled; (2) where the issuing [judge] wholly abandoned his or her judicial role; (3) where the application is so lacking in indicia of probable cause as to render reliance upon it unreasonable; and (4) where the warrant is so facially deficient [such as by failing to particularize the place to be searched or the things to be seized] that reliance upon it is unreasonable." United States v. Moore, 968 F.2d 216, 222 (2d Cir.1992) (citing Leon, 468 U.S. at 922-23, 104 S.Ct. 3405); accord United States v. Cancelmo, 64 F.3d 804, 807 (2d Cir.1995). In such circumstances, reliance on the legal judgment of the issuing judge would not be objectively reasonable. See Leon, 468 U.S. at 923, 104 S.Ct. 3405. Here, Falso claims that the good-faith exception does not apply on the first and third of these grounds; specifically, that the district court's finding of probable cause was based on knowingly or recklessly misleading statements in Agent Lyons's affidavit, and the affidavit otherwise was "so lacking in indicia of probable cause" as to render reliance upon it unreasonable. Falso also seeks to avoid application of the good-faith exception on the ground that district court improperly denied a Franks hearing to challenge the veracity of Agent Lyons's affidavit. A majority of this panel disagrees.

A. The District Court Was Not Knowingly or Recklessly Misled
Generally, the way a defendant demonstrates that statements in an affidavit intentionally or recklessly misled a district court is through a Franks hearing. In Franks v. Delaware, 438 U.S. 154, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978), the Supreme Court held that although a presumption of validity attaches to a law enforcement affidavit, in certain circumstances a defendant is entitled to a hearing to test the veracity of the affiant's statements. Id. at 171, 98 S.Ct. 2674. Specifically, the Court held that the Fourth Amendment entitles a defendant to a hearing if he or she makes a "substantial preliminary showing" that a deliberate falsehood or statement made with reckless disregard for the truth was included in the warrant affidavit and the statement was necessary to the judge's finding of probable cause. Id. at 155-56, 170-71, 98 S.Ct. 2674; see also United States v. Salameh, 152 F.3d 88, 113 (2d Cir.1998). To avoid fishing expeditions into affidavits that are otherwise presumed truthful, the Court in Leon held that to mandate an evidentiary hearing:
[T]he challenger's attack must be more than conclusory and must be supported *126 by more than a mere desire to cross-examine. There must be allegations of deliberate falsehood or of reckless disregard for the truth, and those allegations must be accompanied by an offer of proof. They should point out specifically the portion of the warrant affidavit that is claimed to be false; and they should be accompanied by a statement of supporting reasons. Affidavits or sworn or otherwise reliable statements of witnesses should be furnished, or their absence satisfactorily explained. Allegations of negligence or innocent mistake are insufficient.
Id. at 171, 104 S.Ct. 3405.
In this case, the district court denied Falso's request for a Franks hearing because it concluded that there were no false or recklessly misleading statements in the affidavit. We find no error in the district court's denial of a Franks hearing, nor in its conclusion that the statements at issue were not false or misleading.[21]
Falso claims that the following paragraph from Agent Lyons's affidavit was designed to, and did, mislead the district court:
In or about July 2004, Special Agent Todd Gentry reviewed the competed forensic examination of the website hosting www.cpfreedom.com. The forensic examination revealed several hundred possible subscribers along with e-mail addresses and other information. In or about July 2004, subpoenas were served on appropriate ISP's for each e-mail address identified on the www.cpfreedom. com website. In or about September 2004, all subpoena requests were returned to the FBI. Pursuant to a review of the subpoenaed records [from internet service providers], the following subscriber information (among others) was associated with the www.cpfreedom.com website: David J. Falso, 20 Peaceful Drive, Cortland, New York, Yahoo User ID: cousy1731@yahoo.com. Based upon investigation and examination conducted by Special Agent Todd Gentry and others, it appears that a person with [Falso's] e-mail address either gained access or attempted to gain access to the website www.cpfreedom.com Special Agent Gentry's investigation and review of forensic examination revealed the material associated with the www.cpfreedom.com website is hardcore child pornography. (emphases added).
Falso maintains this passage is misleading because it suggests (1) that the FBI's investigation revealed something more than the existence of Falso's e-mail address on the website; and/or (2) that Falso had actually subscribed to the cpfreedom.com website. As an initial matter, we agree that the passage suggests that the FBI's investigation revealed something more than Falso's e-mail address on the *127 site. But the passage is not misleading because the investigation had in fact revealed additional information. In particular, the immediately preceding paragraph in the affidavit explains that an FBI agent, acting in an undercover capacity, signed up for a one-month membership through the cpfreedom.com website and received an email from the CP Freedom Group containing the membership information. Thus, as the district court explained, the FBI's investigation revealed not only that Falso's e-mail address was on the website, but also that the website's administrators communicated with its members through e-mail. If additional information  not mentioned in the affidavit  led the FBI to the qualified conclusion that "it appear[ed]" that Falso either "gained access or attempted to gain access" to the cpfreedom website, it is hard to understand how the district court could have been misled for purposes of the good-faith exception.[22]
We are no more persuaded by Falso's claim that the affidavit misleadingly suggests that he was, in fact, a subscriber to the cpfreedom.com website. The purported confusion arises from Agent Lyons's use of the word "subscriber" in the affidavit to refer to two types of subscribers: those of the cpfreedom.com website and those of internet service providers such as Yahoo. Considered in context, however, one possible  if not most plausible  reading of the final three sentences of the above-quoted passage is the one adopted by the district court: namely, that the "subscriber information" referred to is for Yahoo, not the cpfreedom.com website.[23] Even if there were any suggestion (intentional or otherwise) in the passage quoted above that Falso was in fact a subscriber to the cpfreedom.com website, it was qualified (if not clarified) in the penultimate sentence, which states that "it appears" Falso either "gained access or attempted to gain access" to the site.
