The smallest prime p in which the concatenation of p with the next prime remains prime throughout two steps of the same procedure. For example, 467 concatenated with the next prime (479) gives the prime 467479, and 467479 concatenated with the next prime (467491) gives the prime 467479467491. 467 is also the smallest whose successive concatenations remain prime throughout three steps. [De Geest and Post]
The smallest prime whose digits form an acute-angle scalene triangle. [Loungrides]
The number of full reptend primes less than ten thousand.
The only known prime p such that (130^p+1)/131 is prime. [Luen]