That was a good post, and I somewhat understand (I will need to read it again).
But you left one question unanswered (unless I missed it somewhere) but does k need to be in a certain form?
Or can it be any random number (of course 2kp+1 might not divide the mersenne number if k is random)?
I also note that you used an r, and you substituted it with a 2k because it is even. Therefore, what are the bounds of testing for k?
Thanks.
