A239503 Numbers n such that n^8+8 and n^8-8 are prime.

3, 1515, 1689, 3327, 4461, 4641, 4965, 5043, 5583, 5709, 6183, 7089, 9291, 9369, 9699, 10125, 11109, 14175, 15081, 18393, 20295, 26955, 27009, 27219, 29067, 30513, 30807, 35355, 35889, 36003, 37935, 40107, 43461, 48045, 49005, 51783, 53289, 55527, 58833, 61203

Offset: 1

Author

Derek Orr, Mar 20 2014

Keywords

• nonn

Comments

All numbers are congruent to 3 mod 6.

Intersection of A239345 and A239416.

Examples

			3^8+8 = 6569 is prime and 3^8-8 = 6553 is prime. Thus, 3 is a member of this sequence.
		

Crossrefs

Cf. A239345, A239416.

Programs

Mathematica

Select[Range[3,62000,6],AllTrue[#^8+{8,-8},PrimeQ]&](* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 07 2020 *)

Python

import sympy
from sympy import isprime
def TwoBoth(x):
  for k in range(10**6):
    if isprime(k**x+x) and isprime(k**x-x):
      print(k)
TwoBoth(8)