Wolfram.mathworld.com defines a unique prime in the following way:
"Following Yates (1980), a prime $p$ such that $\frac{1}{p}$ is a repeating decimal with decimal period shared with no other prime is called a unique prime. For example, $3$, $11$, $37$, and $101$ are unique primes."
OEIS has unique-period primes, and the list they give is finite. My question is whether we know if there are infinitely many unique primes, or if there is an easy way to prove that there are finitely many.
Quick clarification: I know that there are infinitely many primes already and how to prove that. I am particularly focused on unique primes.
Best Answer
Quoting from the 1998 paper "Unique-Period Primes" by Caldwell and Dubner,
If there's any update, Caldwell has not cited it at the Prime Glossary entry.