problem 26

"""
A unit fraction contains 1 in the numerator. The decimal remresentation of the unit fractions with denominators 2 to 10 are given:

1/2	= 	0.5
1/3	= 	0.(3)
1/4	= 	0.25
1/5	= 	0.2
1/6	= 	0.1(6)
1/7	= 	0.(142857)
1/8	= 	0.125
1/9	= 	0.(1)
1/10	= 	0.1
Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.

Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction mart.
"""
import math
num = longest = 1
for n in range(3, 1000, 2):
    if n % 5 == 0:
        continue

    m = 1
    while (pow(10,m)) % n != 1:
        m += 1

    if m > longest:
        num, longest = n, m

print (num)