A124589 Primes p such that q-p <= 4, where q is the next prime after p.

2, 3, 5, 7, 11, 13, 17, 19, 29, 37, 41, 43, 59, 67, 71, 79, 97, 101, 103, 107, 109, 127, 137, 149, 163, 179, 191, 193, 197, 223, 227, 229, 239, 269, 277, 281, 307, 311, 313, 347, 349, 379, 397, 419, 431, 439, 457, 461, 463, 487, 499, 521, 569, 599, 613, 617, 641, 643, 659

Offset

1,1

Comments

Union of A124588 and A029710; complement of A124582. - Reinhard Zumkeller, Dec 23 2006

Links

R. Zumkeller, Table of n, a(n) for n = 1..1000

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

Formula

a(n) >> n log^2 n. Infinite under standard conjectures. - Charles R Greathouse IV, Jun 01 2016

Mathematica

Transpose[Select[Partition[Prime[Range[200]], 2, 1], Last[#]-First[#]<5&]][[1]] (* Harvey P. Dale, Apr 22 2013 *)

Prog

(PARI) is(n)=isprime(n) && (isprime(n+2) || isprime(n+4) || n==2) \\ Charles R Greathouse IV, Jun 01 2016

Crossrefs

CF. A029710, A124582, A124588.

Sequence in context: A127047 A119615 A061771 * A079150 A177000 A117843

Adjacent sequences: A124586 A124587 A124588 * A124590 A124591 A124592

Keyword

nonn

Author

N. J. A. Sloane, Dec 19 2006

Status

approved