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?