I was just looking at a CPU comparison at
http://infopad.eecs.berkeley.edu/CIC/summary/local/
The Alpha 21364 at 1GHz is expected to have specint of around 70, and specfp
around 120 (SPEC-95)!!! Even the 21264 at 667MHz has 44 and 66
respectively.
Compare that to a PIII 500MHz with 20.6 and 14.
Well, looks like factoring on TI calculators won't be feasible or useful. :-(
Before more data comes in, I'd like to state that I believe three things:
A) The 38th Mersenne prime discovered has an exponent in the neighborhood of
6,900,000.
B) We *are* missing a Mersenne prime between 3021377 and
> Do you know of any tools for designing FPGAs?
>
> phma
(hope you don't mind; I'm posting to the list in case anyone else is
interested)
The one I used is from Viewlogic (www.viewlogic.com). They have a full set
of programs for designing, simulating, routing and programming FPGA's. It
is a VE
> For those of you who read PC Magazine, there is a short column by Bill
> Machrone in the July 1999 issue on page 85 that talks about GIMPS, Aaron
> Blosser, and the US West episode. Not a detailed examination of what
> happened but some good press on why you might want to participate
> in such
For those of you who read PC Magazine, there is a short column by Bill
Machrone in the July 1999 issue on page 85 that talks about GIMPS, Aaron
Blosser, and the US West episode. Not a detailed examination of what
happened but some good press on why you might want to participate in such a
search b
> According to the FAQ, "PrimeNet knows when a test result was computed on a
> different computer. It will accept your results for the master database
> log, but it will not credit your account for the test work."
>
> (1) Does this cause a credit problem when a team member gives 2 PCs the
> same C
I request that anyone running exponents that are not assigned to them
by either the IPS or George Woltman pause, and ask George for a
nonoverlapping assignment.
Do not assume that simply because an exponent has been assigned for
a lengthy time, that it is being hoarded and not worked on for no g
Mersenne DigestSaturday, June 19 1999Volume 01 : Number 584
--
Date: Fri, 18 Jun 1999 16:04:58 -0500 (CDT)
From: Robert Stalzer <[EMAIL PROTECTED]>
Subject: Mersenne: Duplicate Computer IDs
According to the
Brian J. Beesley writes:
> If it really is that bad, then it's probably not worth doing. I once
> tested all the prime exponent Mersennes with exponents from about 10
> million thru about 21 million for factors smaller than 2^33 or so,
> using mersfacgmp on a Pentium 90MHz, in a cou
> Also one must take into account the "pseudo-conjecture" that Curt Noll (I
> believe -- if I've misattributed, please forgive) has made about
> "Mersenne
> Islands". If you look at the distribution, they tend to clump, like
> galaxy clusters, with large voids between the islands.
On a whim, I
> >So, based on this conjecture, what would you guess M38 to be (roughly)?
>
> On the average, the ratio of successive exponents that result in
> prims is about
> 3/2, but that doesn't help with individual ones. For the first
> 37, the ratio
> varies from 1.015 to 4.102.
I see...I didn't really
[EMAIL PROTECTED] writes:
Both of Chris Nash's remarks are intended for odd p.
Hm; yes, I didn't notice that all the exceptions were for even
exponents.
The factor 3 of 2^2 - 1 is not congruent to 1 modulo 2*2.
"Primitive factors" should be restricted to primitive prime factor
> If you take the following comma delimited file into a spreadsheet, and
> graph it (say with a line chart) it shows the relationship of Mersenne
> exponents to their index, for the first 37 Mersenne primes. The first
> column is the log of (3/2)^n, the second column is the log of the exponent
>
> Also, to ease finding factors, using a number which is a multiple of 8 is
> a good idea. However, how much work has been done on checking other mods
> other than 120? Like 80, or even 720 to see what happens? just
> wondering...
As often happens (to me at least), as soon as I tell someone somet
At 08:22 AM 6/19/99 -0600, you wrote:
> >There is a conjecture that the nth Mersenne exponent resulting in a prime
> >is approximately (3/2)^n. linear relationship. The linear
> regression >parameters yield the relation M(n) = 1.4796^n + c, where c
> is a small >constant. 1.4796 is pretty c
At 08:22 AM 6/19/99 -0600, Aaron Blosser wrote:
>So, based on this conjecture, what would you guess M38 to be (roughly)?
On the average, the ratio of successive exponents that result in prims is about
3/2, but that doesn't help with individual ones. For the first 37, the ratio
varies from 1.015
If you take the following comma delimited file into a spreadsheet, and
graph it (say with a line chart) it shows the relationship of Mersenne
exponents to their index, for the first 37 Mersenne primes. The first
column is the log of (3/2)^n, the second column is the log of the exponent
of the nth
I've been looking through various bits of factoring code and I really
can't find any speed increases, unsuprisingly :). Managed to get some very
nice equations out of euler's algorithm, but none that compute any
faster...
