Primes p such that there are 7 values of m such that p divides m! + 1.
71, 661, 2267, 3163, 3541, 4241, 5503, 6043, 6359, 11503, 11867, 12239, 15467, 16187, 22853, 26513, 26863, 29881, 31543, 31799, 32303, 34267, 39769, 40939, 41263, 42359, 49363, 51407, 54917, 55603, 55633, 58991, 63907, 64283, 67511, 67679, 67699, 68059
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 = 7; 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