Hello again. <<When I fit an exponential line to the 1st 37 mersenne prime's exponents (since I believe that 6972593 is actually the 39th, but have no proof, so I figured I'd leave it out), the line I got was y=1.7661e^0.301x (hope I wrote that right), and r^2=0.9925.>> I have believed for quite some time (and have proof that I did! :-P) that we are missing a Mersenne prime in there somewhere. However, I've only tried to improve on Wagstaff's conjecture, not fit a whole new line to the data. [Me:] <<Then, I plotted e^gamma log[2] (mersenne) versus the list of 1-37. Alongside this I graphed y=x. This is because the y=x line represents the Wagstaff >> [Someone else:] <<y=x would be a slope of 1/1. According to the "Where is the next larger Mersenne prime?" page -- http://www.utm.edu/research/primes/notes/faq/NextMersenne.html the Wagstaff conjecture suggests a slope of 3/2, which I believe wouldn't look so bad.>> As someone pointed out, Wagstaff did not suggest 3/2, but 2^(1/e^gamma). By the way, if you note exactly how my graph and plot were constructed, y=x is correct to use. At least, I'm pretty sure so. (STL's taking a bold step here). Remember: by playing with the axes you can fiddle with slopes. <<Sorry it didn't register to me that you'd mentioned the equation for this line in this post, thanks. But what was r^2 for it ? I'm very curious.>> I'm not sure if the r^2 would be affected by my choice of variables (which causes the y=x thing). <<On the previously mentioned web page, there are similar computations, but I believe he used M38 (which you and I believe will actually turn out to be M39), so I believe his numbers will be less accurate than yours.>> I saw that web page. The computations are not similar to mine in that the page explains Wagstaff's conjecture and why Erhardt was probably wrong, but I go further and point out how Wagstaff's conjecture often makes a wrong estimate for the Nth Mersenne prime, and present a new conjecture. <<I would really like to try your calculations myself, but I haven't seen my graphing calculator for a while, I'm not sure it'd work, and I'd prefer to use the power of my computer. Can anybody suggest any programs ? Preferably for Linux, even though that would mean I'd have to wait to get my Linux drive back.>> I just used a TI-92+ for the bulk of the work, and Mathematica 4.0 to make the plots/graphs for my paper. By the way, that paper for school is almost finished. I just have to write the conclusion and the abstract. Here's my conjecture, after I decided exactly which constant to use: M(x) ~ e^gamma log[2] x - 2^(1/e^gamma) S. "Figures that eventually he'll have to reveal his last name when he releases that paper" L. _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
