I think what he's getting at is that some individual exponent MIGHT fall into it's own "pattern of division", much the same was the very simple repeating decimals (such as 1/11) turn into a repetitive pattern in long division (i.e. 0.0909090909090.....forever). One doesn't need to KEEP dividing to know with certainty that the "09" pattern will repeat forever. If the value of "s" were tracked, it may be that the value of "S" at some point in a LL test falls into a pattern as well. A fictititous example for a much smaller Mersenne number might look like this: . . . S = 23875123789498 S = 1289358913467911 S = 902356809248560249856 S = 134578613667 S = 23875123789498 S = 1289358913467911 S = 902356809248560249856 S = 134578613667 S = 23875123789498 S = 1289358913467911 S = 902356809248560249856 S = 134578613667 S = 23875123789498 S = 1289358913467911 S = 902356809248560249856 S = 134578613667 . . . . If we found something like this in a test for 2^35,673,121-1 while testing for a 10 million digit prime, and found it at iteration 126,112, we could discard the remaining 35 million interations, and just use a simple modulus calculation to determine WHICH of the values of "S" seen in the early repetition is the true residue of the LAST iteration. Likewise, if we see S hit zero at some intermediary point, and that pattern repeats as well, we might be able to KNOW a number is prime if that modulus calculation shows that the repetitive zero falls on the last iteration -- without doing the entire 35 million calculations. If "S" turns out to repeat in the manner of 0.09090909090909.... then the overhead it takes to check such "might" be worth performing for the first hundred thousand iterations (or some magic threshhold where it becomes less than optimal). I understand where the poster is coming from, as described above, but I don't think anything will come of it -- the overhead WOULD be horrendous at these levels.... At 10:00 PM 6/14/99 -0400, you wrote: >At 08:06 PM 6/14/99 -0500, Gary Diehl wrote: > > >When you square S over and over and over in one LL test, does that same > >value of S come up in a test for another exponent? > > >It could, but I don't think that helps since for each exponent the >calculations >are done to a different modulus. > >+----------------------------------------------+ >| Jud "program first and think later" McCranie | >+----------------------------------------------+ > > >________________________________________________________________ >Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