In addition to the foregoing alleged misstatements, Falso argues that the affidavit contained material omissions. Specifically, Falso claims that because the government did not disclose incriminating evidence to the contrary, "it is reasonable to assume" that: (1) the government identified all subscribers and that Falso was not one; (2) the government determined that Falso had not contacted the website; and (3) Falso's e-mail address was found in a computer file indicative of spam. Falso, however, has made no offer of proof that the allegedly omitted "facts" exist. See Franks, 438 U.S. at 171, 98 S.Ct. 2674 (stating that defendant seeking a Franks hearing must support his allegations with an "offer of proof" and lodge an attack that is "more *128 than a mere desire to cross-examine"). It is for this reason that United States v. Reilly, 76 F.3d 1271 (2d Cir.1996), upon which Falso relies, is distinguishable. In Reilly, this Court held that the good-faith exception did not apply where the affiant knew certain facts that would undermine probable cause yet failed to provide these facts to the magistrate judge. Id. at 1280 ("For the good faith exception to apply, the police must reasonably believe that the warrant was based on a valid application of the law to the known facts. In the instant matter, the officers failed to give these facts to the magistrate [judge]."). By contrast, here there is no evidence  just conjecture  that the government failed to disclose additional information in its possession that might tend to exculpate Falso or otherwise negate the existence of probable cause.
Moreover, even assuming that any of the statements in the affidavit misled the district court, Falso has not met his burden of demonstrating that Agent Lyons made the alleged misrepresentations and that he omitted material information knowingly or recklessly. We thus reject Falso's challenge to the good-faith exception on the ground that he has failed to make even a preliminary showing that the district court was knowingly or recklessly misled by any statements or omissions in Agent Lyons's affidavit.

B. The Affidavit Was Not "So Lacking in Indicia of Probable Cause"
Falso's alternative claim, that the affidavit was "so lacking in indicia of probable cause as to render reliance upon it unreasonable,"[24]see Moore, 968 F.2d at 222, fares no better. Once the district court ruled on the legal sufficiency of the facts alleged in the affidavit, the officers were justified in executing the warrant. Cancelmo, 64 F.3d at 809 ("[W]e decline to hold that the agents acted unreasonably in accepting the magistrate judge's legal conclusion that probable cause existed.").
Even if there may have been an innocent explanation for the presence of Falso's e-mail address on the cpfreedom.com website, that does not undermine the officers' good-faith reliance on the warrant. As this Court explained in Fama: "The fact that an innocent explanation may be consistent with the facts alleged ... does not negate probable cause. Neither should it preclude a good faith belief in probable cause." 758 F.2d at 838 (citations omitted).
Moreover, although a majority on this panel finds that probable cause was lacking, see supra Part I, that is certainly an issue upon which reasonable minds can differ, as reflected by the different approaches to the probable cause issue reflected here[25] as well as the split of opinions among the panel members in Martin and Coreas. See Leon, 468 U.S. at 926, 104 S.Ct. 3405 (applying good-faith exception where the affidavit "provided evidence sufficient to create disagreement among thoughtful and competent judges as to the existence of probable cause"); accord Fama, 758 F.2d at 838 (applying good-faith exception where state of law was *129 unclear); United States v. Smith, 9 F.3d 1007, 1015 (2d Cir.1993) (same).
In short, the error in this case, as found by a majority of the panel, was committed by the district court in issuing the warrant, not by the officers who executed it. See Cancelmo, 64 F.3d at 807. Accordingly, we uphold the district court's application of the good-faith exception to deny Falso's suppression motion.

CONCLUSION
For the foregoing reasons, we hold that the district court's finding of probable cause was not supported by a substantial basis. However, because the district court properly applied the good-faith exception in denying Falso's suppression motion, and for the additional reasons discussed in our accompanying summary order, we AFFIRM the judgment.
LIVINGSTON, Circuit Judge, concurring in part and concurring in the judgment:
I concur in the judgment and join in Part II, which determines both that the affidavit here was not so lacking in indicia of probable cause as to make reliance upon it unreasonable and that there is no basis in the record for concluding that Agent Lyons knowingly or recklessly misled the district court by omitting or misstating information in his search warrant affidavit. I agree fully with Part II's conclusion that the officers acted in "objectively reasonable" reliance on the search warrant, thus rendering the exclusionary rule inapplicable. See United States v. Leon, 468 U.S. 897, 922, 104 S.Ct. 3405, 82 L.Ed.2d 677 (1984). As to Part I, however, I do not join in my colleagues' determination that there was no substantial basis for the district court's finding of probable cause. In my view, this is not a question that need be decided, given that the good faith determination is dispositive. The majority's analysis of the issue, moreover, is troublesome in several respects.
The majority characterizes the "threshold issue" in this case to be whether there was a substantial basis for the district court's finding of probable cause based on two factors alone: (1) that the search warrant affidavit alleged that Falso "`appeared' to `have gained or attempted to gain'" access to a website, cpfreedom.com, that distributed child pornography; and (2) that he was convicted of a misdemeanor eighteen years ago in connection with the sexual abuse of a seven-year-old girl. Concluding that the search warrant affidavit failed to allege that Falso in fact accessed the website at issue, the majority poses the ultimate question to be whether Falso's prior conviction alone "provide[d] a sufficient basis to believe that evidence of child pornography crimes would be found in Falso's home." Op. at 113. The majority not surprisingly answers this question in the negative. With respect, however, I believe the majority sidesteps discussion of the actual facts alleged in the affidavit and thus mischaracterizes both the threshold and ultimate issues involved. In so doing, the majority fails to read the affidavit in its totality and in the commonsense manner the Supreme Court prescribes. See Illinois v. Gates, 462 U.S. 213, 231-32, 103 S.Ct. 2317, 76 L.Ed.2d 527 (1983).
