Primes p such that there are 5 values of m such that p divides m! + 1.
227, 293, 733, 887, 1187, 1423, 1511, 1663, 2053, 2281, 2357, 3313, 3323, 3347, 3637, 3701, 3823, 3923, 3931, 4007, 4073, 4139, 4219, 4457, 4483, 4943, 5479, 5779, 6203, 6299, 6379, 6619, 6967, 7121, 7129, 7321, 7351, 8243, 8627, 8629, 9043, 9433, 9473
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 = 5; 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