WOOD, Circuit Judge.

This is our second encounter with Wisconsin inmate James Kaufman's effort to compel the prison system to treat atheism, which he follows, on the same footing as other religious beliefs. In 2005, this panel addressed Kaufman's claim that the Wisconsin prison in which he was then housed had violated the Free Exercise and Establishment Clauses of the First Amendment by refusing his request to create a religious study group dedicated to atheism, while allowing religious study groups dedicated to other religions. We held that Kaufman's request to form such a group must be treated as a request to form a "religious" group rather than a nonreligious activity group. So understood, the Establishment Clause requires the prison to provide a "legitimate secular reason" for allowing other religious groups, but prohibiting an atheist one. Kaufman v. McCaughtry, 419 F.3d 678, 683-84 (7th Cir.2005) (Kaufman I) (citations omitted).

Kaufman has since been moved to the Stanley Correctional Institution (Stanley), where he has encountered nearly identical resistance to his efforts to create an atheist practice group. After submitting a number of grievances, he filed a new lawsuit asserting among other things that the prison's refusal to permit an atheist group to function violates both the Religious Land Use and Institutionalized Persons Act (RLUIPA), 42 U.S.C. § 2000cc, et seq., and the Free Exercise and Establishment Clauses in the First Amendment to the U.S. Constitution. Kaufman also contended that the prison violated the same provisions by denying his request to wear a "knowledge thought ring" that he regards as a religious symbol and by failing to make atheist books that he donated available in the prison library.

Although the prison officials apparently had not read our 2005 opinion in Kaufman I and thus rejected Kaufman's requests out of hand because his proposed group does not recognize any kind of divine entity or higher power, the district court did not make that mistake. It recognized that the atheist study group is a religious one, but it found that the prison supplied a legitimate secular reason for prohibiting an atheist group: Only two inmates (including Kaufman), it thought, have any interest in an atheist group, and it would be impractical to spend limited resources to create a study group for only two members. The court also found that the prohibition of a "knowledge thought ring" did not impose a substantial burden on Kaufman's religious practice and was justified by the prison's secular interest in security. Finally, it held that there was no evidence that the defendants were responsible for losing the books Kaufman donated or that this loss was anything more than isolated negligence. On appeal, Kaufman contests the district court's grant of summary judgment in favor of defendants on all three of these claims. We affirm in part and vacate in part.

I

Inmates at Stanley Correctional Facility are permitted to practice religion through "Umbrella Religious Groups" designed to allow inmates to congregate with those who share relatively similar beliefs. For reasons of security and logistics, the prison does not create sub-groups for each specific sect within a given faith family. The existing umbrella groups are Protestant, Islam, Native American, Catholic, Jewish, Eastern Religions, and Pagan. When inmates express interest in participating in religious study, they fill out a Religious Preference form that allows them to select one of the recognized umbrella groups, "no preference," or "other." If the inmate selects "other," he may write in a religion. If the religion he specifies does not fall within one of the seven umbrella groups, he is not permitted to attend a religious practice group, though he may practice on his own by visiting the religious library or meeting with the Chaplain individually. The prison does not keep records of what religion inmates write in after selecting "other" on the form, and so the authorities do not know how many inmates have selected "other" and written "atheist," "humanist," "secular," "freethinker," or another similar term. Kaufman has submitted evidence indicating that if an inmate writes in "atheism," the prison does not recognize this as a religion at all, and instead lumps the prisoner in with the "No Preference" group.

An inmate wishing to create a practice group for a religion not covered by the existing umbrella groups must submit a special request form. Kaufman did so on October 22, 2009, stating that he wanted to form "a study group for inmates who are Atheists (also possibly listed as Humanists, Freethinkers, Rationalists, Agnostics, and who may have possibly checked `No Preference' because there is no Atheist option on the preference form), or any other inmates who may be interested in such studies." He explained that the group would be "for the study of the history of religion, where and how religious beliefs originated, the origins of belief, and the possible future of belief systems; responsibilities and privileges in society; right versus wrong, and ethical issues." His request acknowledged that "Atheism `requires' no specific activities, but neither does any other belief system." He maintained, however, that his proposed study group is "`related' to Atheism because of the general human need/urge to learn about everything around us, how we relate to and function with other people, how and why things (life) are the way they are, our relationship with other people."

