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#!/usr/bin/python3
# Challenge 012
#
# Challenge #1
# The numbers formed by adding one to the products of the smallest primes are
# called the Euclid Numbers (see wiki). Write a script that finds the smallest
# Euclid Number that is not prime. This challenge was proposed by
# Laurent Rosenfeld.
import sys
from primePy import primes
def next_prime(n):
if n <= 1:
return 2
else:
n += 1
while not primes.check(n):
n += 1
return n
def euclid_iter():
prime = 1
prime_prod = 1
while True:
prime = next_prime(prime)
prime_prod *= prime
yield prime_prod+1
for n in euclid_iter():
if primes.check(n):
pass
else:
print(n)
break
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