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A243472 Primes p such that p^6 - p^5 - 1 is prime.

%I A243472 #15 Jan 21 2015 18:41:10
%S A243472 2,31,101,151,181,199,229,277,307,317,379,439,479,491,647,691,797,911,
%T A243472 997,1039,1051,1181,1291,1367,1381,1471,1511,1549,1657,1709,1847,1867,
%U A243472 1987,2081,2099,2111,2207,2467,2621,2707,3041,3221,3259,3541,3571,3581,3769
%N A243472 Primes p such that p^6 - p^5 - 1 is prime.
%H A243472 K. D. Bajpai, <a href="/A243472/b243472.txt">Table of n, a(n) for n = 1..4699</a>
%e A243472 31 appears in the sequence because it is prime and 31^6 - 31^5 - 1 = 858874529 is also prime.
%e A243472 101 appears in the sequence because it is prime and 101^6 - 101^5  - 1 = 1051010050099 is also prime.
%p A243472 A243472 := proc() local a, b; a:=ithprime(n); b:= a^6-a^5-1; if isprime (b) then RETURN (a); fi; end: seq(A243472 (), n=1..2000);
%t A243472 c = 0;  Do[k=Prime[n]; If[PrimeQ[k^6-k^5-1], c++; Print[c," ",k]], {n,1,200000}];
%t A243472 Select[Prime[Range[600]],PrimeQ[#^6-#^5-1]&] (* _Harvey P. Dale_, Jan 21 2015 *)
%o A243472 (PARI) s=[]; forprime(p=2, 4000, if(isprime(p^6-p^5-1), s=concat(s, p))); s \\ _Colin Barker_, Jun 06 2014
%Y A243472 Cf. A000040, A091567, A053182, A053183, A053184, A238136.
%K A243472 nonn
%O A243472 1,1
%A A243472 _K. D. Bajpai_, Jun 05 2014