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

if given unlimited memory and time, the following code will print all the prime numbers. and it'll do it without using trial division. it is based on the haskell code in the paper: The Genuine Sieve of Eratosthenes by Melissa E. O'Neill

from heapq import heappush, heappop, heapreplace
def sieve():
    w = [2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2,6,4,2,4,2,10,2,10]
    for p in [2,3,5,7]: print p
    n,o = 11,0
    t = []
    l = len(w)
    p = n
    heappush(t, (p*p, n,o,p))
    print p
    while True:
        n,o = n+w[o],(o+1)%l
        p = n
        if not t[0][0] <= p:
            heappush(t, (p*p, n,o,p))
            print p
            continue
        while t[0][0] <= p:
            _, b,c,d = t[0]
            b,c = b+w[c],(c+1)%l
            heapreplace(t, (b*d, b,c,d))
sieve()