9931

This number is a prime.

The largest 4-digit super-2 emirp. [Loungrides]

The larger prime of any twin prime pair can be expressed as P + 2n^2, where P is any prime. Having checked up to 9931, all twin primes up to 10^5, they can also 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. Can you find a counterexample to this? [Homewood]