test for primality of Mersenne numbers

Suppose $p$ is an odd prime, and define a sequence $L_{n}$ recursively as

L_{0}=4,\qquad L_{n+1}=(L_{n}^{2}-2)\bmod(2^{p}-1).

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

References

1 Donald E. Knuth. The Art of Computer Programming, volume 2. Addison-Wesley, 1969.

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