Statement

Archimedes has just discovered a new concept: the fraction, where an integer number (numerator) is divided by another integer number (denominator). In particular, he is now focusing on the simplest kind of fractions, called unit fraction, where the numerator is exactly 1. Until now, Archimedes managed to compute the decimal representation of all the unit fractions with denominator up to ten, and noticed that some of them contain a recurring cycle of digits. Where 0.1(6) means 0.166666…, and has a 1-digit recurring cycle. Archimedes is particularly excited by long recurring cycles, like the one of 1/7 which is 6 digits long, and would like to discover an even longer one with denominator up to N; but is getting tired of computing all those decimals. Help Archimedes in his quest, by finding the largest number d < N such that 1/d contains the longest possible recurring cycle in its decimal fraction part!