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A124596
Primes p such that q-p = 30, where q is the next prime after p.
10
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
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.
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
See also A052187 and references therein.
Sequence in context: A204400 A271104 A234164 * A224522 A210263 A165067
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 19 2006
STATUS
approved