A236766 Numbers n such that n^4 +/- n +/- 1 are prime for all four possibilities.

6, 9, 7266, 115131, 380529, 536646, 636609, 818526, 922734, 1389015, 1660119, 2045415, 2085726, 2262420, 2469396, 2722260, 2836374, 2954250, 3146904, 3614226, 3949770, 4062465, 4110834, 4211499, 4400100, 5081055, 5324424, 5434794, 5436090

Offset: 1

Author

Derek Orr, Jan 30 2014

Keywords

• nonn

Examples

			380529^4+380529+1 (20967711831335262645811), 380529^4+380529-1 (20967711831335262645809), 380529^4-380529+1 (20967711831335261884753), and 380529^4-380529-1 (20967711831335261884751) are all prime. Thus, 380529 is a member of this sequence.
		

Crossrefs

Intersection of A236759, A049408, A236761 and A126424.

Programs

Mathematica

Select[Range[55*10^5],AllTrue[#^4+{(#-1),(#+1),(-#-1),(-#+1)},PrimeQ]&] (* Harvey P. Dale, Nov 02 2024 *)

PARI

for(n=1, 5000000, if(isprime(n^4+n+1)&&isprime(n^4-n+1)&&isprime(n^4+n-1)&&isprime(n^4-n-1), print1(n, ","))) \\ Colin Barker, Jan 31 2014

Python

import sympy
from sympy import isprime
{print(n) for n in range(10**7) if isprime(n**4+n+1) and isprime(n**4-n+1) and isprime(n**4+n-1) and isprime(n**4-n-1)}