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%I #24 Sep 08 2022 08:45:28
%S 3,7,17,31,41,43,73,79,89,103,109,113,127,137,151,157,199,223,229,233,
%T 241,251,257,271,277,281,283,331,337,353,367,397,401,433,439,449,457,
%U 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
%N Primes p such that 2^x == 3 (mod p) has no solutions.
%C Such primes cannot divide solutions to 2^m == 3 (mod m) (see A050259).
%H J. K. Crump, <a href="https://web.archive.org/web/20120104074339/http://www.immortaltheory.com:80/NumberTheory/">Number Theory Web</a>.
%o (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
%Y Cf. A050259, A001915 (complement in the primes).
%K nonn
%O 1,1
%A _Artur Jasinski_, Nov 23 2006
%E Edited by _Max Alekseyev_, Jan 14 2007
%E Corrected by _Max Alekseyev_, Jun 08 2011
%E Corrected by _Arkadiusz Wesolowski_, Jan 12 2021
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