8821

This number is a prime.

The largest 4-digit prime whose the reversal is a nude number, i.e., a number that is divisible by all of its digits. [Loungrides]

The smallest prime such that replacing each digit d with d^3 yields a perfect square, i.e., 8821 -> 51251281 -> 7159^2. [Bajpai]

8821 is the largest 4-digit magnanimous prime. (A magnanimous number is a number (which we assume to be of at least 2 digits) such that the sum obtained inserting a "+" among its digit in any position gives a prime.) [Pace]