A252042 Primes p such that 2*p^3 + 1 and 2*p^3 + 3 are also primes.

2, 29, 1709, 5849, 6857, 6959, 8999, 10139, 11909, 13127, 13877, 15077, 15749, 17657, 19457, 23357, 23399, 26729, 27407, 27479, 28349, 30047, 31907, 32957, 39569, 46559, 46589, 46817, 50417, 58757, 59219, 60737, 62207, 62687, 62819, 66947, 70589, 71237, 74699

Offset: 1

Author

K. D. Bajpai, Dec 13 2014

Keywords

• nonn

Examples

			a(2) = 29 is prime: 2*29^3 + 1 = 48779 and 2*29^3 + 3 = 48781 are both primes.
a(3) = 1709 is prime: 2*1709^3 + 1 = 9982887659 and 2*1709^3 + 3 = 9982887661 are both primes.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..11485

Crossrefs

Cf. A000040, A153507, A174363, A247101.

Programs

Mathematica

Select[Prime[Range[10000]], And[PrimeQ[2*#^3 + 1], PrimeQ[2*#^3 + 3]] &]
Select[Prime[Range[7500]],AllTrue[2#^3+{1,3},PrimeQ]&] (* Harvey P. Dale, Apr 03 2023 *)

PARI

s=[]; forprime(p=2, 10^5, if(isprime(2*p^3 + 1) && isprime(2*p^3 + 3), s=concat(s, p))); s