Alexa

Alexa's Conjecture on Primality ★★

Author(s): Alexa

Definition Let $r_i$ be the unique integer (with respect to a fixed $p\in\mathbb{N}$ ) such that

$(2i+1)^{p-1} \equiv r_i \pmod p ~~\text{ and } ~ 0 \le r_i < p.$

Conjecture A natural number $p \ge 8$ is a prime iff

$\displaystyle \sum_{i=1}^{\left \lfloor \frac{\sqrt[3]p}{2} \right \rfloor} r_i = \left \lfloor \frac{\sqrt[3]p}{2} \right \rfloor$

Keywords: primality

Posted by princeps
updated June 14th, 2013