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

Author

Derek Orr, Mar 17 2014

Keywords

• nonn

Comments

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.

Examples

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Python

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