"""Return a list of the primes below n."""

prime = [True] * n

result = [2]

append = result.append

sqrt_n = (int(n ** .5) + 1) | 1 # ensure it's odd

for p in range(3, sqrt_n, 2):

if prime[p]:

append(p)

prime[p * p::2 * p] = [False] * ((n - p * p - 1) // (2 * p) + 1)

for p in range(sqrt_n, n, 2):

if prime[p]:

append(p)

"""check if some odd composite can be equal with p prime

# that part is a analytical solution for get the x num:

# the possible numbers to odd composite (not prime odd) is:

# :: odd = prime + 2 * x²

# so, x = sqrt((odd - prime) / 2), whose prime + 2 < odd.

# simplification can be done yet, but I will keep that way

# i don't know the limit, so we start until 10.000 primes and composites

primes = sieve5(heuristic_start)

# n > 1 & doesn't primes

composites = set(range(2, heuristic_start)) - set(primes)

for odd in filter(lambda x: x % 2 != 0, composites):

filtered_primes = filter(lambda x: odd > x - 2, primes)

if not any(goldbach(odd, p) for p in filtered_primes):

return odd