A158295 Primes p such that p^3-p-+1 are twin primes.

2, 11, 31, 41, 239, 521, 2309, 4099, 4409, 4441, 4651, 5009, 5039, 5261, 6481, 6871, 7129, 8609, 9391, 10259, 12841, 13759, 14519, 14879, 14939, 15569, 16871, 18451, 20369, 22441, 24049, 25841, 28151, 28279, 29429, 30181, 30631, 32089, 32299, 36781

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Mar 15 2009

Keywords

• nonn

Comments

Primes p such that p^3+p-+1 are twin primes, so far only one: 3. 3^3+3=30-+1 = primes.

Primes in the sequence A236524. Odd primes are congruent to either 1 mod 10 or 9 mod 10. - Derek Orr, Jan 27 2014

Examples

			2^3-2=6-+1 = 5,7 primes, 11^3-11-+1 = 1319,1321 primes...
		

Links

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

Crossrefs

Cf. A120364, A088483, A236524, A236477, A126421.

Programs

Mathematica

lst={};Do[p=Prime[n];a=p^3-p;If[PrimeQ[a-1]&&PrimeQ[a+1],AppendTo[lst,p]],{n,8!}];lst
Select[Prime[Range[3500]],And@@PrimeQ[#^3-#+{1,-1}]&] (* Harvey P. Dale, Jan 05 2013 *)

PARI

s=[]; forprime(p=2, 40000, if(isprime(p^3-p-1) && isprime(p^3-p+1), s=concat(s, p))); s /* Colin Barker, Jan 28 2014 */

Python

import sympy
from sympy import isprime
{print(p) for p in range(10**5) if isprime(p) and isprime(p**3-p-1) and isprime(p**3-p+1)} # Derek Orr, Jan 27 2014