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

1,1

Comments

All numbers are congruent to 2 mod 20.

Links

Table of n, a(n) for n=1..19.

Example

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

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 *)

Prog

(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)}

Crossrefs

Cf. A002523, A000068.

Sequence in context: A291586 A015077 A015040 * A116296 A324674 A113890

Adjacent sequences: A235979 A235980 A235981 * A235983 A235984 A235985

Keyword

nonn

Author

Derek Orr, Jan 17 2014

Status

approved