#!/usr/bin/env python
from math import sqrt
from util import primes
if __name__ == "__main__":
target = 600851475143
factor_candidates = primes.filter_lt(int(sqrt(target)))
factors = [ x for x in factor_candidates if target % x == 0 ]
print factors[-1]
#!/usr/bin/env python
from operator import add
from util import primes
if __name__ == "__main__":
target = 2000000
primes_lt_target = primes.filter_lt(target)
print reduce(add, primes_lt_target)
from util import primes
from collections import defaultdict
from itertools import permutations
def rotations(orig):
yield orig
cur = orig[-1]+orig[:-1]
while cur != orig:
yield cur
cur = cur[-1]+cur[:-1]
if __name__ == "__main__":
target = 1000000 # a milli
comb_count = defaultdict(int)
circular_set = set()
pr_set = set(primes.filter_lt(target))
print 'total primes len:',len(pr_set)
for i in pr_set:
rot_set = set([int(x) for x in rotations(str(i))])
if( rot_set & pr_set == rot_set ):
circular_set = circular_set | rot_set
# if you could modify pr_set while iterating over it,
# you could optimize to not check for other primes
# in the current rot_set
print 'circ primes len:',len(circular_set)