Lucas-Lehmer Test for Mersenne Primes

M. Gallant 1/99

This applet implements the Lucas-Lehmer method for testing the primality of a Mersenne number. Mersenne numbers are of the form:
2^p-1
where p is odd. In fact, it can easily be shown that for 2^p-1 to be prime, the exponent p must also be prime.

Mersenne primes are of particular interest because they represent the largest known primes to date, and the primality test is easily implemented on supercomputers. (Currently [1/99], the largest known prime number is the Mersenne prime 2^3021377-1 discovered by GIMPS on 1/98.) Since Java 1.1+ supports BigInteger arbitrary-precision math, it is easy to implement the Lucas-Lehmer test in Java. Enter a range of values for the exponent p of the Mersenne numbers in the text-fields below, (the first number must be odd) and click Test for Primes. Click Print to display the value of the Mersenne number in the second text field:

A similar standalone Java application version is available.

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