A007693 Primes p such that 6*p + 1 is also prime.

2, 3, 5, 7, 11, 13, 17, 23, 37, 47, 61, 73, 83, 101, 103, 107, 131, 137, 151, 173, 181, 233, 241, 257, 263, 271, 277, 283, 293, 311, 313, 331, 347, 367, 373, 397, 443, 461, 467, 503, 557, 577, 593, 601, 607, 641, 653, 661, 683, 727, 751, 761, 773, 787, 797, 853

Offset: 1

Author

N. J. A. Sloane and Robert G. Wilson v

Keywords

• nonn
• easy

References

• Joe Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 83.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)
• Andrew Granville, Sophie Germain's theorem for prime pairs p, 6p+1, J. Number Theory 27 (1987), no. 1, 63-72.

Crossrefs

Cf. A002476, A016921, A024899, A051644, A091178, A023256 (subset: 6*(6p+1)+1 also prime).

Prime terms of A024899.

Programs

Magma

[n: n in [0..1000] | IsPrime(n) and IsPrime(6*n+1)]; // Vincenzo Librandi, Nov 18 2010

Mathematica

Select[Prime@Range[150], PrimeQ[6# + 1] &] (* Ray Chandler, Mar 14 2007  *)

PARI

isok(k) = isprime(k) && isprime(6*k+1); \\ Amiram Eldar, Feb 24 2025

Formula

a(n) = (A051644(n)-1)/6.

Extensions

Extended by Ray Chandler, Mar 14 2007