99991

This number is a prime.

The largest five-digit prime contains all square digits. [Bajpai]

All twin primes up to a million can be expressed as P = 2n^2 - Q, where P is the larger of any twin prime pair and Q is the larger of another twin prime pair. [Homewood]

The largest five-digit prime. [Afzal]

The largest five-digit prime has a twin prime in 99989, an emirp, whose sexy prime is 98993, which is also an emirp, whose sexy prime is 39983, which also an emirp, whose cousin prime is 39979. [Harrison]