A124590 Primes p such that q-p <= 6, where q is the next prime after p.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 97, 101, 103, 107, 109, 127, 131, 137, 149, 151, 157, 163, 167, 173, 179, 191, 193, 197, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 277, 281, 307, 311, 313, 331, 347, 349, 353, 367

Offset

1,1

Comments

Goldston, Graham, Pintz, & Yilidirm give a conditional proof that this sequence is infinite; see their Theorem 4. - Charles R Greathouse IV, Jul 31 2013

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

D. A. Goldston, S. W. Graham, J. Pintz, C. Y. Yilidirm, Small gaps between primes or almost primes (2005)

K. Soundararajan, Small gaps between prime numbers: the work of Goldston-Pintz-Yildirim, Bull. Amer. Math. Soc. 44 (2007), pp. 1-18.

Index entries for primes, gaps between

Formula

A000040 MINUS A083371. - R. J. Mathar, Jun 15 2008

A124589 UNION A031924. - R. J. Mathar, Jan 23 2022

a(n) >> n log^2 n. - Charles R Greathouse IV, Jan 31 2017

Prog

(PARI) v=List([2]); p=3; forprime(q=5, 1e3, if(q-p<=6, listput(v, p)); p=q); Vec(v) \\ Charles R Greathouse IV, Jul 31 2013
(PARI) list(lim)=my(v=List(), p=2); forprime(q=3, nextprime(lim\1+1), if(q-p<7, listput(v, p)); p=q); Vec(v) \\ Charles R Greathouse IV, Jan 31 2017

Crossrefs

Cf. A083371, A124589, A031924.

Sequence in context: A061022 A238852 A079152 * A049573 A038616 A228296

Adjacent sequences: A124587 A124588 A124589 * A124591 A124592 A124593

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 19 2006

Status

approved