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A124590
Primes p such that q-p <= 6, where q is the next prime after p.
2
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 97, 101, 103, 107, 109, 127, 131, 137, 149, 151, 157, 163, 167, 173, 179, 191, 193, 197, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 277, 281, 307, 311, 313, 331, 347, 349, 353, 367
OFFSET
1,1
COMMENTS
Goldston, Graham, Pintz, & Yilidirm give a conditional proof that this sequence is infinite; see their Theorem 4. - Charles R Greathouse IV, Jul 31 2013
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
D. A. Goldston, S. W. Graham, J. Pintz, C. Y. Yilidirm, Small gaps between primes or almost primes (2005)
K. Soundararajan, Small gaps between prime numbers: the work of Goldston-Pintz-Yildirim, Bull. Amer. Math. Soc. 44 (2007), pp. 1-18.
FORMULA
A000040 MINUS A083371. - R. J. Mathar, Jun 15 2008
A124589 UNION A031924. - R. J. Mathar, Jan 23 2022
a(n) >> n log^2 n. - Charles R Greathouse IV, Jan 31 2017
PROG
(PARI) v=List([2]); p=3; forprime(q=5, 1e3, if(q-p<=6, listput(v, p)); p=q); Vec(v) \\ Charles R Greathouse IV, Jul 31 2013
(PARI) list(lim)=my(v=List(), p=2); forprime(q=3, nextprime(lim\1+1), if(q-p<7, listput(v, p)); p=q); Vec(v) \\ Charles R Greathouse IV, Jan 31 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 19 2006
STATUS
approved