Disregarding or perhaps unaware of the ruling in Kaufman I, the Chaplain recommended denying Kaufman's atheist group because it "is not viewed as a religious request." His written explanation stated that "[r]eligion or being under a religious umbrella group would require a system of human thought which usually includes symbols, beliefs and practices that give meaning to the practitioner's experiences through a higher power, deity, or deities." The Warden adopted the Chaplain's recommendation and denied the request. Kaufman responded with a second special request on December 24, 2009, in which he took care to explain that the group would do more than conduct a study of the history of religion. The Chaplain and the Warden saw no material difference in the new submission, however, and so they denied it as well. A member of the Religious Practices Advisory Committee added that the "types of discussions listed as examples are more educational and philosophical in nature, therefore would not be considered a religious study group."

RLUIPA, which applies to programs and activities that receive federal financial assistance (like the prisons here), provides that the government may not impose a "substantial burden on the religious exercise of a person residing in or confined to an institution" unless the burden is the "least restrictive means" of serving a "compelling governmental interest." 42 U.S.C. § 2000cc-1; see Cutter v. Wilkinson, 544 U.S. 709, 125 S.Ct. 2113, 161 L.Ed.2d 1020 (2005). The Free Exercise Clause prohibits the state from imposing a "substantial burden" on a "central religious belief or practice." Kaufman I, 419 F.3d at 682-83 (quoting Hernandez v. Comm'n of Internal Revenue, 490 U.S. 680, 699, 109 S.Ct. 2136, 104 L.Ed.2d 766 (1989))(citing Civil Liberties for Urban Believers v. City of Chicago, 342 F.3d 752, 760 (7th Cir.2003)). In the prison context, a regulation that impinges on an inmate's constitutional rights, such as one imposing a "substantial burden" on free exercise, may be justified if it is "reasonably related to legitimate penological interests." O'Lone v. Shabazz, 482 U.S. 342, 349, 107 S.Ct. 2400, 96 L.Ed.2d 282 (1987) (quoting Turner v. Safley, 482 U.S. 78, 89, 107 S.Ct. 2254, 96 L.Ed.2d 64 (1987)). As we explained in Kaufman I, however, the Establishment Clause may be violated even without a substantial burden on religious practice if the government favors one religion over another (or religion over nonreligion) without a legitimate secular reason for doing so. 419 F.3d at 683 (citing Linnemeir v. Bd. of Trustees of Purdue Univ., 260 F.3d 757, 759 (7th Cir.2001); Metzl v. Leininger, 57 F.3d 618, 621 (7th Cir.1995); Berger v. Rensselaer Cent. Sch. Corp., 982 F.2d 1160, 1168-69 (7th Cir.1993)).

In Kaufman I, we explained that religious beliefs protected by the Free Exercise and Establishment Clauses need not involve worship of a supreme being. 419 F.3d at 682 (citing McCreary Cnty., Ky. v. Am. Civil Liberties Union of Ky., 545 U.S. 844, 860, 125 S.Ct. 2722, 162 L.Ed.2d 729 (2005)). In Wallace v. Jaffree, 472 U.S. 38, 105 S.Ct. 2479, 86 L.Ed.2d 29 (1985), the Supreme Court left no room for doubt on this point:

Id. at 52-54, 105 S.Ct. 2479. In Kaufman I, we also pointed out that the administrative code governing Wisconsin prisons prohibits the Warden from considering "the absence from the beliefs of a concept of a supreme being" as a reason not to recognize a new religious group. 419 F.3d at 682 (citing Wis. Admin. Code § DOC 309.61(d)(3)). Accordingly, we found that it was error to treat Kaufman's request to form an atheist study group as a non-religious request. Atheism is "a school of thought that takes a position on religion, the existence and importance of a supreme being, and a code of ethics," and it is thus a belief system that is protected by the Free Exercise and Establishment Clauses. Id.

Notwithstanding these legal principles, Kaufman's Free Exercise claim failed in his first suit because he did not show that the lack of the requested group would impose a substantial burden on his practice of atheism. (Kaufman did not present a RLUIPA theory, see id. at 681.) There was no evidence "that he would be unable to practice atheism effectively without the benefit of a weekly study group." Id. at 683. For the same reason, Kaufman again cannot prevail under the Free Exercise Clause. Similarly, because he cannot prevail under RLUIPA unless he first demonstrates "a substantial burden on [his] religious exercise," 42 U.S.C. § 2000cc-1(a), the prison's policy with respect to groups does not violate his rights under RLUIPA.