The investigation in this case began when FBI agents obtained the IP address of the website cpfreedom.com, which contained approximately eleven images of child pornography. The website advertised additional child pornography that was available upon purchase of a membership. An undercover FBI agent signed up for a one-month membership for $99 and subsequently received an email that provided him with the Internet address of the *130 restricted site, a user name, and a password. Forensic examination of the website hosting cpfreedom.com revealed "several hundred possible subscribers along with e-mail addresses and other information." This examination further revealed "that the material associated with the www.cpfreedom.com website is hardcore child pornography."
According to the search warrant affidavit, "subpoenas were served on appropriate [Internet service providers] for each e-mail address identified on the www. cpfreedom.com website." One of these email addresses, cousy1731@yahoo.com, belonged to Falso, who maintained an active Yahoo! account during the time period relevant to the investigation. Records obtained from Time Warner Cable established the likelihood that Falso maintained a computer at his residence, since Road Runner Internet service had been established there.
Additional investigation revealed that Falso was arrested in 1987 for sexually abusing a seven-year-old girl. Significantly, the victim informed the New York State Police that she referred to the appellant, David J. Falso, as "Cousey." The affidavit also alleged that Falso admitted to the police at the time of his arrest that he "may have latent problems and that he might require some type of counseling." Falso eventually pled guilty to a misdemeanor in state court.
The search of Falso's home pursuant to warrant uncovered over 600 printed-out images of child pornography, many bearing website information in the bottom margins. At least 50 of these images depicted pre-pubescent children engaging in explicit sexual poses and sexual conduct, including intercourse with adults. Falso's computer contained numerous additional images of child pornography, along with videotaped scenes depicting very young children engaged in sexual acts.[1] Inside a box in Falso's bedroom, law enforcement agents found at least eight photographs constituting child pornography, one of which depicted a girl performing a sex act on Falso. During the search, Falso made statements admitting that he had intentionally sought out and obtained child pornography from the Internet and that he had belonged to a site where he obtained child pornography for a fee for about a month. He also stated that he is attracted to young girls and that he traveled to Thailand and other countries to have sex with minors.
The majority errs in two principal ways in reading the search warrant affidavit. First, focusing solely on what it terms the affidavit's "inconclusive" allegation, Op. 121, that "a person with the e-mail address of cousy1731@yahoo.com either gained access or attempted to gain access to the website www.cpfreedom.com," the majority ignores the underlying facts that support this allegation  namely, that Falso's email address, in addition to the email addresses of several hundred others, was found on the site, and that the website used email to correspond with its members. The dissent makes a similar mistake  disregarding the presence of Falso's email address on the website to affirm, erroneously, that Lyons's affidavit "establishes no more than that Falso ... clicked on a website containing child pornography, and may have attempted to view it." Dissent Op. 136.
With respect, a person's email address does not appear on a website because that person has "clicked" on it any more than his mailing address becomes known to the library simply because he's walked in and browsed the stacks. Falso admits as much *131 in his brief before this Court, acknowledging that an individual does not provide his email address to a website simply by visiting it.
Admittedly, Lyons's affidavit is not a model of careful drafting. At oral argument the government revealed that it had failed to include information in the affidavit that would have made the substantial-basis determination easier: specifically, that Falso's email address (along with those of the other individuals) appeared with a corresponding username and password of the type the undercover FBI agent received when he purchased a membership. Nevertheless, the fact that Falso's email address was found on a website containing eleven free images of hardcore child pornography and offering more, for a fee, is probative evidence that Falso visited that website and either signed up or attempted to sign up for a membership. Granted, this evidence is not conclusive. Falso argues that his email could have been on the cpfreedom.com site because "the website intended to send [him] an unsolicited e-mail known as `spam,'" or because it was otherwise taken from a marketing list. As we have repeatedly said, however, "[t]he fact that an innocent explanation may be consistent with the facts alleged ... does not negate probable cause" or the significance of evidence tending to establish it. Panetta v. Crowley, 460 F.3d 388, 395 (2d Cir.2006) (quoting United States v. Fama, 758 F.2d 834, 838 (2d Cir.1985)). And "evidence that a person has visited or subscribed to websites containing child pornography supports the conclusion that he has likely downloaded, kept, and otherwise possessed the material." United States v. Wagers, 452 F.3d 534, 540 (6th Cir.2006).
The majority similarly errs in taking the district court to task for giving weight to Falso's prior conviction. The majority chides the district court for its "fallacious inference," supposedly nowhere supported in the affidavit, that people who sexually abuse children are more likely than others in the general population to collect child pornography. Op. 122-23. The affidavit clearly states, however, that "individuals who exploit children" use computers to "locate, view, download, collect and organize images of child pornography found through the Internet." Moreover, the district court's inference of a connection is one that we, too  citing a congressional finding  have in the past seen fit to draw. See United States v. Brand, 467 F.3d 179, 198 (2d Cir.2006) (noting that "possession of child pornography ... shares a connection... with pedophilia," and endorsing Congress's finding that "child pornography is often used by pedophiles and child sexual abusers to stimulate and whet their own sexual appetites, and as a model for sexual acting out with children" (quoting Pub.L. No. 104-208, § 121, 110 Stat. 3009, 3009-26 (1996))).[2] Our sister Circuits have acted *132 similarly. See, e.g., United States v. Lebovitz, 401 F.3d 1263, 1271 (11th Cir. 2005) ("Law enforcement investigations have verified that pedophiles almost always collect child pornography or child erotica." (emphasis added) (quoting S.Rep. No. 104-358, 104th Cong., 2d Sess., at 12-13 (1996))); United States v. Byrd, 31 F.3d 1329, 1339 (5th Cir.1994) ("[C]ommon sense would indicate that a person who is sexually interested in children is likely to also be inclined, i.e., predisposed, to order and receive child pornography."); see also Osborne v. Ohio, 495 U.S. 103, 111, 110 S.Ct. 1691, 109 L.Ed.2d 98 (1990) (observing that "evidence suggests that pedophiles use child pornography to seduce other children into sexual activity" (emphasis added)).
