A055939 Primes p such that p | ((p-1)/2)! + 1.

7, 11, 19, 43, 47, 67, 79, 103, 127, 131, 163, 179, 191, 199, 227, 263, 347, 367, 383, 419, 431, 443, 479, 491, 503, 523, 563, 571, 599, 607, 619, 631, 683, 691, 727, 739, 743, 787, 823, 839, 863, 887, 947, 991, 1019, 1051, 1087, 1091, 1123, 1151, 1187

Offset: 1

Author

Robert G. Wilson v, Jul 22 2000

Keywords

• nonn

Comments

p | (p-1)! +1 iff p is a prime (Wilson's theorem). Note: all of the above primes are congruent to 3 (mod 4).

All primes == 3 mod 4 are members of either A055939 or A058302. - Zak Seidov, Jan 16 2007

References

• J. B. Cosgrave, A Mersenne-Wieferich Odyssey, Manuscript, May 2022. See Section 18.5.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002145, A058302.

Programs

Mathematica

Select[ Range[ 1225 ], PrimeQ[ # ] && Mod[ ((# - 1)/2)! + 1, # ] == 0 & ]
Select[Prime[Range[200]],Divisible[((#-1)/2)!+1,#]&] (* Harvey P. Dale, Dec 17 2014 *)