A250407 Near-Wilson primes (p = prime(n) satisfying (p-1)! == -1-A250406(n)*p (mod p^2)) with A250406(n) < 10.

2, 3, 5, 7, 13, 61, 71, 79, 157, 281, 563, 1277, 1777, 2339, 6311, 8233, 8543, 11047, 22907, 27689

Offset: 1

Author

Felix Fröhlich, Nov 22 2014

Keywords

• nonn
• hard
• more

Comments

A250406(n) is essentially A007619(n) modulo A000040(n) (see Crandall et al. (1997), p. 442).

Links

• E. Costa, R. Gerbicz and D. Harvey, A search for Wilson primes, Math. Comp., 83 (2014), 3071-3091.
• R. Crandall, K. Dilcher and C. Pomerance, A search for Wieferich and Wilson primes, Math. Comp., 66 (1997), 433-449.

Crossrefs

Cf. A007540, A246568, A250406.

Programs

PARI

forprime(p=1, 1e9, for(b=0, 9, if(Mod((p-1)!, p^2)==-1-b*p, print1(p, ", "); break({1}))))