PlanetMath: Lucas-Lehmer primality test

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Lucas-Lehmer primality test

(Theorem)

Theorem: Let be a prime, and let be a Mersenne number, then is prime iff divides $s_{p-1}$ where the numbers $(s_n)_{n\geq1}$ are given by the following recurrence relation: , and

$\displaystyle s_{n+1}={s_n}^2-2$

for $n\geq1$ .

"Lucas-Lehmer primality test" is owned by CWoo. [ full author list (2) | owner history (1) ]

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Attachments:: 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
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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 2767 times total.

Classification:

11A51 (Number theory :: Elementary number theory :: Factorization; primality)

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