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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 Numbers k such that sigma(k*(k+2)) = (k+1)*(k+3). - Wesley Ivan Hurt, May 08 2022 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) twinl(n) = { c=0; x=1; while(c

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Last modified September 11 01:27 EDT 2024. Contains 375813 sequences. (Running on oeis4.)