Python Eratosthenes Sieve Algorithm Optimization

Question

I\'m attempting to implement the Sieve of Eratosthenes. The output seems to be correct (minus \"2\" that needs to be added) but if the input to the function is larger than 1

Answer 1

I followed this link: Sieve of Eratosthenes - Finding Primes Python as suggested by @MAK and I've found that the accepted answer could be improved with an idea I've found in your code:

def primes_sieve2(limit):
    a = [True] * limit               # Initialize the primality list
    a[0] = a[1] = False
    sqrt = int(math.sqrt(limit))+1
    for i in xrange(sqrt):
        isprime = a[i]
        if isprime:
            yield i
            for n in xrange(i*i, limit, i):     # Mark factors non-prime
                a[n] = False
    for (i, isprime) in enumerate(a[sqrt:]):
        if isprime:
            yield i+sqrt