I had this post saved as a draft for quite awhile. Python’s reliance on indentions made finding a code formatting plugin mandatory. This isn’t the fastest Python prime number generator, but it’s pretty good. I saw one somewhere else that was twice as fast, but it was a bit obtuse. This is a slight variation on the Sieve of Eratosthenes.


#------------------------------------------------------–
# optimized sieve - pretty good and still understandable
#                        generates primes up to 'limit'
#------------------------------------------------------–
def fast_primes( limit ):
  if limit < 2:
    return []
   elif limit == 2:
        return [2]
    # fill the array with odds
    map = range(3,limit+1,2)
    stopat = limit ** 0.5
    cur = mstart = 3
    # only go up to the sqrt of the limit
    while cur <= stopat:
        multy = limit / cur
          while( mstart <= multy ):
              idx =  ( cur*mstart-3 )/2
              map[idx] = 0
              mstart += 2
        # get rid of this multiplier
        mstart = cur + 2
        # move up to the next digit
        cur += 2
  
    return [2] + [x for x in map if x]