A243471 Primes p such that p^6 - p^5 + 1 is prime.

3, 31, 73, 181, 367, 373, 523, 631, 733, 1021, 1039, 1171, 1489, 1723, 1777, 2203, 2557, 2683, 3121, 3187, 3319, 4441, 4591, 4621, 4801, 4957, 5113, 5167, 5323, 5431, 5659, 5839, 5851, 5857, 6883, 7057, 7129, 7297, 7309, 7477, 7993, 8017, 8209, 8221, 8689, 8821

Offset: 1

Author

K. D. Bajpai, Jun 05 2014

Keywords

• nonn

Examples

			31 appears in the sequence because it is prime and 31^6 - 31^5  + 1 = 858874531 is also prime.
73 appears in the sequence because it is prime and 73^6 - 73^5  + 1 = 149261154697 is also prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..5457

Crossrefs

Cf. A000040, A091567, A053182, A053183, A053184, A238136.

Programs

Maple

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);

Mathematica

c=0; Do[k=Prime[n]; If[PrimeQ[k^6-k^5+1], c++; Print[c," ",k]], {n,1,200000}];