A124588 Primes p such that q - p <= 2, where q is the next prime after p.

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

Offset: 1

Author

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

Keywords

• nonn

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

Numbers k such that sigma(k*(k+2)) = (k+1)*(k+3). - Wesley Ivan Hurt, May 08 2022

Links

• 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

Crossrefs

Cf. A001359.

Programs

Mathematica

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

PARI

twinl(n) = { c=0; x=1; while(cCino Hilliard, Mar 29 2008