A239347 -id:A239347 - cp's OEIS frontend

A239418 Numbers n such that n^10 - 10 is prime.

21, 201, 267, 321, 369, 459, 537, 651, 669, 699, 723, 753, 1071, 1113, 1197, 1203, 1209, 1323, 1401, 1503, 1587, 1647, 1773, 1791, 1797, 1917, 1941, 2007, 2139, 2223, 2427, 2493, 2613, 2733, 2769, 2787, 2847, 3147, 3249, 3267, 3297, 3399, 3423, 3441, 3771

Offset: 1

Derek Orr, Mar 17 2014

nonn

All of the numbers in this sequence are odd multiples of 3 and, thus, congruent to 3 (mod 6).

The tenth powers modulo 6 are 1, 4, 3, 4, 1, 0, ... (A070431). Subtracting 10 (still modulo 6), we get 3, 0, 5, 0, 3, 2, ... which means that only n = 3 mod 6 can produce a potential prime p = 5 mod 6.

			21^10 - 10 = 16679880978191 is prime. Thus, 21 is a member of this sequence.

Cf. A028870, A153974, A239413, A239414, A239415, A239416, A239417, A239347.

Select[Range[1000], PrimeQ[#^10 - 10] &] (* Alonso del Arte, Mar 18 2014 *)

is(n)=isprime(n^10-10) \\ Charles R Greathouse IV, Feb 20 2017

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

A239506 Numbers n such that n^10+10 and n^10-10 are prime.

Original entry on oeis.org

4983, 105369, 113289, 150051, 191829, 208131, 277167, 305349, 363957, 400323, 494241, 541233, 577269, 656271, 668547, 995247, 1141503, 1218261, 1360623, 1494537, 1501863, 1528857, 1531959, 1534533, 1535919, 1621653, 1651551, 1864863, 1950597, 1969539, 2130513

Offset: 1

Derek Orr, Mar 20 2014

nonn

All numbers are congruent to 33 mod 66.

Intersection of A239347 and A239418.

			4983^10+10 = 9438628041688305771192954743294050459 is prime and 4983^10-10 = 9438628041688305771192954743294050439 is prime. Thus, 4983 is a member of this sequence.

Cf. A239347, A239418.

Select[Range[22*10^5],AllTrue[#^10+{10,-10},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 04 2018 *)

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

cp's OEIS Frontend

A239418 Numbers n such that n^10 - 10 is prime.

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