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 Python given by following Code:

import math
is_prime = list()
limit = 100
for i in range(5,limit):
    is_prime.append(False)

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):
            # print "1st if"
            is_prime[n] = not is_prime[n]
        n = 3*x**2+y**2
        if n<= limit and n%12==7:
            # print "Second if"
            is_prime[n] = not is_prime[n]
        n = 3*x**2 - y**2
        if x>y and n<=limit and n%12==11:
            # print "third if"
            is_prime[n] = not is_prime[n]

for n in range(5,int(math.sqrt(limit))):
    if is_prime[n]:
        for k in range(n**2,limit+1,n**2):
            is_prime[k] = False
print 2,3
for n in range(5,limit):
    if is_prime[n]: print n

Now I get error as

is_prime[n] = not is_prime[n]
IndexError: list index out of range

this means that I am accessing the value in list where the index is greater than length of List. Consider the Condition when x,y = 100, then of-course the condition n=4x^2+y^2 will give value which is greater than length of list. Am I doing something wrong here? Please help.

EDIT 1 As suggested by Gabe, using

is_prime = [False] * (limit + 1)

insted of :

for i in range(5,limit):
    is_prime.append(False)

did solved the problem.

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.