Proof that 16 is an Erdős-Woods number

erdos-woods.py

from fractions import gcd

k = 0
a = 0
UPPER_CHECK = 10000
while True:
    while a < UPPER_CHECK:
        ew = True
        for i in xrange(a+1, a+k):
            if gcd(i, a) == 1 and gcd(i, a+k) == 1:
                ew = False
        if ew == True:
            print "Erdos Number:", k
            print "Proof:", a
            a = 0
            break
        a += 1
    a = 0
    k += 1