It does make a difference that Falso's conviction occurred eighteen years earlier, though perhaps less of a difference than the majority makes out. The Supreme Court has noted empirical research on child molestation that suggests that most reoffending after a prison sentence does not occur within the first several years, but may occur as long as twenty years following release. Smith v. Doe, 538 U.S. 84, 104, 123 S.Ct. 1140, 155 L.Ed.2d 164 (2003). This Court, moreover, has noted that the staleness inquiry in child pornography cases is unique, due to the tendency of persons interested in such material to hoard it, see United States v. Irving, 452 F.3d 110, 125 (2d Cir.2006), a fact clearly referenced in the search warrant affidavit in this case. Given the evidence we cited in Brand that child pornography is often used by pedophiles and child sexual abusers to stimulate themselves and to entice young victims, see Brand, 467 F.3d at 198, "a person of reasonable caution would take into account predilections revealed by past crimes or convictions as part of the inquiry into probable cause." Wagers, 452 F.3d at 541 (internal quotation marks omitted). Because the issue is complex and unnecessary to the resolution of this case, I would not opine, as the majority freely does, that the lapse of time since Falso's conviction rendered it "marginally relevant, if at all." Op. 123.
In sum, I concur in the judgment and join in Part II. As to Part I, this Court has said that even when the probable cause question is close, "we need not resolve the issue [if] we conclude that the good faith exception applies." United States v. Cancelmo, 64 F.3d 804, 807 (2d Cir.1995). I fear the majority's analysis is more likely to cloud than clarify understanding of Fourth Amendment issues in the difficult and rapidly evolving context of Internet searches. Finding it unnecessary to reach the issues addressed by the majority in Part I, I respectfully decline to do so.
DENNIS JACOBS, Chief Judge, dissenting:
I subscribe to Part I of the majority opinion, which holds that Agent Lyons' affidavit failed to establish a substantial basis for probable cause. As to Part II, however, I conclude that the affidavit was recklessly misleading (at best), and that Agent Lyons  because he was both the affiant and the executing officer  could not rely in good faith on the imprimatur of the district judge. Accordingly, I would reverse the denial of the motion to suppress, vacate Falso's conviction, and remand for further proceedings.
Judge Sotomayor's majority opinion says why the affidavit, taken at face value, was insufficient to confer probable cause; and as to that I agree. But in my view the affiant tried to paper over the insufficiency with a statement that is crucial and that is *133 misleading. Therefore, though I agree with Judge Sotomayor that the warrant was signed in error and that an arresting officer may ordinarily rely on such a warrant, I conclude that Agent Lyons, as the affiant of the misleading affidavit could not rely in good faith on the judge's imprimatur. I draw principles from Franks v. Delaware, 438 U.S. 154, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978), to arrive at the conclusion that the arresting officer cannot rely on a warrant obtained by his own misleading affidavit.

[A]
Agent Lyons' affidavit sets forth the following salient facts:
[1] The website contained eleven images of child pornography with more images available to persons who joined as members;
[2] New members received an e-mail upon joining;
[3] There were several hundred possible members;
[4] Most collectors of child pornography retain digital images online and seek out like-minded individuals on the internet;
[5] Most such collectors are also sexually attracted to children;
[6] Falso's name, address, and e-mail address were associated with the website;
[7] It appears that someone with Falso's e-mail address either gained access to the website, or attempted to do so;
[8] Eighteen years earlier, Falso was convicted for conduct involving sexual abuse of a minor.
The majority of these facts ([1] through [5]) are not specific to Falso, or anyone else. As to [5], the affidavit provided evidence that Falso was sexually attracted to children, but the fact of attraction (of any sexual kind) does not make it more or less likely that a person collects pornography (as the majority opinion explains). As to [4], the observation that collectors of child pornography tend to retain their collections online (and seek out like-minded individuals), puts it backwards: "The alleged `proclivities' of collectors of child pornography... are only relevant if there is probable cause to believe that [defendant] is such a collector." United States v. Coreas, 419 F.3d 151, 156 (2d Cir.2005). Thus, the affidavit's generic assertions "added fat... but certainly no muscle" to this otherwise "`bare bones' affidavit." United States v. Weber, 923 F.2d 1338, 1346 (9th Cir.1990) (quoting United States v. Leon, 468 U.S. 897, 926, 104 S.Ct. 3430, 82 L.Ed.2d 677 (1984)).
At most, items [1] through [5] might have established probable cause if conjoined with evidence that Falso collected child pornography. But this is precisely where the affidavit is fatally deficient: it fails to allege the requisite substantial "nexus" between Falso and the website. See United States v. Martin, 426 F.3d 68, 75 (2d Cir.2005). Martin rooted the illegality of possessing child pornography in the "trading" of such material on a website, see Majority Op., supra p. 119 (quoting Martin, 426 F.3d at 75-76), which shows dominion. (This is consistent with the approach of some other circuits.[1]) But *134 Facts [6] through [8] show only that Falso, a pedophile, appeared to have accessed  or appeared to have tried to access  the website, and that his e-mail address was somewhere on it. No evidence suggested that Falso downloaded any image or took any other active steps with respect to the illicit material. Because there was no probable cause to believe that Falso did anything with images of child pornography, the government lacked probable cause to believe that he committed a crime. Therefore, Agent Lyons had need to create the impression that more was known than was known in fact.

