A230217 List of those primes p with p + 6 and 3*p + 8 also prime.

5, 7, 11, 13, 17, 31, 41, 47, 53, 61, 73, 83, 101, 103, 131, 151, 157, 167, 193, 223, 251, 263, 271, 277, 307, 311, 347, 367, 433, 563, 571, 593, 601, 613, 641, 647, 677, 733, 823, 857, 977, 1097, 1117, 1217, 1223, 1231, 1291, 1301, 1361, 1427

Offset: 1

Author

Zhi-Wei Sun, Oct 11 2013

Keywords

• nonn

Comments

Clearly, no term is congruent to 4 modulo 5.

This sequence is interesting because of the conjecture in the comments in A230219.

Examples

			a(1) = 5 since neither 2 + 6 nor 3 + 6 is prime, but 5 + 6 = 11 and 3*5 + 8 = 23 are both prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023201, A230219.

Programs

Mathematica

PQ[p_]:=PrimeQ[p+6]&&PrimeQ[3p+8]
m=0
Do[If[PQ[Prime[n]],m=m+1;Print[m," ",Prime[n]]],{n,1,225}]
Select[Prime[Range[300]],AllTrue[{#+6,3#+8},PrimeQ]&] (* Harvey P. Dale, Sep 01 2023 *)