A235982 Numbers n of the form p^4 + 1 (for prime p) such that n^4 + 1 is also prime.

82, 38950082, 47458322, 131079602, 1982119442, 25856961602, 58120048562, 602425897922, 1053022816562, 1267247769842, 3491998578722, 7181161893362, 7759350084722, 10756569837842, 16948379819282, 28424689653362, 33122338550402, 36562351115762, 50897394646082

Offset: 1

Author

Derek Orr, Jan 17 2014

Keywords

• nonn

Comments

All numbers are congruent to 2 mod 20.

Examples

			10756569837842 = 1811^4 + 1 (1811 is prime) and 10756569837842^4 + 1 is prime, so 10756569837842 is a member of this sequence.
		

Crossrefs

Cf. A002523, A000068.

Programs

Mathematica

nfp4Q[n_]:=Module[{p=Surd[n-1,4]},AllTrue[{p,n^4+1},PrimeQ]]; Select[ Range[ 2700]^4+ 1,nfp4Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 08 2019 *)

Python

import sympy
from sympy import isprime
{print(n**4+1) for n in range(10000) if isprime(n) if isprime((n**4+1)**4+1)}