A123988 Primes p such that 2^x == 3 (mod p) has no solutions.

3, 7, 17, 31, 41, 43, 73, 79, 89, 103, 109, 113, 127, 137, 151, 157, 199, 223, 229, 233, 241, 251, 257, 271, 277, 281, 283, 331, 337, 353, 367, 397, 401, 433, 439, 449, 457, 463, 487, 521, 569, 571, 593, 601, 607, 617, 631, 641, 673, 683, 691, 727, 733, 739, 751, 761, 809, 811, 823, 857, 881, 911

Offset: 1

Author

Artur Jasinski, Nov 23 2006

Keywords

• nonn

Comments

Such primes cannot divide solutions to 2^m == 3 (mod m) (see A050259).

Links

• J. K. Crump, Number Theory Web.

Crossrefs

Cf. A050259, A001915 (complement in the primes).

Programs

Magma

lst:=[3]; for p in [5..911 by 2] do if IsPrime(p) then t:=0; e:=Ceiling(Log(2, p+1)); for x in [e..p-2] do if 2^x mod p eq 3 then t:=1; break; end if; end for; if t eq 0 then Append(~lst, p); end if; end if; end for; lst; // Arkadiusz Wesolowski, Jan 12 2021

Extensions

Edited by Max Alekseyev, Jan 14 2007

Corrected by Max Alekseyev, Jun 08 2011

Corrected by Arkadiusz Wesolowski, Jan 12 2021