10111

This number is a prime.

The only prime less than a googol formed by concatenating in descending order the first n multidigit palindromic primes (case n=2). [Capelle]

The only anti-Yarborough prime that splits up into the smallest prime number (101) of distinct terms needed to form a numerical sequence that contains a strictly monotonic increasing (or decreasing) subsequence with another prime number (11) of terms, in accordance with the Erdős-Szekeres theorem. [Beedassy]

The smallest anti-Yarborough near-repunit non-palindromic prime is also the only anti-Yarborough prime that is the reverse concatenation of the prime factors of a repunit number, i.e., 1111=11*101. [Loungrides]

The smallest 5-digit prime formed from two primes with the same sum of digits. [Loungrides]