def solve():
n = 600851475143
greatest = 0
for prime in prime_gen():
if(n < prime):
break
if(n % prime == 0):
greatest = prime
n = n / prime
else:
continue
print greatest
It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.
9 = 7 + 2 x 1^2
15 = 7 + 2 x 2^2
21 = 3 + 2 x 3^2
25 = 7 + 2 x 3^2
27 = 19 + 2 x 2^2
33 = 31 + 2 x 1^2
It turns out that the conjecture was false.
What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
"""
from eulertools import prime_gen
primes = prime_gen(10000)
odd_comps = {o for o in range(1, 10001) if o % 2 != 0} - set(primes)
found = False
for odd_comp in odd_comps:
for prime in primes:
if prime >= odd_comp:
break
num = ((odd_comp - prime)/2) ** 0.5
if int(num) != num:
found = True
else:
found = False
break
if found:
print odd_comp
"""
The number can't have 5 digits because it will be divisible by 3 ( 1+2+3+4+5 = 15)
Similarly, 8 digits and 9 digits wouldn't work as well.
And the minimum digits is 4 from the example. Thus we are looking for a prime of 7 digits
"""
from eulertools import prime_gen
primes = prime_gen(7654321)
for i in range(len(primes) - 1, 0, -1):
p = primes[i]
s = str(p)
if len(s) == len(set(s)):
if set(s) == set(str(i) for i in range(1, len(s) + 1)):
print p
break
