On Wed, Jun 16, 1999 at 06:21:54AM -0700, Mersenne Digest wrote:
>> Also, if a is co-prime to n, a^T=1 mod n
>> 2 is obviously co-prime to n, so 2^T=1 mod n
Excuse me if I'm very stupid here, but isn't 1 mod n = 1 for _any_ n? We
are talking about the remainder of a division here, right?
> If q (= 2kp + 1 in Chris's notation) is an odd prime
Again, primes happen to be odd, don't they?
---snip---
>- ---snip---
Oh, BTW, an era is over; this is my last digest. I'll be replying to
single messages from now on... (As if you were interested.)
---snip---
>Or, was the problem just that David S. won't be able to verify this number
>quickly like he usually does?
George said something about `not being any free time on a Cray', so there's
a Cray double-checking it at idle priority right now. Wasn't the estimate
4 weeks?
---snip---
>- -----BEGIN PGP SIGNED MESSAGE-----
Whee! :-) Your key first, perhaps? And some signatures? Generally, I'd love
to see people use PGP more often...
>Comment: 92G5S="!!;F]T:&5R(%!E<FP@2&%C:V5R"@``
Interesting...
---snip---
>Actually this is NOT true, if we're talking about tracking iterations
>up to 2^n then I can find the cycle with a storage space of 8n bytes,
>provided you let me have a "false alarm" rate of 1 in 2^64.
You don't even need a false alarm probability. I got a mail with a
very interesting way of doing it: _If_ you hit an alarm, save the
whole array (LL residue) to memory. Then compute until the (64-bit)
value repeats itself again (it's bound to happen again, remember),
and now checking the _full_ LL residues against each other should
be trivial.
Of course, letting the cycle go twice (_without_ storing the full
FFT array) should give us even smaller error rates. If I had not
been so tired, I would, of course, have remembered what (2^64)^2
was. Hmmm, (2^64)*(2^64) = 2^(64+64) = 2^128, or something.
---snip---
>I think all of us are at least a bit impatient ...
Who knows, perhaps we will find another one even before the first one is
finished? Now, _that_ would be media coverage. (`GIMPS is spitting out
record primes quicker than the supercomputers can double-check them!')
>I think that the verification job has also been sent to at least one
>other user who can definitely finish the job in 4 weeks.
Not `definitely', we're talking about idle time here. But I guess they
know how much those Crays will be used :-)
>If I was George, I'd wait until the verification comes in, then get
>in touch with the EFF people and ask for permission to make a public
>announcement, pending publication of the paper. But I _would_ wait
>until the verification comes in.
Agreed.
---snip---
>I agree that this should be put in the FAQ, so that we don't have to
>go through this every 1-2 months...
Yes, please. In the short time I've attended this list, I've seen it
pop up at least twice, and I've thought of it once myself. (Seems
like most everybody else on this list have, too... :-) )
>Looks like it. To toss a date out for fun, sometime during October. Recent
>non-linear positive effects on GIMPS participation like SETI@home
SETI@Home brought positive effects to GIMPS? Wow, this thing must be bigger
than we thought, considering the people who left us.
>radio ads
Radio ads? Is somebody paying to get out `join GIMPS' on everybody's radio?
>and the last newsletter have made an accurate guess tough.
Do you mean the `v17 bug' newsletter, or has there been one (with M?38) that
I didn't get? I _have_ signed up for the newsletter on the web page.
>How about this: if the FBI quote is right, GIMPS/PrimeNet is at today's rate of
>738 GFLOP/s worth between $182,000 and $486,000 per day in CPU time. Of course,
>'past performance is no guarantee of future results'!
Looks like we should not go for decamillion digits, but million dollars a
day :-) Oh no, I'm wasting too much money on this project, I guess I must
stop all my computers from GIMPS work. (What FBI quote, BTW?)
---snip---
>At this pace it might take until
>the start of October to clear this range.
Be patient, please. If it was 2010, I would have reacted, but October is
in fact close!
>Notwithstanding this, I believe that those 35 souls that are still
>owing exponents, should be looked upon. Perhaps some have completely
>stalled. The computer might not be connected to the internet anymore or
>some funny mishap might be preventing them from reporting the results.
>There are ONLY 35 now and perhaps some focussing on them might be of
>use.
Well, that's what the `poaching' debate (which is now officially over,
I believe) has been all about.
---snip---
>Apologies for the flippancy. Let's put Peter's well-crafted reasoning in the
>FAQ.
The day somebody asks that question and I can answer `look in the FAQ' or
even `RTFM' will be a nice day :-) Now, only for _constructing_ a FAQ, I'm
not sure if this is within scope of any existing FAQ that we have.
Now, as the last `---snip---' has been made, school's over and summer is
outside, could I please ask godoni a question: Why are _all_ my beautiful
`---snip---'s (and other people's `-----BEGIN PGP etc.' prepended with `- '???
Let us have our initial dashes! Leave them alone!
/* Steinar */
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