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%I #10 Dec 05 2020 04:09:15
%S 163,331,499,1171,1459,2179,2203,2371,2683,3019,5179,5923,6043,6211,
%T 6379,6883,7219,7411,7723,8059,8443,8563,9643,10099,10651,10723,11083,
%U 11131,11251,12739,12763,13099,13963,14779,14851,15091,15451,16963,17203
%N Primes p of the form 8*k + 3 such that every prime divisor of p-2 has the form 8*t + 7.
%D L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 2, p. 476.
%H Amiram Eldar, <a href="/A306931/b306931.txt">Table of n, a(n) for n = 1..10000</a>
%p with(numtheory);
%p s:=[];
%p for n from 3 to 5000 do
%p p:=ithprime(n); p2:=((p+16) mod 8);
%p if (p2=3) then sw:=1;
%p for q in factorset(p-2) do if (q mod 8) <> 7 then sw:=-1; break; fi; od:
%p if sw=1 then s:=[op(s),p]; fi;
%p fi;
%p od:
%p s; # A306931
%t Select[8*Range[0, 2500] + 3, PrimeQ[#] && AllTrue[FactorInteger[# - 2][[;; , 1]], Mod[#1, 8] == 7 &] &] (* _Amiram Eldar_, Dec 05 2020 *)
%Y Cf. A306930, A306932.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Mar 16 2019
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