2

This number is a prime.

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2 is the only prime of form nⁿ + n. [Luhn]

The only difference between two consecutive primes which is prime. [Luhn]

(2^2^2 + 1)^(2^2^2 + 1) - (2^2^2 + 1) - 1 is a 21 digit prime. [Luhn]