def problem3(num):
""" Largest prime factor.
>>> problem3(13195)
29
>>> problem3(600851475143)
6857
"""
primes_dict = lib.prime_factors(num)
primes = primes_dict.keys()
primes.sort()
return primes[-1]
def problem12(n):
""" return first triangle number to have over n divisors.
where triangle number is the sum of first natural numbers.
>>> problem12(500)
76576500
>>> problem12(5)
28
"""
divisors, count = 1, 1
while divisors < n:
count += 1
triangle = lib.sum_frist_N_numbers(count)
primes_dict = lib.prime_factors(triangle)
divisors = lib.product(map(lib.increment, primes_dict.values()))
return triangle
# -*- coding: utf-8 -*- """ Created on Thu Jul 21 06:37:11 2016 @author: robbie """ import lib reload(lib) n = 600851475143 #n = 10086647L print(lib.prime_factors(n,999999))
from lib import prime_factors def multiples(n): for i in xrange(1, (n/2)): if n % i == 0: yield i if __name__ == '__main__': print(max(prime_factors(600851475143)))
from lib import prime_factors
def multiples(n):
for i in xrange(1, (n / 2)):
if n % i == 0:
yield i
if __name__ == '__main__':
print(max(prime_factors(600851475143)))
#!/usr/bin/env python3
import lib
from collections import Counter
# The prime factors of each number 1 to 20
counts = ([Counter(lib.prime_factors(i)) for i in range(2, 21)])
total = Counter()
# Get the max count of each factor
for count in counts:
for n in count:
if total[n] < count[n]:
total[n] = count[n]
res = lib.multiply([n**total[n] for n in total.keys()])
print(res)
#!/usr/bin/env python3
import lib
from collections import Counter
N = 1000000
D = 4
for i in range(N):
pfactors = set()
ok = True
j = 0
while j < D and ok:
f = Counter(lib.prime_factors(i + j))
if len(f.keys()) != D:
ok = False
if ok:
pfactors.update(f.items())
j += 1
if ok and len(pfactors) == D * D:
print(i)
break
#!/usr/bin/env python3 import lib N = 600851475143 print(max(lib.prime_factors(N)))
