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Aug 16, 2021 at 16:21 comment added JoshuaZ @მამუკაჯიბლაძე I would suspect that for any fixed k, the set of $n$ where $n!^2 -1$ has $k$ prime factors is finite. A similar heuristic to the above will agree.
Aug 16, 2021 at 16:11 comment added მამუკა ჯიბლაძე @StefanKohl You got me :)
Aug 16, 2021 at 15:51 comment added Stefan Kohl @მამუკაჯიბლაძე Do you know such $n$ which is greater than 38?
Aug 16, 2021 at 13:45 comment added მამუკა ჯიბლაძე It seems not very rare that $n!^2-1$ is a product of three primes.
Aug 16, 2021 at 13:20 history edited JoshuaZ CC BY-SA 4.0
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Aug 16, 2021 at 13:12 history answered JoshuaZ CC BY-SA 4.0