Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #14 Apr 07 2014 15:50:37
%S 2,5,131,2129,9689,27809,36821,46619,611729,746171,987491,1121189,
%T 1486451,2215529,2701931,4202171,4481069,4846469,5162141,5605949,
%U 6931559,7181039,8608571,9276821,9762611,11427491,11447759,12208019
%N 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 Harvey P. Dale, <a href="/A236045/b236045.txt">Table of n, a(n) for n = 1..150</a>
%t Select[Prime[Range[810000]],And@@PrimeQ[Table[#^n+#+1,{n,4}]]&] (* _Harvey P. Dale_, Apr 07 2014 *)
%o (Python)
%o import sympy
%o from sympy import isprime
%o {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 (PARI) list(maxx)={n=2; cnt=0; while(n<maxx,
%o 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 Cf. A219117.
%K nonn
%O 1,1
%A _Derek Orr_, Jan 18 2014