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All primes less than      10 1000 {10^{1000}}       of the form      n ! ±  1 n! \pm 1       or      2 ⋅  3 ⋅  5 ⋯  p ±  1 2 \cdot 3 \cdot 5 \cdots p \pm 1       are determined. Results of Brillhart, Lehmer, and Selfridge are used together with a fast algorithm that applies to primality tests of integers  N  for which many factors of      N ±  1 N \pm 1       are known.

Primes of the form 𝑛!±1 and 2⋅3⋅5⋯𝑝±1