A230227 Primes p with 3*p - 10 also prime.

5, 7, 11, 13, 17, 19, 23, 31, 37, 41, 47, 53, 59, 61, 67, 79, 83, 89, 97, 101, 107, 109, 131, 137, 151, 157, 163, 167, 173, 191, 193, 199, 223, 229, 251, 257, 269, 277, 283, 307, 313, 317, 331, 347, 353, 367, 373, 397, 401, 409

Offset: 1

Author

Zhi-Wei Sun, Oct 12 2013

Keywords

• nonn

Comments

Conjecture: For any integer n > 4 not equal to 76, we have 2*n = p + q for some terms p and q from the sequence.

This is stronger than Goldbach's conjecture for even numbers.

Examples

			a(1) = 5 since 3*5 - 10 = 5 is prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
• Zhi-Wei Sun, Conjectures involving primes and quadratic forms, preprint, arXiv:1211.1588.

Crossrefs

Cf. A000040, A002375, A230138, A230140, A230141, A230217, A230219, A230223, A230224, A230230.

Programs

Mathematica

PQ[p_]:=PQ[p]=p>3&&PrimeQ[3p-10]
m=0
Do[If[PQ[Prime[n]],m=m+1;Print[m," ",Prime[n]]],{n,1,80}]
Select[Prime[Range[100]],PrimeQ[3#-10]&] (* Harvey P. Dale, Jun 28 2015 *)