However, a couple of things did crop up. Firstly, if two numbers have a
sim
> There is a conjecture that the nth Mersenne exponent resulting in a prime
> is approximately (3/2)^n. Consider Mersenne primes through M37. (I don't
> know exactly what M38 is yet, and there may be other small ones.
> Also, the
> double checks of the range through M37 haven't been completed.)
> Chris Nash writes:
>
>The smallest factor of 2^p-1, p a prime, is at least as big as
>2p+1. All factors of a Mersenne number of prime exponent are of the
>form 2kp+1 - similarly for all 'new' factors of a composite
>exponent (ie that haven't appeared in any Mersenne number with a
There is a conjecture that the nth Mersenne exponent resulting in a prime
is approximately (3/2)^n. Consider Mersenne primes through M37. (I don't
know exactly what M38 is yet, and there may be other small ones. Also, the
double checks of the range through M37 haven't been completed.)
You can
<>
So, is this:
(2^p mod f) - 1
Congruent to this:
(2^p -1) mod f
I believe so. If that's true, whoo hoo! I have code to do this already. And
it's relatively speedy. (It makes up the core of my RSA key generation and
encryption machine, which of course is heavy on exponentiation modulo some
o
Using the wonderful modpwr() from Paul Pollack's NTH library for the TI-92, I
have quickly verified the following results I found on Entropia.com:
7017133 61 F 1901619961404080441 14-May-99 11:35 jay2001
PII_40
7029787 62 F 3764452186385609519 31-May-99
I hacked up a quick TI-92 factoring program. It is slower than I wanted. :-(
It's "testing" 2^25,000,009 - 1 right now. It can test one factor every 1.3
seconds. AUGH! At that rate it would take 95 *billion* years to trial divide
by all odd numbers under 2^62. N.
However, a semi-reasonable t
[EMAIL PROTECTED] writes:
So, is this:
(2^p mod f) - 1
Congruent to this:
(2^p -1) mod f
Yes, though be careful about the case of 2^p mod f being 0. The first
will give you -1 and the second is f-1. They are congruent, mod f, of
course, but not identical.
This is doubly great,
Will Edgington <[EMAIL PROTECTED]> writes:
> Foghorn Leghorn writes:
> >Could you factor a Mersenne number without storing it in memory?
> >(Answer: I don't *think* so) Ptoo bad. If we could factor
> >Mersenne numbers on an unmodified TI-92+, then there'd be a lot of
> >people
Foghorn Leghorn writes:
>Could you factor a Mersenne number without storing it in memory?
>(Answer: I don't *think* so) Ptoo bad. If we could factor
>Mersenne numbers on an unmodified TI-92+, then there'd be a lot of
>people who'd run that program.
Uh, that's exactly what Pri
lrwiman writes:
However, I cannot think of any way to do an LL test without storing
the number in memory. Is there way?
Yes. All of the GIMPS programs do the LL test without the Mersenne
number itself.
The LL test programs do, however, need to store numbers as large as
the Mersenne num
> However, a semi-reasonable task would be to test numbers for factors up to
> 2^16.
Done.
> Pitiful, I know, but a TI could test a single number in 12 hours.
An optimized algorithm will do it in about zero seconds.
> B) To Mr. Woltman or Mr. Kurowski - how "useful" would factoring (most
like
In my haste in programming that TI-92 Mersenne factoring program, I
*completely* forgot about the special structure of Mersenne factors, of which
several people hastened to remind me. :-O I should have known better. I
actually did. My memory must be going. (Not to mention my brain drain before
[EMAIL PROTECTED] writes:
Using the wonderful modpwr() from Paul Pollack's NTH library for
the TI-92, I have quickly verified the following results I found on
Entropia.com: [...]
Good.:)
For each of them, the TI-92 quickly returned that 2^exponent mod
factor = 1, and very quickl
Will Edgington commented:
> Chris Nash writes:
>
> The smallest factor of 2^p-1, p a prime, is at least as big as
> 2p+1. All factors of a Mersenne number of prime exponent are of the
> form 2kp+1 - similarly for all 'new' factors of a composite
> exponent (ie that haven't appeared i
Chris Nash writes:
The smallest factor of 2^p-1, p a prime, is at least as big as
2p+1. All factors of a Mersenne number of prime exponent are of the
form 2kp+1 - similarly for all 'new' factors of a composite
exponent (ie that haven't appeared in any Mersenne number with an
expon
> If it really is that bad, then it's probably not worth doing. I once
> tested all the prime exponent Mersennes with exponents from about 10
> million thru about 21 million for factors smaller than 2^33 or so,
> using mersfacgmp on a Pentium 90MHz, in a couple of days.
The factoring program I u
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