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

Author

N. J. A. Sloane, Dec 19 2006

Keywords

• nonn

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

Crossrefs

CF. A029710, A124582, A124588.

Programs

Mathematica

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

PARI

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

Formula

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