A240693 Primes p such that p^10 + p^9 + p^8 + p^7 + p^6 + p^5 + p^4 + p^3 + p^2 + p + 1 is prime.

5, 17, 53, 137, 229, 389, 467, 619, 709, 787, 1091, 1103, 1213, 1249, 1433, 1459, 1601, 1993, 2029, 2039, 2087, 2089, 2393, 2687, 3217, 3299, 3529, 3547, 3691, 3793, 4019, 4091, 4099, 4231, 4507, 4561, 4679, 5351, 5399, 5471, 5521, 5581, 5669, 5783, 5813, 5861, 5939, 6247, 6841, 6899, 6961

Offset: 1

Author

Derek Orr, Apr 10 2014

Keywords

• nonn

Comments

These are the primes in A162862.

Examples

			5^10 + 5^9 + 5^8 + 5^7 + 5^6 + 5^5 + 5^4 + 5^3 + 5^2 + 5 + 1 = 12207031 is prime. Thus, 5 is a term of this sequence.
		

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A162862.

Programs

Mathematica

Select[Prime[Range[200]], PrimeQ[1 + Sum[#^i, {i, 10}]] &] (* Alonso del Arte, Apr 11 2014 *)
Select[Prime[Range[900]],PrimeQ[Total[#^Range[0,10]]]&] (* Harvey P. Dale, Oct 11 2023 *)

PARI

for(n=1,10^4,if(ispseudoprime(n^10+n^9+n^8+n^7+n^6+n^5+n^4+n^3+n^2+n+1)&&ispseudoprime(n),print(n)))

Python

import sympy
from sympy import isprime
{print(n) for n in range(10**4) if isprime(n) and isprime(n**10+n**9+n**8+n**7+n**6+n**5+n**4+n**3+n**2+n+1)}