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With the recent interest in Mersenne primes, I got thinking whether there was any mathematical expression for the pattern of intervals (or sequence composed of interval lengths) between ordinary prime numbers. For example, for the first ten primes,

2 3 5 7 11 13 17 19 23 29

The sequence would be:

1 2 2 4 2 4 2 4 6

Has anyone in mathematics taken enough interest in these intervals to express them as the sequence of a formula, or even give the sequence (if it's random can't be expressed with a formula) a name?

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up vote 1 down vote accepted

See the terminology used, prime gap,

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Some references and information are also listed in the The On-Line Encyclopedia of Integer Sequences.

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