A236951 Primes p such that p^4 + p +/- 1 are twin primes.

2, 1049, 1847, 1871, 2129, 2789, 5351, 10709, 11279, 13907, 14321, 17627, 27179, 27809, 29921, 30029, 31859, 37511, 39359, 40559, 40841, 43577, 46091, 46301, 58271, 62207, 62981, 66347, 66947, 68777, 72341, 75617, 79397, 85091, 86579

Offset

1,1

Comments

Intersection of A236044 and A236950.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..900

Example

2 is prime and 2^4+2+1 (19) and 2^4+2-1 (17) are twin primes. Thus, 2 is a member of this sequence.

Mathematica

Select[Prime[Range[100000]], PrimeQ[#^4 + # - 1] && PrimeQ[#^4 + # + 1]&] (* Vincenzo Librandi, Feb 14 2014 *)

Prog

(Python)
import sympy
from sympy import isprime
{print(p) for p in range(10**6) if isprime(p) and isprime(p**4+p+1) and isprime(p**4+p-1)}
(Magma) [p: p in PrimesUpTo(90000) | IsPrime(p^4+p-1) and IsPrime(p^4+p+1)]; // Vincenzo Librandi, Feb 14 2014

Crossrefs

Cf. A236044, A236950.

Sequence in context: A182447 A218437 A166852 * A111203 A159858 A108963

Adjacent sequences: A236948 A236949 A236950 * A236952 A236953 A236954

Keyword

nonn

Author

Derek Orr, Feb 01 2014

Status

approved