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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.
1
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
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
KEYWORD
nonn
AUTHOR
Derek Orr, Jan 18 2014
STATUS
approved