3

This number is a prime.

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Jason Funk © 2002

In the fifth and all higher dimensions there are only 3 regular polytopes. [Rupinski]

The greatest number of consecutive integers which are pairwise relatively prime. [Rupinski]

The function n^(1/n) achieves its maximum value for integers n at n = 3. [Rupinski]

According to the quadratic reciprocity theorem, if p and q are distinct primes of the form 4k+3, then exactly one of the following congruences is solvable in integers: x^2 = p mod q or x^2 = q mod p. [Rupinski]

The only Sophie Germain Prime p of the form 4k+3 such that M_p is prime. All larger M_p for such p are composite as shown by Euler and Lagrange. [Rupinski]

The smallest possible Proth prime, k*2ⁿ+1 with k < 2ⁿ, here k=1, n=1. [Rupinski]