Prime number generator

[Ian Kelly]

On Wed, Jul 10, 2013 at 8:00 AM, Chris Angelico <rosuav at gmail.com> wrote:
> And now for something completely different.
>
> I knocked together a prime number generator, just for the fun of it,
> that works like a Sieve of Eratosthenes but unbounded. It keeps track
> of all known primes and the "next composite" that it will produce -
> for instance, after yielding 13, the prime map will be {2: 20, 3: 18,
> 5: 20, 7: 21, 11: 22, 13: 26}, each one mapped to the first multiple
> greater than 13.

Cool! I have a similar generator, and instead of mapping primes to
next composites, it maps next composites to lists of primes.  It works
using increment-by-2 and checking the dictionary rather than searching
for the min of the dictionary.  You could though adapt that data
structure and just use min(prime) to find the next composite (although
as somebody else noted, a heap would probably be more efficient).

The other interesting thing about my sieve is that it's a recursive
generator.  I'll dig it up later and share it.