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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 (list; graph; refs; listen; history; text; internal format)
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: A093865 A139484 A088271 * A183128 A145620 A130412

Adjacent sequences:  A236042 A236043 A236044 * A236046 A236047 A236048

KEYWORD

nonn

AUTHOR

Derek Orr, Jan 18 2014

STATUS

approved

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Last modified September 23 19:41 EDT 2020. Contains 337315 sequences. (Running on oeis4.)