I'm hoping what I have to say in this email might be important. On Tue, 12 Oct 1999, George Woltman wrote: > At 04:12 PM 10/12/99 -0400, you wrote: > >> >And how is the probability of finding a prime calculated ? > >> > >> It is roughly how-far-factored-in-bits * 2 / exponent > > > >Okay.. what's "how-far-factored-in-bits" mean ? > > I think trial factoring is done to 2^68 for an exponent around 33 million. > Thus your chance is 2 * 68 / 33000000. Okay, so as far as we know, each number is equally likely to be prime, and this probability is just based on how much has already been tested ? I'd been meaning to chart p for all mersenne primes (n^p)-1. Ugh... I apparently had bad math teachers, and GIMPS is really making me feel it. I *really* wanna play with these numbers, but I feel intellectually cripled. I charted p.. with the value of p on the y axis, and the number of the prime on the x axis. I omitted the latest one (the 2million-some digit one), since we don't know what number it actually is, since everything smaller than it hasn't been tested. I took the numbers from http://www.utm.edu/research/primes/mersenne.shtml#known The chart ooked interesting. Approximately exponential. But it didn't fit real cleanly. So I stared at it for a long time. I noticed that the last 6 mersenne primes appeared to be in pairs... #32 756839 #33 859433 #34 1257787 #35 1398269 #36 2976221 #37 3021377 Each pair seemed too close to each other for it to be random chance. So I split up the numbers... I put the odd p's (by number order in which they were discovered) in 1 column, and the even p's in another column, and charted them. I want you to do this right now. Please. In Excel, or something (what else might you use?). At least with this last 6. Like: 756839 859433 1257787 1398269 2976221 3021377 And graph each column as a seperate line on the same graph. They match up. They're like, on top of each other. If you do this for all known mersenne primes, the lines are off by one... remove the 1st even p, or add 1 to the odd p's to get the lines to be practically on top of each other (is this an argument that 1 should be on the list?). Does anybody see what I'm talking about ? Is there any significance to this ? Has somebody already written extensive papers on this ? I don't have access to a charting program this instant, or I'm sure I'd be up the rest of the night playing with this. Hopefully I'll get some time to do so tomorrow. Ugh, I can't wait. I really wanna graph the difference between the pairs... well, I have, but not with them in 2 sets... I'm hoping there's a relationship between the pairs, and a relationship between the distances between the pairs. __________________________________________________________________ PGP fingerprint = 03 5B 9B A0 16 33 91 2F A5 77 BC EE 43 71 98 D4 [EMAIL PROTECTED] / http://www.op.net/~darxus Join the Great Internet Mersenne Prime Search http://www.mersenne.org/prime.htm _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