Kaufman's new Establishment Clause claim, in contrast, presents a different question (just as it did before): we must evaluate whether the prison has provided a legitimate secular justification for discriminating between the proposed atheist study group and the seven recognized umbrella groups. The record on this point is not as clear as it needs to be. First, the idea that the prison's action was justified because not enough people were interested in an atheist group came late to the game. The contemporaneous explanations indicate that the authorities denied Kaufman's request because they thought that an atheist group does not qualify as a "religious" one. Kaufman I conclusively held to the contrary. The district court properly spotted the error, but it found nonetheless that the prison had a legitimate secular reason for denying Kaufman's request because, as it understood the record, only two inmates had expressed any interest in an atheist group.

But a closer look at Kaufman's submissions in both the district court and this court reveals that Kaufman is challenging the finding that he was one of a group of only two. He contends that the prison made it impossible to know how many inmates would have joined such a group, because it ignored "write-in" votes for atheism (or related schools of thought) and re-characterized them as "No Preference." He does not challenge the prison's interest in using umbrella groups; to the contrary, he would like a non-theistic, secular umbrella group. He points to general evidence such as almanacs suggesting that as many as 10 to 14% of the population self-identifies as atheistic, and he suggests that hidden in the mass of "No Preference" inmates are enough people to justify a group that would meet once or twice a month. The district court suggested that insofar as Kaufman's request included sub-groups such as "Humanist" and "Freethinker," it was not a religious request because it swept in too many dissimilar schools of thought. But it is hard to believe that Kaufman's group included more variants than the Native American group (the Bureau of Indian Affairs recognizes 566 tribes), most of which have their own religion, see "Indian Entities Recognized and Eligible To Receive Services from the United States Bureau of Indian Affairs," 77 Fed.Reg. 47868-01 (Aug. 10, 2012), or the "Eastern Religions" group, or even the Protestant sects (which number in the thousands, see WORLD CHRISTIAN ENCYCLOPEDIA: A COMPARATIVE SURVEY OF CHURCHES AND RELIGIONS IN THE MODERN WORLD (David B. Barrett et al. eds., 2001)). In his request, Kaufman was attempting to sweep in the like-minded inmates who he thought would be interested in his proposed umbrella group.

The prison has one other argument that deserves attention. Putting the preference forms to one side, it points out that Kaufman was the only inmate who asked for the formation of an atheist umbrella group. If there were others, it suggests, it would have seen more such requests. Kaufman responds that atheist inmates less persistent than he has proven to be would have been deterred from submitting a form, because their efforts to designate atheism as an alternate religious viewpoint were, metaphorically, thrown in the trash. In our view, the fact that Kaufman alone made such a request is evidence on the prison's side, but it is not conclusive. We cannot tell, on the record as it stands, if more inmates would have designated atheism if it had been an option on the preference form. (That is why political candidates push so hard to get their names on ballots; it is cold comfort to be told that one can run as a write-in.)

A recent PEW survey of prison chaplains suggests that Kaufman may be on to something, and that there might be at least as many prisoners interested in an atheist group as one sees in the Pagan, Eastern Religions, or Jewish groups. Religion in Prisons: A 50-State Survey of Prison Chaplains, The PEW Forum on Religion and Public Life, available at http://www.pewforum.org/SocialWelfare/ prison-chaplainsperspectives.aspx (last visited August 15, 2013). According to the survey, 1.7% of prisoners identify as Jewish and Pagan, and 0.9% identify as Buddhist, while "[o]n average, chaplains say that about 11% of the inmate population is atheist, agnostic or has no particular religious affiliation." If only one-tenth of this 11% category would select the "atheist" option if it were included among the umbrella groups, there would be a comparable number of atheists to Pagans, Jews, and Buddhists. If this is the case, then there may be no objective basis for refusing to create an umbrella atheist group, unless the prison could show that the expansion from seven to eight groups was somehow prohibitive. Because we have no evidence on this, we cannot determine how much weaker (if at all) the inmates' interest in an atheist group is, nor are we in a position to say whether the prison's justification is compatible with the Establishment Clause.

