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

1,1

Links

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

Example

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.

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}];

Prog

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

Crossrefs

Cf. A000040, A237639, A237641, A237642.

Sequence in context: A106755 A320876 A304383 * A118200 A163303 A259956

Adjacent sequences: A238080 A238081 A238082 * A238084 A238085 A238086

Keyword

nonn

Author

K. D. Bajpai, Feb 17 2014

Extensions

More terms from Michel Marcus, Feb 27 2014

Status

approved