I wrote a prime number generator using Sieve of Eratosthenes and Python 3.1. The code runs correctly and gracefully at 0.32 seconds on ideone.com to generate prime numbers up to 1,000,000.

# from bitstring import BitString

def prime_numbers(limit=1000000):
    '''Prime number generator. Yields the series
    2, 3, 5, 7, 11, 13, 17, 19, 23, 29 ...    
    using Sieve of Eratosthenes.
    '''
    yield 2
    sub_limit = int(limit**0.5) 
    flags = [False, False] + [True] * (limit - 2)   
#     flags = BitString(limit)
    # Step through all the odd numbers
    for i in range(3, limit, 2):       
        if flags[i] is False:
#        if flags[i] is True:
            continue
        yield i
        # Exclude further multiples of the current prime number
        if i <= sub_limit:
            for j in range(i*3, limit, i<<1):
                flags[j] = False
#                flags[j] = True

The problem is, I run out of memory when I try to generate numbers up to 1,000,000,000.

    flags = [False, False] + [True] * (limit - 2)   
MemoryError

As you can imagine, allocating 1 billion boolean values (1 byte 4 or 8 bytes (see comment) each in Python) is really not feasible, so I looked into bitstring. I figured, using 1 bit for each flag would be much more memory-efficient. However, the program's performance dropped drastically - 24 seconds runtime, for prime number up to 1,000,000. This is probably due to the internal implementation of bitstring.

You can comment/uncomment the three lines to see what I changed to use BitString, as the code snippet above.

My question is, is there a way to speed up my program, with or without bitstring?