test for primality of Mersenne numbers

Suppose $p$ is an odd prime, and define a sequence $L_n$ recursively as

$$L_0=4,L_{n+1}=(L_n^2-2)mod(2^p-1).$$

The number $2^p-1$ is prime if and only if $L_{p-2}=0$.

Title	test for primality of Mersenne numbers
Canonical name	TestForPrimalityOfMersenneNumbers
Date of creation	2013-03-22 13:39:48
Last modified on	2013-03-22 13:39:48
Owner	bbukh (348)
Last modified by	bbukh (348)
Numerical id	8
Author	bbukh (348)
Entry type	Algorithm
Classification	msc 11A41
Classification	msc 11Y11
Classification	msc 11A51