[B]
The Fourth Amendment entitles a criminal defendant to a hearing if he or she makes a "substantial preliminary showing" that a "deliberate falsehood" or a statement made with "reckless disregard for the truth" was included in the warrant affidavit, and the statement was "necessary to the judge's probable cause finding." United States v. Salameh, 152 F.3d 88, 113 (2d Cir.1998) (per curiam)(internal cites omitted); see Majority Op., supra pp. 125-26 (applying this standard). In Franks v. Delaware, the Supreme Court explained that "[t]here must be allegations of deliberate falsehood or of reckless disregard for the truth." 438 U.S. 154, 171, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978) (emphasis added). Thus, recklessly misleading statements suffice for Franks purposes. Moreover, "`Franks protects against omissions that are designed to mislead, or that are made in reckless disregard of whether they would mislead, the magistrate.'" United States v. Awadallah, 349 F.3d 42, 68 (2d Cir.2003) (emphasis added; other emphasis in original omitted) (quoting United States v. Colkley, 899 F.2d 297, 300-01 (4th Cir.1990)); see also United States v. Levasseur, 816 F.2d 37, 43 (2d Cir.1987) ("[M]aterially misleading omissions as well as misrepresentations may be challenged by the defense."). Importantly, "[r]ecklessness may be inferred where the omitted information was clearly critical to the probable cause determination." Rivera v. United States, 928 F.2d 592, 604 (2d Cir.1991) (internal quotation marks omitted).
Agent Lyons' affidavit contained a recklessly misleading (if not outright deliberately false) statement. Paragraph 31 makes very slippery use of the critical word "subscriber":
In or about July 2004, Special Agent Todd Gentry reviewed the completed forensic examination of the website hosting www.[]cpfreedom[].com. The forensic examination revealed several hundred possible subscribers along with e-mail addresses and other information. In or about July 2004, subpoenas were served on appropriate ISP's for each e-mail address identified on the www.[]cpfreedom[].com website. In or about September 2004, all subpoena requests were returned to the FBI. Pursuant to a review of the subpoenaed records, the following subscriber information (among others) was associated with the www.[]cpfreedom[].com website: David J. Falso, 20 Peaceful Drive, *135 Cortland, New York, Yahoo User ID: cousy1731@yahoo.[]com.[2]
Affidavit of James T. Lyons ¶ 31 (emphasis added). The natural reading of these words and the logical inference is that Falso was a subscriber to the illicit website. This misimpression was created by repetition of the word "subscriber" to reference two distinct groups: members of the illicit website ("several hundred possible subscribers") and members of Yahoo! ("subscriber information"). That misimpression was set up in the pages immediately preceding this paragraph: Agent Lyons consistently designates Yahoo! members as "users"  at least five times, not once calling them "subscribers". See id. ¶ 27.
The majority says that, "[c]onsidered in context ... one possible  if not most plausible" way to construe this paragraph is that the "subscriber information" referred to in the last sentence of the quoted passage refers to Yahoo! members, not members of the website. Majority Op., supra p. 127. Maybe so. But, so read, the word "subscriber" would mean two different things within three sentences: the "several hundred possible subscribers" referred to in the first sentence means possible members of the illicit website; the "subscriber information" "associated with" that website (from the third sentence) means Yahoo! members. The majority opinion blandly recites that "Agent Lyons's affidavit alleged only that Falso was perhaps one of several hundred possible subscribers to the cpfreedom[].com website." Majority Op., supra p. 120 (emphasis added). But the caveat "possible" is dropped two sentences later: so even an attentive reader of the whole passage gets the impression that Falso's membership was a fact known to the affiant.
The repetition of the word "subscriber" to reference two types of membership in close textual proximity was consequential: whether a suspect is a member of a child pornography website is important to the probable cause inquiry. See Rivera, 928 F.2d at 604 ("Recklessness may be inferred where the omitted information was clearly critical to the probable cause determination." (internal quotation marks omitted)).
Judge Livingston considers that "." Concurring Op. of Livingston, J., supra p. 131. I respectfully disagree: the misleading effect is achieved by artifice that carefully confuses a very important question of fact.
The district court maintained that it was not actually misled; but that is neither here nor there. The test for whether an affidavit contains recklessly misleading or false statements is an objective one. We ask whether a false or misleading statement "was included by the affiant in the warrant affidavit," not whether the issuing magistrate or district court was misled by it. Franks, 438 U.S. at 155-56, 98 S.Ct. 2674 (emphasis added). Surely, if a district court granted a suppression motion on the ground that the judge had been misled by an affidavit that we judged to be fair, we would not hesitate to reverse.
As the government conceded at oral argument, our review is necessarily confined to the affidavit's four corners. (We must therefore disregard any litigation backfill, such as the government's extra-record statement at oral argument, cited by Judge Livingston, that Falso's e-mail address appeared with a corresponding password *136 and username of the type the undercover FBI agent received when he became a member.) Once we excise the misleading statement, see Salameh, 152 F.3d at 113, Lyons' affidavit establishes no more than that Falso, an individual with a misdemeanor conviction for conduct involving sexual abuse of a minor from eighteen years earlier, clicked on a website containing child pornography, and may have attempted to view it. Assessed in light of "all the circumstances set forth in the affidavit," Illinois v. Gates, 462 U.S. 213, 238, 103 S.Ct. 2317, 76 L.Ed.2d 527 (1983), these three facts blatantly fail the test of probable cause.

