'''
It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.

9 = 7 + 2×12
15 = 7 + 2×22
21 = 3 + 2×32
25 = 7 + 2×32
27 = 19 + 2×22
33 = 31 + 2×12

It turns out that the conjecture was false.

What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
'''

# So I guess I just go past all odd non-prime numbers and keep subtracting all double squares that fit and see if the rest is a prime

import math
import numpy as np

def sieve(n):
    assert n > 1

    ns = [True] * n

    for i in range(2, math.ceil(np.sqrt(n))):
        if ns[i]:
            j = pow(i, 2)

            while j < n:
                ns[j] = False
                j = j + i

    return [i for i,val in enumerate(ns) if val][2:]

def main():
    print("Hello this is Patrick")

    end = 10000

    primes = set(sieve(end))

    for n in range(9, end, 2):
        termination = True

        if n not in primes:
            x = 1
            while n - 2 * x*x > 0:
                if n - 2 * x*x in primes:
                    termination = False
                    break
                
                x += 1
            
            if termination:
                print(n)
                break

if __name__ == "__main__":
    main()