This directory includes some files produced during the verification of the known Mersenne Prime #39 This number is M13466917 = 2^13466917 - 1 M13466917 M13466917.res64 includes the 64 less significant bits of the residues in a Lucas-Lehmer test, every 10000 iterations. Iteration number 0 is 4, number 1 is 14 and so on. You know, the recurence sequence is L(i)=L(i-1)*L(i-1) - 2 , 0 < i <= 13466917 - 2 L(0)=4; So, in the file there are the 64 less significant bits of L(10000), L(20000).... s13466917_nnnnnnnn These are save files obtained from the program Glucas. The format of this files is explained in the document: http://glucas.sourceforge.net/mformat.htm and is inteded to be universal an compatible among all platforms. The nnnnnnnn in the name of file is the iteration saved. As you can see, there is a near_the_end save file at the iteration 13460000. If you want to finish a L-L test from one of these save files 1) Download Glucas. (source code or prebuild binary) at http://sourceforge.net/project/showfiles.php?group_id=24518&release_id=56998 2) download the file you want to restart, as example ftp://ftp.oxixares.com/pub/M13466917/s13466917_13460000 3) In your local Glucas directory, rename the file downloaded mv s13466917_13460000 s13466917 4) Launch Glucas ./Glucas 13466917 & Depending on your system, you will get in a while a file 'results' with the result of the test. It should be announcing the discovery of a new Mersenne Prime.