from tools import number_theory
import math

def try_root(n):
    root = int(n ** 0.5)
    if root ** 2 == n:
        return root
    raise ValueError

def solve(p, k):
    num, mod = divmod((3 * k + try_root(k * (4 * p - 3 * k))) * k, 2 * (p - 3 * k))
    if not mod:
        return num
    raise ValueError

def try_n(p, offset):
    for k in range(int(p * offset) + 1, p // 3 + 1):
        try:
            return solve(p, k), k / p
        except:
            pass

def find(limit):
    offset = 0
    for p in number_theory.make_prime(limit):
        try:
            solve, offset = try_n(p, offset)
            print(solve, offset)
            yield solve
        except:
            pass

print(list(find(1000000)))