%I #13 Jun 07 2014 02:44:48
%S 3,31,73,181,367,373,523,631,733,1021,1039,1171,1489,1723,1777,2203,
%T 2557,2683,3121,3187,3319,4441,4591,4621,4801,4957,5113,5167,5323,
%U 5431,5659,5839,5851,5857,6883,7057,7129,7297,7309,7477,7993,8017,8209,8221,8689,8821
%N Primes p such that p^6 - p^5 + 1 is prime.
%H K. D. Bajpai, <a href="/A243471/b243471.txt">Table of n, a(n) for n = 1..5457</a>
%e 31 appears in the sequence because it is prime and 31^6 - 31^5 + 1 = 858874531 is also prime.
%e 73 appears in the sequence because it is prime and 73^6 - 73^5 + 1 = 149261154697 is also prime.
%p A243471 := proc() local a, b; a:=ithprime(n); b:= a^6-a^5+1; if isprime (b) then RETURN (a); fi; end: seq(A243471 (), n=1..2000);
%t c=0; Do[k=Prime[n]; If[PrimeQ[k^6-k^5+1], c++; Print[c," ",k]], {n,1,200000}];
%Y Cf. A000040, A091567, A053182, A053183, A053184, A238136.
%K nonn
%O 1,1
%A _K. D. Bajpai_, Jun 05 2014
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