[C]
"If a reviewing court determines that a search warrant was not supported by probable cause, a motion to suppress will still be denied if the court finds that the officers who conducted the search acted in good faith reliance on a facially valid warrant." Id. at 114.
Agent Lyons was both the affiant and the executing officer. Accordingly, it is perhaps "somewhat disingenuous, after having gone to the [district judge] with the paltry showing seen here, to suggest, as the government suggests, that at bottom it was the [judge] who made the error and the search and seizure are insulated because the officer's reliance on that error was objectively reasonable." United States v. Zimmerman, 277 F.3d 426, 438 (3d Cir.2002).
As the Supreme Court instructs, "suppression is appropriate ... if the officers were dishonest or reckless in preparing their affidavit." United States v. Leon, 468 U.S. 897, 926, 104 S.Ct. 3405, 82 L.Ed.2d 677 (1984). This comports with the purposes of the exclusionary rule: it is designed to "deter[ ] some police misconduct and provide[ ] incentives for the law enforcement profession as a whole to conduct itself in accord with the Fourth Amendment." Id. at 918-19, 104 S.Ct. 3405. Consequently, the good-faith exception applies only when evidence is seized "in objectively reasonable reliance on" a warrant issued by a detached and neutral judge. Id. at 922, 104 S.Ct. 3405.
The majority says that "the error in this case was committed by the district court in issuing the warrant, not by the officers who executed it." Majority Op., supra p. 129. I respectfully disagree. Normally, the judge's imprimatur assures the executing officer that there is probable cause. But where, as here, the executing officer is the same officer who misled the judge, the good-faith exception to the exclusionary rule cannot apply. See, e.g., United States v. Alexander, 740 F.Supp. 437, 448 (N.D.Ohio 1990) (ruling that a fraudulent and "deliberately incomplete" affidavit precluded officer's reliance on Leon); United States v. Boyce, 601 F.Supp. 947, 954 (D.Minn.1985) (denying good faith defense for an affiant who had, at best, recklessly disregarded the truth by "creat[ing] unmistakable false impressions").
An executing officer can hardly claim good-faith reliance on a warrant issued by a judge who was mis-directed by the officer himself: the same principle explains why, at a magic show, the credulity of the audience does not cause the magician to fear that the lady has been sawn in half.
NOTES
[1]  In this opinion we address only Falso's challenges to the district court's denial of his motion to suppress physical evidence seized from his home pursuant to the search warrant. We address and reject Falso's remaining claims in a companion summary order.
[2]  Sometimes we have eschewed analyzing probable cause when we rely on the good faith exception, see, e.g., United States v. Jasorka, 153 F.3d 58, 60-61 (2d Cir.1998), but here we elect to decide both issues, Leon, 468 U.S. at 925, 104 S.Ct. 3405 ("[N]othing will prevent reviewing courts from deciding the [Fourth Amendment] question before turning to the good-faith issue.").
[3]  In actuality, the conviction records introduced in connection with the pretrial motions clarify that Falso pled guilty to the misdemeanor of Endangering the Welfare of a Child under New York Penal Law § 260.10-1 by knowingly acting in a manner likely to be injurious to the physical, mental or moral welfare of a child under the age of seventeen. The district court took notice of this fact when adjudicating Falso's suppression motion.
[4]  See Franks v. Delaware, 438 U.S. 154, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978) (holding that, under certain limited circumstances, a defendant is entitled under the Fourth Amendment to attack collaterally the veracity of a warrant affidavit in the context of challenging the existence of probable cause).
[5]  The district court identified the following similarities among the search warrants: (1) generalized information about the use of computers by those who collect child pornography; (2) the general characteristics and proclivities of child pornography collectors; (3) the illicit purposes of the websites at issue in each case to share and view child pornography; and (4) the nexus between the defendants and the respective websites.
[6]  Many of the cases discussed herein involve or refer to probable cause determinations made by magistrate judges. In Falso's case, the probable cause determination was made by the district judge, who both issued the warrant and denied Falso's subsequent suppression motion. The law draws no distinction, of which we are aware, between a magistrate judge's and district judge's duties in making probable cause determinations.
[7]  The girls 12-16 webpage contained the following welcome message:

Hi all, This group is for all those ho [sic] appreciate the young female in here [sic] finest form. Watching her develop and grow is like poetry in motion [sic], to an age where she takes an interest in the joys and pleasures of sex. There is probably nothing more stimulating than watching a young teen girl discover the pleasures of the orgasm. The joy of feeling like she is actually coming into womanhood. It's an age where they have no preconditions about anything, just pure opennes [sic]. What a joy to be a part of that wonderful experience and to watch the development of this perfect form. This is the place to be if you love 11 to 16 yr olds. You can share experiences with others, share your views and opinions quite freely without censorship. You can share all kinds of other information as well regarding-your [sic] current model: if you are a photographer. Where the best place to meet gitls [sic] is. The difficulties you experience in your quest. The best way to chat up. Good places to pick girls up. Girls you would like to share with others. The choice is all yours. Welcome home! Post videos and photographs... and how about your true life experiences with them so that other viewers can paint a mental picture andin [sic] some ways share the experience with you. You could connect with others from the same country as you and get together sociall [sic] if you wish. The choice is all yours. How about a model resource for photographers? It's all up to you and is only limited by your own imaginations. Membership is open to anyone, but you will need to post something. Mybe [sic] a little bit about yourself/what your interests are (specifically), your age, location ... and a pic or vid would be a good to [sic]. By doing this other members (or potential members) with the same interest may then contact you if you wish them to.
