On Fri, 15 Oct 1999 [EMAIL PROTECTED] wrote:
> 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
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.
> So, I graphed e^gamma log [2] (mersenne) - (1, 2, 3, 4, etc). This represents
> how far off the Wagstaff conjecture is when applied to the data. (The
> Wagstaff conjecture *should* say that M(3021377) = 37, but it doesn't. This
> is why I graph this jibberish). This graph was INCREDIBLY disturbing. Save
> for one Mersenne prime, all these "errors" were above 0, and often big. Ech!
> So, I used my TI-92+ to take a linear regession line of this data (because I
> had recently learned how to do regression lines and correlation
> coefficients). This line was Y = .004769x + 1.4615. See what's happening
> here? It seems that there's a consistent error (1.4615) in the Wagstaff
> conjecture that doesn't change as the Mersenne primes grow (the .004769). So
> I went back and applied this correction to the graph "that seemed a little
> strange" and it fit y=x much better.
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.
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 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 am most anxious to take M1-M36 & extrapolate M37, down through having
just, say, M1-M10 & extrapolating M11 & see how accurate that process is.
I really thing the GIMPS client should have an option to test the mersenne
number closest to this estimate of M38 that has not been and is not being
tested -- implemented in a scalable fasion, so that when/if the missing
prime is found, and it finishes the number it's on (since knowing what
isn't prime is valuble), it'll then go to the next estimated prime.
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