According to the OEIS, these are the only three below a n=4*10^9. https://oeis.org/A085692 It is also known as Brocard’s problem. https://en.wikipedia.org/wiki/Brocard%27s_problem<https://en.wikipedia.org/wiki/Brocard's_problem> Steve On May 2, 2019, at 12:57 PM, Tomas Rokicki <rokicki@gmail.com<mailto:rokicki@gmail.com>> wrote: So, I recently came across this: 4!+1 = 5^2 5!+1 = 11^2 7!+1 = 71^2 Is there any other n such that n!+1 is a perfect square? A perfect square of a prime? Also, n!+1 seems to generate a fair number of primes. For instance, 73!+1 appears to be prime. But this is apparently well known. -- -- https://urldefense.proofpoint.com/v2/url?u=http-3A__cube20.org_&d=DwICAg&c=e... -- https://urldefense.proofpoint.com/v2/url?u=http-3A__golly.sf.net_&d=DwICAg&c... -- _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com> https://urldefense.proofpoint.com/v2/url?u=https-3A__mailman.xmission.com_cg...