A049488 Primes p such that p+16 is prime.

3, 7, 13, 31, 37, 43, 67, 73, 97, 151, 157, 163, 181, 211, 223, 241, 277, 331, 337, 367, 373, 433, 463, 487, 541, 547, 571, 577, 601, 631, 643, 661, 727, 757, 811, 823, 937, 967, 997, 1033, 1087, 1093, 1171, 1201, 1213, 1291, 1303, 1423, 1471, 1483, 1543

Offset: 1

Author

Labos Elemer

Keywords

• nonn
• easy

Comments

Using the Elliott-Halberstam conjecture, Goldston et al. prove that there are an infinite number of primes here. - T. D. Noe, Nov 26 2013

Examples

			7 and 7+16=23 are prime.
		

References

• P. D. T. A. Elliott and H. Halberstam, A conjecture in prime number theory, Symposia Mathematica, Vol. IV (INDAM, Rome, 1968/69), pages 59-72, Academic Press, London, 1970.

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms up to a(1000) by T. D. Noe)
• D. A. Goldston, J. Pintz, and C. Y. Yildirim, Primes in Tuples I, arXiv:math/0508185 [math.NT], Aug 10 2005.
• A. Granville and G. Martin, Prime number races, arXiv:math/0408319 [math.NT], Aug 24 2004.

Crossrefs

Cf. A001359, A023200, A023202.

Programs

Mathematica

Select[Range[1000], PrimeQ[#] && PrimeQ[#+16]&] (* Vladimir Joseph Stephan Orlovsky, Dec 25 2008 *)
Select[Prime[Range[250]],PrimeQ[#+16 ]&] (* Harvey P. Dale, Oct 30 2015 *)

PARI

select(p->isprime(p+16),primes(100)) \\ Charles R Greathouse IV, Jul 08 2013