def pe012():
"""Find the smallest triangular number with over 500 divisors"""
from tools import triangularGenerator, factorize
gen = triangularGenerator()
while True:
num = next(gen)
if len(factorize(num)) > 500:
return num
def mod_sqrt(x, n, fact_n = []):
if x == 0 or n == 0:
return [0]
elif n == 1:
if x == 0:
return [0]
else:
return [1]
if not fact_n:
fact_n = factorize(n)
return mod_sqrt_pf(x, n, fact_n)
#!/usr/bin/env python
import math
from tools import factorize
for i in range(1,40000):
tri = i*(i+1)/2
factors = factorize(tri)
div_count = reduce(lambda x,y: x*(y+1), factors.values(), 1)
print "(i: %d|%d, %s): %s" % (i, tri, factors, div_count -1)
if div_count > 500: break
The first three consecutive numbers to have three distinct prime factors are:
644 = 2^2 x 7 x 23
645 = 3 x 5 x 43
646 = 2 x 17 x 19.
Find the first four consecutive integers to have four distinct primes factors. What is the first of these numbers?
'''
from tools import factorize
i = 120000
consec = 0
while i < 1000000:
print i
if len(factorize(i)) == 4:
consec += 1
else:
consec = 0
if consec == 4:
print i
break
i += 1
print 'done'
#!/usr/bin/python ''' The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ? ''' from tools import factorize N = 600851475143 factors = factorize(N) print max(factors.keys())
def pe003():
"""Find the largest prime factor of the number '600851475143'"""
from tools import isPrime, factorize
return max(filter(isPrime,
factorize(600851475143)))