#! /usr/bin/env python """\ Largest prime factor Problem 3 The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ?\ """ from eulerutils import get_primes n = 600851475143 greatest_prime = 0 for prime in get_primes(n): if n % prime == 0: if prime > greatest_prime: greatest_prime = prime # In order to avoid going through all the primes from # 2 to sqrt(n) take advantage of the Fundamental # Theorem of Arithmetic, and reduce n by each of its # prime factors as much as possible. while n % prime == 0: n /= prime if n == 1: # Since 1 is divisible only by itself, there is no more # work to be done. break print greatest_prime
#! /usr/bin/env python
# coding: utf-8
"""\
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.\
\
What is the 10 001st prime number?\
"""
if __name__ == "__main__":
from eulerutils import get_primes
import sys
prime_goal = 10001
cntr = 0
for prime in get_primes():
cntr += 1
if cntr == prime_goal:
break
print cntr, prime
