Sieve of Eratosthenes - Finding Primes Python

Question

Just to clarify, this is not a homework problem :)

I wanted to find primes for a math application I am building & came across Sieve of Eratosthenes approach.

Answer 1

By combining contributions from many enthusiasts (including Glenn Maynard and MrHIDEn from above comments), I came up with following piece of code in python 2:

def simpleSieve(sieveSize):
    #creating Sieve.
    sieve = [True] * (sieveSize+1)
    # 0 and 1 are not considered prime.
    sieve[0] = False
    sieve[1] = False
    for i in xrange(2,int(math.sqrt(sieveSize))+1):
        if sieve[i] == False:
            continue
        for pointer in xrange(i**2, sieveSize+1, i):
            sieve[pointer] = False
    # Sieve is left with prime numbers == True
    primes = []
    for i in xrange(sieveSize+1):
        if sieve[i] == True:
            primes.append(i)
    return primes

sieveSize = input()
primes = simpleSieve(sieveSize)

Time taken for computation on my machine for different inputs in power of 10 is:

• 3 : 0.3 ms
• 4 : 2.4 ms
• 5 : 23 ms
• 6 : 0.26 s
• 7 : 3.1 s
• 8 : 33 s