A124596 Primes p such that q-p = 30, where q is the next prime after p.

4297, 4831, 5351, 5749, 6491, 6917, 7253, 7759, 7963, 8389, 8893, 13063, 13187, 13933, 13967, 14251, 14983, 16381, 16573, 17627, 18553, 18869, 20563, 21283, 21347, 21617, 23633, 23689, 24251, 25189, 26053, 26597, 27299, 27367, 27551, 28319, 28979, 29537

Offset

1,1

Comments

These are the primes p = prime(k) where A001223(k) = 30. - N. J. A. Sloane, Dec 25 2019

Primes p such that r-q=q-p=30, where p, q, r are three successive primes, are A052195 = (69593, 110651, 134609, 228647, 237791, 250889, 303157, 24907,...). Primes p such that s-r=r-q=q-p=30, where p, q, r, s are four successive primes, are A052243 = (642427, 1058861, 3431903, 4176587, 4560121, 4721047, 5072269, 5145403, ...). - Zak Seidov, Dec 20 2006, edited by M. F. Hasler, Apr 04 2013

Links

Remi Eismann, Table of n, a(n) for n = 1..10000

K. Soundararajan, Small gaps between prime numbers: The work of Goldston-Pintz-Yildirim, Bull. Amer. Math. Soc., 44 (2007), 1-18. DOI: 10.1090/S0273-0979-06-01142-6

K. Soundararajan, Small gaps between prime numbers: The work of Goldston-Pintz-Yildirim, arXiv:math/0605696 [math.NT], 2006.

Index entries for primes, gaps between

Mathematica

max = 30000;
Reap[For[p = 2; q = 3, p < max, p = q, q = NextPrime[p]; If[q - p == 30, Sow[p]]]][[2, 1]] (* Jean-François Alcover, Sep 02 2018 *)
Select[Partition[Prime[Range[5000]], 2, 1], #[[2]]-#[[1]]==30&][[All, 1]] (* Harvey P. Dale, Dec 25 2019 *)

Crossrefs

Cf. A001223, A052195, A052243.

See also A052187 and references therein.

Sequence in context: A204400 A271104 A234164 * A224522 A210263 A165067

Adjacent sequences: A124593 A124594 A124595 * A124597 A124598 A124599

Keyword

nonn

Author

N. J. A. Sloane, Dec 19 2006

Status

approved