A239429 Numbers n such that n^6+6 and n^6-6 are prime.

175, 12635, 18445, 30275, 32585, 38885, 41125, 46235, 53165, 71785, 74935, 92645, 108115, 117775, 121625, 146125, 151655, 173635, 184765, 191765, 196175, 204505, 208705, 229775, 237965, 241255, 243635, 246365, 283115, 335755, 344365, 345485, 352625, 353395, 354445

Offset: 1

Author

Derek Orr, Mar 20 2014

Keywords

• nonn

Comments

All numbers are congruent to 35 mod 70.

Intersection of A109836 and A239414.

Examples

			175^6+6 = 28722900390631 is prime and 175^6-6 = 28722900390619 is prime. Thus, 175 is a member of this sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A109836, A239414.

Programs

Mathematica

Select[Range[35,360000,70],AllTrue[#^6+{6,-6},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 22 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(6)