Look at the first few primes: 2, 3, 5, 7, 11, and 13. Notice
they have irregular gaps between them: 2 is followed immediately by
the prime 3, 3 is followed by one composite, 5 by one, but 7 by three.
We call the number of composites following a prime the length of
the prime gap. For example, the prime gaps after 2, 3, 5 and
seven are 0, 1, 1 and 3 respectively. By the prime number theorem, the
"average gap" between primes less than n is log(n). See
the page on prime gaps (linked below) for much more information.
Warning: Some authors define the prime gap to be the
difference between consecutive primes, this is a number one larger
than our definition.
See Also: TwinPrime, JumpingChampion, GilbreathsConjecture
Related pages (outside of this work)
- R. P. Brent, "The distribution of small gaps between succesive primes," Math. Comp., 28 (1974) 315--324. MR 48:8356
- T. Nicely, "New maximal prime gaps and first occurrences," Math. Comp., 68:227 (July 1999) 1311--1315. MR 99i:11004 (Abstract available) [Reprint available at http://www.trnicely.net/index.html]
- T. Nicely and B. Nyman, "First occurrence of a prime gap of 1000 or greater," preprint available at http://www.trnicely.net/index.html.
- J. Young and A. Potler, "First occurrence prime gaps," Math. Comp., 53:185 (1989) 221--224. MR 89f:11019 [Lists gaps between primes up to the 777 composites following 42842283925351.]