Riemann official code

# import numpy as np
import math

def is_prime(num):
    if num < 2:
        return False
    for i in range(2, int(num**0.5) + 1):
        if num % i == 0:
            return False
    return True

def generate_primes(to_x):
    prime_numbers = [ 2 ]
    x = 0
    while x < to_x:
        x += 1
        # First Law: A number, of square root, whose floor is equal to the square root,
        # being then an integer itself, must not be a prime.
        #
        # Second Law: The number may not be equal in a MOD of any previous prime.
        if ((x % 2 == 0) or (math.sqrt(x)) == math.floor(math.sqrt(x)) ):
            continue
        y = 1
        for i in prime_numbers:
            if (i != x) and (x % i == 0): # highly improved
                y = 0
                break
        if (y != 0):
            prime_numbers.append(x)
            x += 1
    return  (prime_numbers)

# Example usage:
start_x = 2
prime_numbers0 = generate_primes(1000)
g = 0
olist = []
for i in prime_numbers0:
    if is_prime(i):
        g += 1;
    else:
        olist.append(i)

print(f"{g} {len(prime_numbers0)} {len(olist)}")
print(prime_numbers0)
print(olist)