A236045 Primes p such that p^1+p+1, p^2+p+1, p^3+p+1, and p^4+p+1 are all prime.

2, 5, 131, 2129, 9689, 27809, 36821, 46619, 611729, 746171, 987491, 1121189, 1486451, 2215529, 2701931, 4202171, 4481069, 4846469, 5162141, 5605949, 6931559, 7181039, 8608571, 9276821, 9762611, 11427491, 11447759, 12208019

Offset: 1

Author

Derek Orr, Jan 18 2014

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A219117.

Programs

Mathematica

Select[Prime[Range[810000]],And@@PrimeQ[Table[#^n+#+1,{n,4}]]&] (* Harvey P. Dale, Apr 07 2014 *)

PARI

list(maxx)={n=2; cnt=0; while(nBill McEachen, Feb 05 2014

Python

import sympy
from sympy import isprime
{print(p) for p in range(10**8) if isprime(p) and isprime(p**1+p+1) and isprime(p**2+p+1) and isprime(p**3+p+1) and isprime(p**4+p+1)}