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Lucas-Lehmer primality test (Theorem)

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 $(s_n)_{n\geq1}$ are given by the following recurrence relation: $s_1=4$ , and $$s_{n+1}={s_n}^2-2$$ for $n\geq1$ .




"Lucas-Lehmer primality test" is owned by CWoo. [ full author list (2) | owner history (1) ]
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examples of the Lucas-Lehmer primality test on small numbers (Example) by PrimeFan
proof of Lucas-Lehmer primality test (Proof) by rm50
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Cross-references: recurrence relation, numbers, divides, iff, Mersenne number, prime, theorem
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This is version 5 of Lucas-Lehmer primality test, born on 2004-06-11, modified 2008-03-08.
Object id is 5910, canonical name is LucasLhemer.
Accessed 3182 times total.

Classification:
AMS MSC11A51 (Number theory :: Elementary number theory :: Factorization; primality)

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