goldbach.py

"""
https://twitter.com/fermatslibrary/status/1067423316095508480

Today's paper is a good example of an unsolved conjecture being disproved by counterexample.
Goldbach stated that every positive odd integer is either prime or the sum of a prime and
twice a square. 5777 and 5993 are the only known counterexamples.
https://fermatslibrary.com/s/a-not-so-famous-goldbach-conjecture#email-newsletter
"""

# this is python 2, not python3
import sys

primes = [2, 3, 5, 7]

def test_primality(n):
    m = primes[-1] + 2
    while m ** 2 <= n:
        if test_primality(m):
            primes.append(m)
        m += 2
    for k in primes:
        if (n % k) == 0:
            return False
        if k ** 2 > n:
            break
    return True

def test_goldbach(n):
    test_primality((n + 1) ** 2)
    if n in primes:
        return True
    for p in primes:
        if p >= n:
            break
        diff = n - p
        halfdiff = 0.5 * diff
        sqrthalfdiff = halfdiff ** 0.5
        if sqrthalfdiff == int(sqrthalfdiff):
            return True
    return False

max = 10000
if len(sys.argv) > 1:
    max = int(sys.argv[1])

for i in range(3, max, 2):
    try:
        if not test_goldbach(i):
            print i
    except KeyboardInterrupt:
        print "Got as far as", i
        raise SystemExit

"""
Running this code => 5777, 5993
"""