A239345 -id:A239345 - cp's OEIS frontend

A239416 Numbers n such that n^8-8 is prime.

3, 7, 19, 39, 73, 75, 101, 107, 145, 147, 171, 213, 235, 247, 263, 285, 319, 353, 359, 369, 399, 443, 445, 521, 523, 557, 613, 675, 693, 707, 733, 781, 791, 805, 815, 829, 837, 879, 927, 943, 961, 999, 1033, 1097, 1103, 1109, 1129, 1137, 1141, 1155, 1157

Offset: 1

Derek Orr, Mar 17 2014

nonn

Note that all the numbers in this sequence are odd.

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

Cf. A028870, A153974, A239413, A239414, A239415, A239417, A239418, A239345.

Select[Range[3,1200,2],PrimeQ[#^8-8]&] (* Harvey P. Dale, Jun 27 2014 *)

is(n)=isprime(n^8-8) \\ Charles R Greathouse IV, Feb 20 2017

import sympy
from sympy import isprime
{print(n) for n in range(10**4) if isprime(n**8-8)}

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

Original entry on oeis.org

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

Derek Orr, Mar 20 2014

nonn

All numbers are congruent to 3 mod 6.

Intersection of A239345 and A239416.

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

Cf. A239345, A239416.

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 *)

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)

cp's OEIS Frontend

A239416 Numbers n such that n^8-8 is prime.

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