# gaps between primes

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)

- The gaps between primes (an expanded article on prime gaps)
- An extensive table of prime gaps by T. Nicely (updated very regularly)
- Gaps between consecutive primes by Tomás Oliveira e Silva (nice graphs!)

**References:**

- Brent74
R. P. Brent, "The distribution of small gaps between succesive primes,"Math. Comp.,28(1974) 315--324.MR 48:8356- Nicely99
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]- NN99
T. NicelyandB. Nyman, "First occurrence of a prime gap of 1000 or greater," preprint available at http://www.trnicely.net/index.html.- YP89
J. YoungandA. 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.]

Printed from the PrimePages <t5k.org> © Reginald McLean.