Sieve Of Atkin Implementation in Python

Question

I am trying to implement the algorithm of Sieve of Atkin given in Wikipedia Link as below:

Sieve Of Atkin

What I\'ve tried so far is the implementation in Py

Answer 1

Here is a solution

import math

def sieveOfAtkin(limit):
    P = [2,3]
    sieve=[False]*(limit+1)
    for x in range(1,int(math.sqrt(limit))+1):
        for y in range(1,int(math.sqrt(limit))+1):
            n = 4*x**2 + y**2
            if n<=limit and (n%12==1 or n%12==5) : sieve[n] = not sieve[n]
            n = 3*x**2+y**2
            if n<= limit and n%12==7 : sieve[n] = not sieve[n]
            n = 3*x**2 - y**2
            if x>y and n<=limit and n%12==11 : sieve[n] = not sieve[n]
    for x in range(5,int(math.sqrt(limit))):
        if sieve[x]:
            for y in range(x**2,limit+1,x**2):
                sieve[y] = False
    for p in range(5,limit):
        if sieve[p] : P.append(p)
    return P

print sieveOfAtkin(100)

Answer 2

You problem is that your limit is 100, but your is_prime list only has limit-5 elements in it due to being initialized with range(5, limit).

Since this code assumes it can access up to limit index, you need to have limit+1 elements in it: is_prime = [False] * (limit + 1)

Note that it doesn't matter that 4x^2+y^2 is greater than limit because it always checks n <= limit.