There is unfortunately no known pattern to the sequence of gaps between consecutive primes, but mathematicians did manage to prove that the density of primes below a given number x converges to a nice function of x. That function is Li(x), the logarithmic integral function. See Mathworld reference:
Like bubba-math said, there is no pattern in the sequence of prime numbers. I wish there was, though. The largest known prime number right now has nearly 13 million digits and the computer that got the answer was able to claim a $100,000 for being the first to find a prime number with more than 10 million digits.
Prizes are still available for the first ones who can find a prime number with more than 100 million digits ($150,000) and another for one with a billion digits ($250,000).
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