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A124588 Primes p such that q-p <= 2, where q is the next prime after p. 7
2, 3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487, 1607 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Consists of 2 together with the lower members of twin primes, A001359. See the latter entry for references.

"Assuming certain (admittedly difficult) conjectures on the distribution of primes in arithmetic progressions, [Goldston-Pintz-Yildirim] prove the existence of infinitely many prime pairs that differ at most by 16." - Soundararajan

Lesser of twin primes together with 2; union with A029710 gives A124589. - Reinhard Zumkeller, Dec 23 2006

Primes p such that either p+3/2+-1/2 is prime. [Juri-Stepan Gerasimov, Jan 29 2010]

The prime differences of 2 primes (without repetition). [Juri-Stepan Gerasimov, Jun 01 2010, Jun 08 2010]

LINKS

Table of n, a(n) for n=1..52.

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

Index entries for primes, gaps between

MATHEMATICA

Transpose[Select[Partition[Prime[Range[300]], 2, 1], #[[2]]-#[[1]]<3&]] [[1]] (* Harvey P. Dale, Feb 11 2015 *)

PROG

(PARI) print1(2", "); (for(x=1, 200, print1(twinl(x)", "))) \\ Cino Hilliard, Mar 29 2008

CROSSREFS

Cf. A001359.

Sequence in context: A038909 A073534 A063091 * A059428 A084571 A345471

Adjacent sequences:  A124585 A124586 A124587 * A124589 A124590 A124591

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 19 2006; edited May 15 2008 at the suggestion of R. J. Mathar

STATUS

approved

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Last modified October 26 08:00 EDT 2021. Contains 348267 sequences. (Running on oeis4.)