findPrimes (sieve of Atkin)

local function findPrimes(range)
    local lim, num, j;
    local is_prime = {};
    is_prime[2] = true;
    is_prime[3] = true;
    for i = 5, range do
        is_prime[i] = false;
    end
    local lim = math.ceil(math.sqrt(range));
    for x = 1, lim do
        for y = 1, lim do
            num = (4 * x^2 + y^2);
            if(num <= range and (num % 12 == 1 or num % 12 == 5)) then
                is_prime[num] = true;
            end
            num = (3 * x^2 + y^2);
            if(num <= range and (num % 12 == 7)) then
                is_prime[num] = true;
            end
            if(x > y) then
                num = (3 * x^2 - y^2);
                if(num <= range and (num % 12 == 11)) then
                    is_prime[num] = true;
                end
            end
        end
    end
    for i = 5, lim do
        if(is_prime[i]) then
            j = i^2;
            while(j <= range) do
                is_prime[j] = false;
                j = j + i;
            end
        end
    end
    local primes = {};
    for i = 2, range do
        if(is_prime[i]) then
            table.insert(primes, i);
        end
    end
    table.sort(primes);
    return primes;
end