A240126 Primes p such that p - 2 and p^3 - 2 are also prime.

19, 31, 109, 151, 241, 619, 859, 1489, 1951, 2131, 2791, 2971, 3559, 4129, 4651, 4789, 4801, 5659, 6661, 6781, 7591, 8221, 8629, 8821, 8971, 9241, 9721, 9931, 10891, 11971, 12109, 12541, 13831, 14011, 15271, 15289, 15331, 16831, 17029, 17419, 17839, 17989, 18121, 18541, 20149, 20899, 21019

Offset: 1

Author

K. D. Bajpai, Apr 01 2014

Keywords

• nonn

Comments

All the terms in the sequence are congruent to 1 mod 3.

Examples

			19 is in the sequence because 19 is a prime: 19 - 2 = 17 and 19^3 - 2 = 6857 are also prime.
151 is in the sequence because 151 is a prime: 151 - 2 = 149 and 151^3 - 2 = 3442949 are also prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..3085

Crossrefs

Intersection of A006512 and A178251.

Cf. A048637, A140454, A175234, A236687, A236688, A240110.

Programs

Maple

KD := proc() local a,b,d; a:=ithprime(n); b:=a-2; d:=a^3-2;  if isprime(b)and isprime(d) then RETURN (a); fi; end: seq(KD(), n=1..10000);

Mathematica

Select[Prime[Range[2000]], PrimeQ[# - 2] && PrimeQ[#^3 - 2] &]

PARI

s=[]; forprime(p=2, 22000, if(isprime(p-2) && isprime(p^3-2), s=concat(s, p))); s \\ Colin Barker, Apr 02 2014