Hello everybody, I think the main reason is that : the test has to be conducted on 1 single CPU and it takes more than 2 months on 1 machine to test 1 exponent. Even if the project is distributed and has a cpu work force of 150000 machines, 1 test = 1 computer = several months. ... there are many prime numbers and as fas as I know there is no reason to think that one particular prime might be a candidate or not apart from some basic filtering techniques, like to take primes of the form 4n+1 or 4n+3, ... I know that since I tried that a long time ago, it does not really work. to test your own machine you may take a look at the following web page : http://www.mersenne.ca/cudalucas.php or here : http://www.mersenne.ca/bench.php beware : the page is huge in width. Best regards, Simon Plouffe