Primes p such that there are 6 values of m such that p divides m! + 1.
401, 1753, 1847, 1907, 2503, 3119, 3449, 3581, 3947, 4259, 4591, 4663, 5051, 5791, 8863, 9437, 10321, 10477, 11069, 11833, 11903, 13009, 15131, 15313, 15391, 15497, 16361, 16747, 16883, 17839, 19379, 20117, 20551, 21139, 21419, 22441, 23563, 24551, 24659
1
By Wilson’s therom, p - 1 is always one of the values.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Eric W. Weisstein, MathWorld: Wilson’s Theorem
(Mma) nn = 6; t = {}; p = 1; While[Length[t] < 50, p = NextPrime[p]; cnt = 0; f = 1; Do[f = Mod[f*m, p]; If[f + 1 == p, cnt++], {m, p - 1}]; If[cnt == nn, AppendTo[t, p]]]; t
nonn
T. D. Noe, Jun 12 2015