Primes p such that there are 2 values of m such that p divides m! + 1.
7, 11, 19, 29, 43, 47, 109, 127, 131, 139, 149, 163, 179, 191, 193, 199, 233, 239, 263, 277, 311, 347, 359, 367, 443, 449, 461, 491, 499, 523, 557, 577, 593, 641, 719, 743, 811, 839, 853, 857, 863, 907, 919, 953, 1051, 1061, 1087, 1123, 1153, 1217, 1229, 1249
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 = 2; 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