Python Atkin

atkin_f.py

def atkin(buffer, end):
    limit = int(math.ceil(math.sqrt(end)))
    
    for x in range(1, limit + 1):
        x2 = x * x
        x2_3 = 3 * x2

        for y in range(1, limit + 1):
            y2 = y * y

            n = 4 * x2 + y2
            if (n < end) and (n % 12 == 1 or n % 12 == 5):
                buffer[n] = not buffer[n]

            n = x2_3 + y2
            if (n < end) and (n % 12 == 7):
                buffer[n] = not buffer[n]

            n = x2_3 - y2
            if (x > y) and (n < end) and (n % 12 == 11):
                buffer[n] = not buffer[n]

    for n in range(5, limit+1):
        if buffer[n]:
            k = n * n
            m = k
            i = 1
            
            while m < end:
                buffer[m] = False
                i += 2
                m = i * k

    buffer[2] = True
    buffer[3] = True
    return buffer