e46.py

#!/usr/bin/env python3
import pytest
from itertools import islice, count, takewhile, tee
from math import sqrt


def divisable(a, b):
    return a % b == 0


def _prime_gen():
    yield 2
    primes = set()
    for n in count(3, 2):
        for p in primes:
            if divisable(n, p):
                break
        else:
            yield n
            primes.add(n)


_prime_gen_singleton = _prime_gen()
def prime_gen():
    global _prime_gen_singleton
    _prime_gen_singleton, ret = tee(_prime_gen_singleton, 2)
    return ret


def is_twice_a_square(n):
    if n % 2 == 1:
        return False
    s = n // 2
    r = int(sqrt(s))
    return r ** 2 == s


def smallest_odd_non_goldbach():
    for n in count(3, 2):
        for p in takewhile(lambda x: x <= n, prime_gen()):
            if is_twice_a_square(n - p):
                break
        else:
            return n


def test_prime_gen():
    primes = [2, 3, 5, 7, 11, 13, 17, 19, 23]
    assert list(islice(prime_gen(), len(primes))) == primes


@pytest.mark.parametrize("input,expected", [
    (0, True),
    (1, False),
    (2, True),
    (3, False),
    (4, False),
    (8, True),
    (12, False),
    (18, True),
])
def test_is_twice_a_square(input, expected):
    assert is_twice_a_square(input) == expected


def test_smallest_odd_non_goldbach():
    assert smallest_odd_non_goldbach() == 5777


if __name__ == '__main__':
    print(smallest_odd_non_goldbach())