We can assume that the district court was correct when it ruled that the prison has no duty to recognize every minor religion or belief system that attracts at least two inmates. But we think that further exploration of the degree of interest that actually prevails at Stanley is necessary before it will be possible to rule on Kaufman's claim. Kaufman points out that in December 2011, Stanley had a total of 1,465 inmates: 178 Catholics, 236 Muslims, 166 Pagans, 517 Protestants, 28 from Eastern Religions, 67 Jewish, and 67 Native American. That left 206 inmates of unknown affiliation — approximately 14% of the total. In his brief, Kaufman cites a number of studies from the U.S. Census Bureau, the New York Times 2004 Almanac, the 2003 World Almanac, and so forth, showing that somewhere between 7 and 14% of adult Americans describe themselves as being atheist, agnostic, or humanist. That suggests that out of the 1,465 inmates, somewhere between 102 and 206 might fall within the proposed group. Only a credible survey of the inmate population, or the simple expedient of adding "atheist, agnostic, or humanist" to the preference form and collecting new data, can resolve this uncertainty.

II

Inmates are permitted to possess religious property or wear religious emblems only if it is approved by the Chaplain. Permissible religious emblems are determined by an inmates' membership in an umbrella group. The Chaplain maintains a list of religious emblems associated with each umbrella group's specific practices, and inmates must belong to the umbrella group in order to possess associated religious emblems. The prison's strict policy on religious emblems arises from concern about their use as symbols of gang membership. For instance, caps worn in a distinct way, or jewelry with a particular color or pattern, may be usurped to symbolize gang loyalty rather than religious faith.

Kaufman wanted to acquire a new religious emblem, which he described as a "knowledge thought ring" — a sterling silver ring engraved with the word "knowledge." He admitted that the ring was not commonly recognized among atheists, but he argued that the choice of an Atheist symbol is individualized, "unique to each person." The Chaplain denied the request for at least two independent reasons: atheism is not a recognized umbrella group, and the ring was not on the list of permissible religious emblems.

The district court correctly dismissed this claim. It cannot succeed under RLUIPA or the Free Exercise Clause because the inability to wear the ring does not impose a "substantial burden" on Kaufman's ability to practice atheism. Kaufman admits this when he concedes that the ring is an individualized symbol. For the same reason, the prison's control of religious emblems does not discriminate against atheism in violation of the Establishment Clause. Cf. Easterling v. Pollard, No. 12-1532, ___ Fed.Appx. ___, 2013 WL 3787486 (7th Cir. July 22, 2013) (nonprecedential) (no RLUIPA violation by prison that refused to recognize inmate's idiosyncratic belief that Ramadan began one month in 2010 earlier than date recognized by Fiqh Council of North America and used universally). It is entitled to draw a distinction between, on the one hand, religious emblems that are common to the members of other umbrella religious groups, easy to recognize, and difficult to abuse as a gang symbol, and on the other hand, emblems that are unique to each prisoner and potential security risks.

III

Three used books were mailed to Kaufman through the prison mail system. Kaufman was not permitted to receive them because prisoners may receive only new books mailed directly from the publisher or a commercial retailer. (This is because of the risk that used books from private senders may conceal contraband.) Kaufman filed a form electing to donate the used books to the chapel library, but they never showed up there. Five other books that Kaufman has donated are maintained in the general library. Kaufman claims that the loss of these three books violates RLUIPA and the Free Exercise Clause.

Although the state argues that Kaufman has abandoned this claim on appeal, we are satisfied that he has done enough to preserve it. That said, however, the claim is going nowhere. The absence of the books does not impose a substantial burden on Kaufman's ability to follow his atheistic beliefs. Indeed, there is no evidence that the prison intentionally lost Kaufman's books, and thus there is nothing to support the accusation that it was discriminating in this way against atheism. Nor is there any evidence that the prison made other religious books donated by inmates available in the chapel library, but consciously refused to make atheist books available.

IV

We VACATE the grant of summary judgment on Kaufman's claim that the defendants violated the Establishment Clause by denying his request for an atheist religious group and REMAND for further proceedings consistent with this opinion. We AFFIRM the grant of summary judgment in favor of the defendants on all other claims. Each party is to bear its own costs on appeal.