Martin, 426 F.3d at 71.
[8]  The original affidavit contained the false statement that all members of the website "automatically" received e-mails and images of child pornography posted to the site. In fact, however, members had the optionwith the click of a buttonto receive or not receive these postings. Id. at 70-71; see also Coreas, 419 F.3d at 154 (noting that a later investigation revealed that 85% of the e-group members elected not to receive any automatic e-mails).
[9]  The Candyman e-group, at issue in Coreas, contained the following welcome message:

This group is for People who love kids. You can post any type of messages you like too [sic] or any type of pics or vids you like too [sic]. P.S. IF WE ALL WORK TOGETHER WE WILL HAVE THE BEST GROUP ON THE NET. Id., 419 F.3d at 152. The Coreas panel explained that "the Martin majority regarded the differences between the [girls 12-16 and Candyman] websites as immaterial and regarded the Candyman welcome message as explicit enough to warrant an inference of unlawful purpose." Coreas, 419 F.3d at 157 (citing Martin, 426 F.3d at 73 n. 4).
[10]  After rehearing was denied by the panels in Martin and Coreas, this Court denied a consolidated petition for rehearing en banc. See United States v. Martin, 430 F.3d 73 (2d Cir.2005). In his concurring opinion denying en banc review, Judge Wesley stressed that the welcome message on the e-group at issue in Martin made plain the illegal purposes of the site, and that the defendant enlisted and remained on the group's membership rolls for two weeks until it was shut down by the FBI. Id. at 74. Thus, and in response to Judge Pooler's concerns, he stated that "this case is not about a `passing curiosity,' mere `guilt by association' or `search[ing] the homes of innocent individuals.'" Id. at 75 (quoting Judge Pooler's dissent). In dissent, Judge Pooler "urge[d] the defense attorneys in these cases to seek certiorari." Id. at 77. Defense counsel did so, and the Supreme Court denied their requests. Martin v. United States, 547 U.S. 1192, 126 S.Ct. 2861, 165 L.Ed.2d 895 (2006); Coreas v. United States, 547 U.S. 1192, 126 S.Ct. 2861, 165 L.Ed.2d 895 (2006).
[11]  Wagers may provide the only exception with respect to the principle-purpose prong. There, the defendant was a paying subscriber to websites that provided illegal images of child pornography. But the affidavits supporting the warrants at issue were "silent on whether these sites also included legal pornography," 452 F.3d at 543, and there was no finding that the websites' principal purpose was the viewing and/or sharing of child pornography.
[12]  Again, by this we mean a website whose principal purpose is to view and share child pornography.
[13]  In Martin, we left open the issue of whether merely "viewing" child pornography via the internet is a crime. 426 F.3d at 77. There is, yet again, no need to decide the issue here.
[14]  In Martin, Judge Pooler criticized the majority's inference that because collectors of child pornography are likely to be subscribers of e-groups, that the inverse also is true: namely, that subscribers are likely to collect child pornography. Id. at 82.
[15]  By analogy, it may be said that "most people who sell drugs do drugs." That is not to say, however, that "most people who do drugs sell drugs."
[16]  The district court itself does not appear to have relied on this passage; correctly so, for the reasons explained in the text.
[17]  Falso pled guilty to the offense of Endangering the Welfare of a Child, which criminalizes acts that do not necessarily involve sexual contact with minors. The police report and information, however, allege that Falso digitally penetrated a young girl.
[18]  Our decision in United States v. Brand, 467 F.3d 179, 198 (2d Cir.2006), is not to the contrary. In Brand, we affirmed the district court's evidentiary ruling permitting the government, in its prosecution of a defendant for traveling in interstate commerce for the purpose of engaging in illicit sexual contact with a minor, to present the jury with images of child pornography found on the defendant's computer. We explained that the defendant's collection of child pornography indicated an "abnormal sexual attraction to children," and thus was relevant to the offense for which the defendant stood trial, which involved the same abnormalcy. See id. at 198 ("The `similarity or some connection' requirement [for purposes of establishing relevance under the Federal Rules of Evidence] is satisfied in the instant case because a direct connection exists between child pornography and pedophilia."). We drew our conclusion, in part, from the Child Pornography Prevention Act of 1996, in which "Congress found that `child pornography is often used by pedophiles and child sexual abusers to stimulate and whet their own sexual appetites, and as a model for sexual acting out with children,'" id. at 198 (quoting Pub.L. No. 104-208, § 121, 110 Stat. 3009, 3009-26 (1996)), and from congressional testimony of the FBI, which noted "`a strong correlation between child pornography offenders and molesters of children' and that the `correlation between collection of child pornography and actual child abuse is too real and too grave to ignore,'" id. at 198 n. 17 (quoting Enhancing Child Protection Laws After the April 16, 2002 Supreme Court Decision, Ashcroft v. Free Speech Coalition: Hearing Before the Subcomm. on Crime, Terrorism, and Homeland Security of the H. Comm. on the Judiciary, 107th Cong. (2002) (statement of Michael J. Heimbach, Crimes Against Children Unit, Criminal Investigative Division, FBI)). It is worthy of observation, however, that the correlation in Brand that the government relied upon was that the defendant, a known collector of child pornography, was predisposed or intended to commit the charged offense involving an intended sexual act against a minor. That is precisely the inverse of the correlation relied upon by the district court in Falso's case: that a person convicted of a crime involving the sexual abuse of a minor would likely collect child pornography. But, as explained above, the latter correlation is not supported by the affidavit itself and thus cannot support a probable-cause finding. Moreover, the test of whether evidence is "relevant" for purposes of admission under the rules of evidence is a more flexible standard than whether evidence of a past crime gives rise to an inference of probable cause that a different crime has been committed. Cf. Brand, 467 F.3d at 197 (discussing relevancy standard).
