A236173 Primes p such that p^2 - p - 1, p^3 - p - 1 and p^4 - p - 1 are all prime.
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
Keywords
Examples
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.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
-
Mathematica
Select[Prime[Range[32000]],AllTrue[#^{2,3,4}-#-1,PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 08 2019 *) -
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
-
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)}
Comments