cp's OEIS Frontend

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.

%I A236045 #14 Apr 07 2014 15:50:37
%S A236045 2,5,131,2129,9689,27809,36821,46619,611729,746171,987491,1121189,
%T A236045 1486451,2215529,2701931,4202171,4481069,4846469,5162141,5605949,
%U A236045 6931559,7181039,8608571,9276821,9762611,11427491,11447759,12208019
%N 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.
%H A236045 Harvey P. Dale, <a href="/A236045/b236045.txt">Table of n, a(n) for n = 1..150</a>
%t A236045 Select[Prime[Range[810000]],And@@PrimeQ[Table[#^n+#+1,{n,4}]]&] (* _Harvey P. Dale_, Apr 07 2014 *)
%o A236045 (Python)
%o A236045 import sympy
%o A236045 from sympy import isprime
%o A236045 {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)}
%o A236045 (PARI) list(maxx)={n=2; cnt=0; while(n<maxx,
%o A236045 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
%Y A236045 Cf. A219117.
%K A236045 nonn
%O A236045 1,1
%A A236045 _Derek Orr_, Jan 18 2014