# 3

This number is a prime.

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Jason Funk © 2002 |

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**2^{n}+1 with *k* < 2^{n}, here *k*=1, *n*=1. [Rupinski]