A236072 Numbers n such that n^4 + n + 1 and n^4 - n - 1 are prime.

2, 5, 6, 9, 11, 26, 44, 60, 77, 147, 239, 384, 545, 690, 770, 779, 1071, 1127, 1190, 1271, 1296, 1331, 1506, 1659, 1707, 1871, 1880, 1986, 2037, 2442, 2520, 2541, 2714, 2960, 2982, 3045, 3060, 3110, 3189, 3287, 3464, 3609

Offset: 1

Author

Derek Orr, Jan 19 2014

Keywords

• nonn

Examples

			384^4 + 384 + 1 and 384^4 - 384 - 1 are both prime, so 384 is a member of this sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Numbers in both A126424 and A049408.

Programs

Mathematica

Select[Range[4000],AllTrue[#^4+{#+1,-#-1},PrimeQ]&] (* Harvey P. Dale, Jan 20 2025 *)

PARI

s=[]; for(n=1, 4000, if(isprime(n^4+n+1) && isprime(n^4-n-1), s=concat(s, n))); s \\ Colin Barker, Jan 19 2014

Python

import sympy
from sympy import isprime
{print(p) for p in range(10**4) if isprime(p**4-p-1) and isprime(p**4+p+1)}