[19]  The Falso may have attempted, but failed, to gain access to the cpfreedom.com site requires a separate, but related, inference: that Falso nevertheless obtained child pornography from other unidentified sources.
[20]  As we admonished in Coreas, the "[g]overnment could easily have obtained more information" about Falso. See Coreas, 419 F.3d at 158. Among other things, it could have monitored the traffic of the cpfreedom.com website and ascertained whether Falso (and others) actually downloaded pornography from the site. See id.
[21]  In United States v. One Parcel of Property Located at 15 Black Ledge, 897 F.2d 97 (2d Cir.1990), we reviewed the denial of a Franks hearing in a forfeiture case for clear error to the extent that denial rested on factual findings. Id. at 100. We did not explain why that was the appropriate standard, however, and we note the existence of a circuit court split on the issue. Compare United States. v. Reiner, 500 F.3d 10, 14 (1st Cir.2007) (reviewing denial of Franks hearing for clear error); United States v. Stewart, 306 F.3d 295, 304 (6th Cir.2002) (same); United States v. Buchanan, 985 F.2d 1372, 1378 (8th Cir.1993) (same); United States v. Skinner, 972 F.2d 171, 177 (7th Cir.1992) (same), with United States v. Gonzalez, Inc., 412 F.3d 1102, 1110 (9th Cir.2005) (applying de novo standard); United States v. Martin, 332 F.3d 827, 833 (5th Cir.2003) (same). To the extent the issue remains open in our circuit, we need not decide whether the clear error or de novo standard applies because, under either standard, we find no error in the district court's denial of a Franks hearing.
[22]  At oral argument, the government revealed additional information that was not reflected in the affidavit: namely, that Falso's e-mail address on the site appeared with a password and username associated with it. Although the government's revelation at oral argument cannot support its probable cause claim, cf. Whiteley v. Warden, Wyo. State Penitentiary, 401 U.S. 560, 565 n. 8, 91 S.Ct. 1031, 28 L.Ed.2d 306 (1971) ("[A]n otherwise insufficient affidavit cannot be rehabilitated by testimony concerning information possessed by the affiant when he sought the warrant but not disclosed to the issuing magistrate [judge]."), it does tend to support the officers' good-faith reliance on the warrant.
[23]  That the district court reasonably read the term "subscriber" as referring to a Yahoo subscriber is supported by an earlier portion of the affidavit describing the use of computers by persons who collect child pornography. In that section, Agent Lyons notes that collectors of child pornography use services offered by companies, "such as Yahoo!," which include online storage accounts. It then states that a "subscriber assigned to a free online storage account" can set one up with little identifying information, and goes on to use the term "subscriber" or "subscribing" seven more times, in each case clearly referring to Yahoo or similar Internet services.
[24]  This is a very difficult threshold to meet, as evidenced by the many decisions of this Court rejecting objections to the good-faith exception on this basis. See, e.g., United States v. Jasorka, 153 F.3d 58, 60-61 (2d Cir.1998); United States v. Cancelmo, 64 F.3d 804, 807-08 (2d Cir.1995); Moore, 968 F.2d at 222-23 (2d Cir.1992); United States v. Fama, 758 F.2d 834, 837-38 (2d Cir.1985).
[25]  As noted in her opinion concurring in the judgment and in Part II, Judge Livingston would not reach the question whether probable cause was present here.
[1]  At least four of the children who suffered the depicted abuse have been identified.
[2]  The majority dismisses Brand as inapposite because the correlation on which the government relied in that case  that collectors of child pornography are more likely to abuse children, see Brand, 467 F.3d at 197-99 (permitting use of defendant's possession of child pornography to prove defendant's intent to abuse a minor)  is the inverse of the one on which the government relied here  that those who abuse children are more likely to collect child pornography. Slip Op. 123-24 n. 18. Regardless of whether the facts of Brand are analogous to the facts of this case, what matters here is that we cited with approval the congressional finding that "child pornography is often used by pedophiles and child sexual abusers to stimulate and whet their own sexual appetites." Id. at 198 (emphasis added) (quoting Pub.L. No. 104-208, § 121, 110 Stat. 3009, 3009-26 (1996)). Such a finding indicates that pedophiles and child sexual abusers are more likely than others in the general population to possess child pornography  precisely the reasoning relied on by the district court to give weight to the prior conviction in its probable cause calculus.
[1]  See, e.g., United States v. Romm, 455 F.3d 990, 998-1001 (9th Cir.2006) (upholding conviction for receipt and possession of child pornography recovered from defendant's computer cache where defendant acknowledged viewing, "saving" and "downloading" the illicit images); United States v. Stulock, 308 F.3d 922, 925 (8th Cir.2002) (noting the district court's acquittal of defendant of possession charges on the ground that "one cannot be guilty of possession for simply having viewed an image on a web site, thereby causing the image to be automatically stored in the browser's cache, without having purposely saved or downloaded the image"); United States v. Tucker, 305 F.3d 1193, 1205 (10th Cir.2002) (affirming conviction for possession of child pornography because defendant "continued to view child pornography knowing that the pornography was being saved, if only temporarily, on his computer" (emphasis added)); see also United States v. Perez, 247 F.Supp.2d at 459 n. 12 (S.D.N.Y.2003) (observing that 18 U.S.C. § 2252A (a)(5)(B) "does not criminalize `viewing' the images")
[2]  I have inserted brackets in the cpfreedom website and the e-mail address lest a word processing program automatically convert the terms into hyperlinks that might be inadvertently loaded, with untoward consequences.
