A023209 Primes p such that 3p + 4 is also prime.

3, 5, 11, 13, 19, 23, 31, 41, 53, 59, 73, 79, 89, 101, 103, 109, 131, 139, 151, 173, 179, 181, 191, 199, 223, 229, 241, 251, 269, 283, 293, 311, 331, 349, 353, 373, 383, 389, 409, 431, 433, 439, 509, 521, 541, 563, 593, 599, 619, 643, 661, 683, 709, 719, 733, 739, 761

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• easy

Comments

In order for 3p + 4 to also be in the sequence, it is a necessary but not sufficient condition that p is not congruent to 7 modulo 10. - Alonso del Arte, Nov 08 2018

Examples

			3 and 3 * 3 + 4 = 13 are both prime, so 3 is in the sequence.
5 and 3 * 5 + 4 = 19 are both prime, so 5 is in the sequence.
7 is prime but 3 * 7 + 4 = 25 = 5^2, which is not prime, so 7 is not in the sequence.
		

Links

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

Crossrefs

Cf. A258261 (3p - 4).

Programs

Magma

[n: n in [0..1000] | IsPrime(n) and IsPrime(3*n+4)]; // Vincenzo Librandi, Nov 18 2010

Mathematica

Select[Prime[Range[500]], PrimeQ[3# + 4] &] (* Harvey P. Dale, Mar 09 2014 *)

PARI

isok(p) = isprime(p) && isprime(3*p+4); \\ Michel Marcus, Nov 09 2018

Extensions

Name adjusted by Alonso del Arte, Nov 08 2018