Finding primes is a programming rite of passage and very frequently a first serious program someone crates (usually with trial division).

But primes alone are already worn out. A next far more interesting thing is to get the prime gaps: the so-far-longest gaps between consecutive primes. These are quite rare and "precious". A first few pairs and their differences are:

2 3 1
3 5 2
7 11 4
23 29 6
89 97 8
113 127 14
...

My father used to calculate these by hand for fun up to 10k. Let's see how short a code you can get.

Rules:

• no builtin functions for prime testing, prime generation or prime gaps
• no retrieving http://oeis.org/A002386 or similar (I can smell you cheaters from far away :) )
• no precomputed arrays
• keep printing until your internal integer type fails on you

Lowest character count wins. +10 characters if you only print the gaps without the primes.

You can also show off versions with builtin functions if they are interesting. Be creative.