3

This number is a prime.

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Jason Funk © 2002

3 is the smallest prime such that if F(p) = 2*p^2-1, then F(3), F(F(3)), and F(F(F(3))) are all primes. [Opao]

The only twin prime triplet starts at 3. I.e., 3+2 and 3+2+2 are also prime. [Opao]

The only cousin prime triplet starts at 3. I.e., 3+4 and 3+4+4 are also prime. [Opao]

The only value of p such that p and p + 2 are twin primes and p(p + 2) + p - 1 and p(p + 2) + p + 1 are also twin primes. [Opao]