A238083 Primes p such that p^4 - p^3 + 1 is also prime.

67, 139, 337, 409, 577, 607, 631, 1297, 1321, 1429, 1459, 1549, 1627, 2377, 2557, 2767, 2851, 2917, 3001, 3187, 3319, 3499, 4027, 4099, 4621, 4861, 4969, 5059, 5431, 5449, 5581, 5827, 5857, 6007, 6037, 6379, 6481, 6781, 6997, 7411, 7927, 8089, 8191, 8311

Offset: 1

Author

K. D. Bajpai, Feb 17 2014

Keywords

• nonn

Examples

			67 is in the sequence because 67 is prime and 67^4 - 67^3 + 1 = 19850359 is also prime.
337 is in the sequence because 337 is prime and 337^4 - 337^3 + 1 = 12859645009 is also prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..3409

Crossrefs

Cf. A000040, A237639, A237641, A237642.

Programs

Maple

KD := proc() local a,b;  a:= ithprime(n);  b:= a^4 - a^3 + 1;  if isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..2000);

Mathematica

c=0; a=2; Do[k=Prime[n];  If[PrimeQ[k^4-k^3+1], c=c+1;  Print[c," ",k]],    {n,1,100000}];
Select[Prime[Range[1100]],PrimeQ[#^4-#^3+1]&] (* Harvey P. Dale, Jun 11 2025 *)

PARI

isok(p) = isprime(p) && isprime(p^4 - p^3 + 1); \\ Michel Marcus, Feb 27 2014

Extensions

More terms from Michel Marcus, Feb 27 2014