Unique Period Prime/Examples

In base 10, 3, 11, 37, and 101 are the only primes with periods one, two, three, and four respectively, so they are unique primes. But 41 and 271 both have period five, 7 and 13 both have period six, 239 and 4649 both have period seven, 73 and 137 both have period eight, thus these primes are not unique primes.