A058320 Distinct even prime-gap lengths (number of composites between primes), from 3+2, 7+4, 23+6,...

2, 4, 6, 8, 14, 10, 12, 18, 20, 22, 34, 24, 16, 26, 28, 30, 32, 36, 44, 42, 40, 52, 48, 38, 72, 50, 62, 54, 60, 58, 46, 56, 64, 68, 86, 66, 70, 78, 76, 82, 96, 112, 100, 74, 90, 84, 114, 80, 88, 98, 92, 106, 94, 118, 132, 104, 102, 110, 126, 120, 148, 108

Offset: 0

Author

Warren D. Smith, Dec 11 2000

Keywords

• hard
• nice
• nonn

Comments

Nicely and Nyman have sieved up to 1.3565*10^16 at least. They admit it is likely they have suffered from hardware or software bugs, but believe the probability the sequence up to this point is incorrect is <1 in a million. This sequence is presumably all even integers (in different order). It is not monotonic. The monotonic subsequence of record-breaking prime gaps is A005250.

Essentially the same as A014320. [From R. J. Mathar, Oct 13 2008]

Links

• Richard P. Brent, The first occurrence of large gaps between successive primes, Math. Comp. 27:124 (1973), 959-963.
• Thomas R. Nicely, New maximal prime gaps and first occurrences, Math. Comput. 68,227 (1999) 1311-1315.
• Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101]

Crossrefs

Cf. A008996, A005250.

Equals 2*A014321(n-1).

Programs

Mathematica

DeleteDuplicates[Differences[Prime[Range[2,200000]]]] (* Harvey P. Dale, Dec 07 2014 *)

Extensions

Comment corrected by Harvey P. Dale, Dec 07 2014