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

1,1

Links

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

Mathematica

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

Prog

(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)}
(PARI) list(maxx)={n=2; cnt=0; while(n<maxx,
if(isprime(2*n+1) && isprime(n^2+n+1) && isprime(n^3+n+1) && isprime(n^4+n+1), cnt++; print(cnt, "  ", n ) ); n=nextprime(n+1)); } \\ Bill McEachen, Feb 05 2014

Crossrefs

Cf. A219117.

Sequence in context: A139129 A139484 A088271 * A183128 A145620 A130412

Adjacent sequences: A236042 A236043 A236044 * A236046 A236047 A236048

Keyword

nonn

Author

Derek Orr, Jan 18 2014

Status

approved