def primes(limit):
    """
    generate lazy (finite) sequence of primes below limit

    >>> list(primes(100))
    [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
    >>> sum(primes(1000*1000))
    37550402023

    """
    sieve = [False]*limit

    for j in xrange(2, limit):
        if sieve[j]: continue
        yield j # got new prime
        if j*j > limit: continue # optimization
        for i in xrange(j, limit, j):
            sieve[i] = True # fastest to just update even if redundant

if __name__ == '__main__':
    import doctest
    doctest.testmod()

    from timeit import timeit
    print("starting timing tests...")
    print(timeit("sum(primes(100*1000))", "from __main__ import primes", number=100)/100)
    print(timeit("sum(primes(1000*1000))", "from __main__ import primes", number=10)/10)
    print(timeit("sum(primes(10*1000*1000))", "from __main__ import primes", number=3)/3)
    print("done with timing tests...")