A236044 -id:A236044 - cp's OEIS frontend

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

Derek Orr, Feb 01 2014

nonn

Intersection of A236044 and A236950.

			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.

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

Cf. A236044, A236950.

[p: p in PrimesUpTo(90000) | IsPrime(p^4+p-1) and IsPrime(p^4+p+1)]; // Vincenzo Librandi, Feb 14 2014

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

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)}

A236073 Primes p such that p^4 + p + 1 and p^4 - p - 1 are also prime.

Original entry on oeis.org

2, 5, 11, 239, 1871, 4001, 4397, 6971, 12647, 12689, 13337, 13619, 15401, 19391, 19559, 19739, 20201, 20297, 22871, 22937, 28307, 30029, 32561, 36299, 36929, 39569, 44279, 45497, 47441, 48767, 50069, 53897, 55871

Offset: 1

Derek Orr, Jan 19 2014

nonn

Primes in the sequence A236072.

			6971 is prime, 6971^4 - 6971 - 1 is prime, and 6971^4 + 6971 + 1 is prime. So 6971 is a member of this sequence.

Cf. A236072, A236071, A236044.

s=[]; forprime(p=2, 55871, if(isprime(p^4+p+1)&&isprime(p^4-p-1), s=concat(s, p))); s \\ Colin Barker, Jan 19 2014

import sympy
from sympy import isprime
{print(p) for p in range(10**5) if isprime(p**4+p+1) and isprime(p**4-p-1) and isprime(p)}

cp's OEIS Frontend

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

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