On Thu, 14 Oct 1999, Darxus wrote:
> On Thu, 14 Oct 1999 [EMAIL PROTECTED] wrote:
>
> > missing. #2: That the discovered M38, which all we knew about was that it was
> > in the 6M range, was actually around 6.9M, which I was correct about, and #3:
>
> How did you make this estimate ? Fit an exponential curve to the known
> primes, and extrapolate the 1st one that should have at least 1m digits ?
Okay, I figured out how to do exponential extrapolation in Excel.
Omitting the 38th prime (p=6,972,593), and exponentially extrapolating
from the 1st through 37th primes, I got the folowing:
P digits
#38 5,014,947 1,408,773
#39 7,414,614 2,070,471
Which is... intresting.
The # of digits extrapolated for #39 (p=7414614) is only 1.36% different
from the actual number of digits in 2^6972593-1. I wish I had time
tonight to remove more entries and see if this extrapolation continued to
be this accurate.
Also, if this extrapolation of the number of digits is accurate, there is
another prime between the 37th & 38th(p=6972593) discovered primes.
Unfortunately, the extrapolation of P just didn't go well. Actually, the
extrapolated 39th mersenne prime is 6.34% off of 2^6972593-2. I suppose
that's not so bad. That would also mean one was skipped.
So it is currently my fairly strong opinion that a mersenne prime was
skipped between the 37th & 38th discovered primes. I reserve the right to
change my mind at any instant :)
I'd also guess that the skipped prime may have been pretty close to
2^5014947-1, and have a number of digits close to 1408773.
So does any of this sound at all valid ?
Most people seem to agree that the distribution of mersenne primes is at
least roughly exponential, and that the variances are truly random. The
above is based on these asumptions.
I don't actually agree with those asumptions, but the distribution fits an
exponential curve better with those assumptions than if you graph them as
pairs.
[EMAIL PROTECTED]: I'm really looking forward to hearing how you made your
estimates.
Hmm... I just changed my worktodo.ini to Test=5014947,63 (where's the 63
come from ? it was used for the last number I was assigned).
It's saying "Error: Work-to-do file contained composite exponent: 5014947"
I suppose that means it's already been tested & found to be non-prime ?
(composite = non-prime, right?)
I think that manual & primenet should not be seperate optinos on the test
menu. I think manual should be another option on the "type of work to
request" box.
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