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# Lucas-Lehmer primality test

Theorem: Let $p>2$ be a prime, and let $M_{p}$ be a Mersenne number, then $M_{p}$ is prime iff $M_{p}$ divides $s_{{p-1}}$ where the numbers $(s_{n})_{{n\geq 1}}$ are given by the following recurrence relation: $s_{1}=4$, and

$s_{{n+1}}={s_{n}}^{2}-2$ |

for $n\geq 1$.

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Theorem

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Reference

## Mathematics Subject Classification

11A51*no label found*

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