[Edu-sig] Pythonic Math must include...

[Scott David Daniels]

michel paul wrote:
> ... An interesting fact is that, except for 2 and 3, all primes are adjacent 
> to a multiple of 6....
Having once been interested in prime pairs, I remember having written
a lot of code based on this "back in the day."  Here is my version of
your generator:

     def primes():
         for x in -1, 2, 3:
             yield x
         gen = primes().next
         for top in iter(gen, 3):
             pass # skip useless tests (we skip all multiples of 2 or 3)
         factors = []
         # get pump ready for a 5
         check = -1
         limit = 3 * 3 - 2 # How far will 3 work as top prime?
         factors = []
         while True:
             check += 6
             if check >= limit: # move if this pair needs another factor
                 top = gen()
                 limit = top * top - 2 # limit for both candidates
                 factors.append(top)
             for element in check, check + 2:
                 for factor in factors:
                     if element % factor == 0:
                         break
                 else:
                     yield element

--Scott David Daniels
Scott.Daniels at Acm.Org