A049488 - OEIS

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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

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OFFSET

1,1

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

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.

EXAMPLE

7 and 7+16=23 are prime.

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 *)

PROG

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

CROSSREFS

Cf. A001359, A023200, A023202.

Sequence in context: A136060 A023227 A031157 * A136051 A100750 A105435

Adjacent sequences: A049485 A049486 A049487 * A049489 A049490 A049491

KEYWORD

nonn,easy

AUTHOR

Labos Elemer

STATUS

approved