A051647 Primes p such that 210*p + 1 is also prime.

2, 3, 5, 7, 11, 13, 17, 23, 29, 47, 53, 59, 67, 73, 83, 89, 101, 137, 139, 157, 163, 179, 181, 191, 193, 223, 229, 251, 271, 277, 281, 313, 317, 347, 349, 353, 359, 401, 419, 421, 431, 433, 449, 457, 463, 479, 523, 577, 599, 601, 631, 653, 701, 709, 719, 727

Offset: 1

Author

Labos Elemer

Keywords

• nonn
• easy

Comments

Analogous to A005384, Sophie Germain primes.

A002110(4)*p + 1 = 210*p + 1 and p are both primes.

Examples

			11 is in the sequence because 210*11 + 1 = 2311 is also prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)

Crossrefs

Cf. A005384, A005385, A007693, A051648.

Programs

Magma

[p: p in PrimesUpTo(900) | IsPrime(210*p+1)]; // Vincenzo Librandi, Apr 11 2013

Mathematica

Select[Prime[Range[200]],PrimeQ[210#+1]&]  (* Harvey P. Dale, Apr 25 2011 *)

PARI

isok(k) = isprime(k) && isprime(210*k+1); \\ Amiram Eldar, Feb 24 2025

Formula

a(n) = (A051648(n)-1)/210. - Amiram Eldar, Feb 24 2025