The decimal expansion of 1/13 has a period of six digits. Find all primes p for which 1/p has a period of exactly four digits.
The reciprocal of every prime p (other than two and five) has a period, that is the decimal expansion of 1/p repeats in blocks of some set length. This period is the period of p. ... For example: 3, 11, 37 and 101 are the only primes with periods one, two, three and four respectively−so they are unique-primes.
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.693.5325&rep=rep1&type=pdf
