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A236173
Primes p such that p^2 - p - 1, p^3 - p - 1 and p^4 - p - 1 are all prime.
1
11, 71, 11621, 28151, 32089, 37501, 39209, 45329, 66161, 76649, 114599, 122131, 136949, 154991, 202999, 228901, 243391, 270269, 296911, 313909, 318679, 333701, 343309, 359291, 369979, 371281, 371981, 373171, 373459
OFFSET
1,1
COMMENTS
Primes in A236171. All primes appear to end in a 1 or a 9 (congruent to either 1 mod 10 or 9 mod 10).
LINKS
EXAMPLE
228901 is prime, 228901^2 - 228901 - 1 is prime, 228901^3 - 228901 - 1 is prime, and 228901^4 - 228901 - 1 is prime. So 228901 is a member of this sequence.
MATHEMATICA
Select[Prime[Range[32000]], AllTrue[#^{2, 3, 4}-#-1, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 08 2019 *)
PROG
(Python)
import sympy
from sympy import isprime
{print(p) for p in range(10**6) if isprime(p) and isprime(p**2-p-1) and isprime(p**3-p-1) and isprime(p**4-p-1)}
(PARI)
s=[]; forprime(p=2, 400000, if(isprime(p^2-p-1) && isprime(p^3-p-1) && isprime(p^4-p-1), s=concat(s, p))); s \\ Colin Barker, Jan 20 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Derek Orr, Jan 19 2014
STATUS
approved