Mersenne Digest Thursday, April 8 1999 Volume 01 : Number 542
----------------------------------------------------------------------
Date: Tue, 06 Apr 1999 14:26:53 -0700
From: Rudy Ruiz <[EMAIL PROTECTED]>
Subject: Mersenne: Re:Mersenne Twin Primes
Mon, 05 Apr 1999 "Foghorn Leghorn" wrote":
~~~~~~~~~~~~begin quote~~~~~~~~~
To be completely sure of this, I found as many first factors as possible
for numbers of this form.
p First factor of 2^p-3
- - ----------------------------------------
3* 5
5* 29
7 5
13 19
17 53
19 5
31 5
61 29
89 29
107 5
127 5
521 5296777
607 5
1279 5
2203 5
2281 19
3217 19
4253 No factor to 2^32
4423 5
9689 53
9941 23
11213 No factor to 2^32
19937 47
21701 53
23209 53
44497 29
86243 5
110503 5
132049 17040433
216091 5
756839 5
859433 4219
1257787 5
1398269 29
2976221 293
3021377 10513
*Indicates that 2^p-3 is prime.
~~~~~~~~~~~~end quote~~~~~~~~~
Obviously "IFF p == 3 mod 4 " 2^p-3== 0 mod 5, so there you have a
trivial pattern.
Therefore, only cases where p==1 mod 4 need to be investigated.
For what it's worth, there are 15 incidences of a factor "5".
In the following chart, I'll simply put the factors <>5 with their
occurrence.
"Table of Frequencies" (for the 21 instances where p==1 mod 4)
---Assuming that the two "factors >2^32" are different---
factor |ocurrence
====+========
29 | 5
53 | 4
19 | 3
23 | 1
47 | 1
293 | 1
4219 | 1
10513 | 1
5296777 | 1
17040433 | 1
number>2^32| 1
number>2^32+2| 1
While there is no foreseeable reason for a number of the form
2^p-3, (subject to p==1 mod 4 and p>5) _not_ to be prime,
the odds are so overwhelmingly stacked against it that if
ever "found" the probability of computer error, programmer error,
operator error would have to be a factor to consider.
The pattern seems interesting in that:
1.- there are no factors 7,11,13,17
2.- the distribution is somewhat skewed. (IMHO)
Rodolfo
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Date: Tue, 06 Apr 1999 19:34:16 -0400
From: "Allan G. Schrum" <[EMAIL PROTECTED]>
Subject: Mersenne: Testing of software
A couple of cents from the south on testing.
First, testing each version is exactly what is needed, but a full run of
an exponent is not. Using something similar to Prime95's current
self-test, let's develop a more complete set of exponents for testing.
Using a couple hundred iterations from each exponent would be more than
adequate for a test suite. Also, it is something that can be run and
tested in a reasonable amount of time.
So in that vain, let's extract a set of exponents and start putting
together a testing master of 100, 500, 1000, 5000 and 10000 iterations
for each one. Make sure the list includes exponents near the beginning
and end of an FFT range, any just before and just after any power of two
for the exponent, etc.
Next, there are several independant programs already that work on
several architectures for independant verification. Namely, Richard
Crandall's lucdwt code is portable and works. The algorithm is used by
George's Prime95 but is completely in C so it works on many
architectures. Certainly a good starting point. I'm sure there are
others. Use these suites of programs to construct our testing master.
Test what needs testing. Exhaustive tests are tiring.
- -Allan
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Date: Wed, 07 Apr 1999 00:31:51 -0400
From: Pierre Abbat <[EMAIL PROTECTED]>
Subject: Mersenne: How to tell when mprime wants to get on the Net
This is a multi-part message in MIME format.
- --------------8311A01B738B12CC77DAA998
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
I am running mprime on my home machine and prime95 at the office.
Prime95 tells me when it wants to get on the Net, but I couldn't tell
with mprime. George Woltman told me about the -d option, but it resulted
in a humongous file which reset only when I rebooted, which wasn't very
often. Last I checked, it was half as big as the program itself. (Good
thing my cat has a tail.) So I wrote the attached tcl script (which can
be used with other programs too) and pipe the output of mprime to it.
Now I have just the last 25 lines and I can tell when it wants to get on
the Net.
phma
- --------------8311A01B738B12CC77DAA998
Content-Type: text/plain; charset=us-ascii; name="runtail"
Content-Transfer-Encoding: 7bit
Content-Disposition: inline; filename="runtail"
#!/usr/bin/tclsh
# Reads standard input and writes the last n lines to a file.
# Usage: runtail n file
proc outem {} {
global n ;
global file;
global line ;
set f [open $file w];
for {set i 0} {$i < $n} {incr i} {puts $f $line($i)};
close $f;
}
proc scroll {str} {
global n;
global line;
for {set i 1} {$i < $n} {incr i} {set line([expr $i - 1]) $line($i)};
set line([expr $n - 1]) $str;
}
foreach {n file} $argv {}
for {set i 0} {$i < $n} {incr i} {set line($i) ""}
while {1} {
scroll [gets stdin];
outem;
}
- --------------8311A01B738B12CC77DAA998--
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Date: Wed, 7 Apr 1999 02:30:22 -0400 (EDT)
From: lrwiman <[EMAIL PROTECTED]>
Subject: Mersenne: 1050 people?
All,
Scott Kurowski wrote
"The virtual machine has slowed about 25 gigaflops from 550 to absorb
the bug hit, but this should be offset by at least a factor of 2 in
the next 2 weeks by the 1050 people who joined in the last 7 days."
1050 people in 7 days?!?!?
This smells of a rat...
Sounds like, maybe when some people upgraded they accidentally created an
extra username...
- -Lucas Wiman
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Date: Wed, 7 Apr 1999 02:49:33 -0400 (EDT)
From: lrwiman <[EMAIL PROTECTED]>
Subject: Mersenne: 2^n-3
All,
In the function, 2^n-3, in [3,94] the following values for n yield a prime
result:
3,4,5,6,9,10,12,14,20,24,29, and 94 seems like a likely canidate as well,
my computer ran for about 3 hours trying to find a factor, but didn't
suceed.
Could some form of the LL test be aplied for odd values?
a posibility, for odd n:
2^n-3=(2^n-2)-1 = 2*(2^(n-1)-1)-1 = 2*(2^((n-1)/2)-1)*(2^((n-1)/2))-1
or for even n:
2*(2^(n-1)-1)-1, if M(n-1) is prime
I will have to investigate this...
Cheers,
Lucas Wiman
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Date: Wed, 7 Apr 1999 02:56:52 -0400 (EDT)
From: lrwiman <[EMAIL PROTECTED]>
Subject: Mersenne: oops, 2^n-3
all,
in my previous message, I gave the expression:
2*(2^((n-1)/2)-1)*(2^((n-1)/2))-1
This should have read:
2*(2^((n-1)/2)-1)*(2^((n-1)/2)+1)-1
Guess that's what I get for writing about primes at 2:00 in the morning ;)
Cheers,
Lucas Wiman
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Date: Wed, 7 Apr 1999 09:19:07 +0100 (BST)
From: Nick Craig-Wood <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Testing of software
In <URL:news:local.mersenne> on Wed 07 Apr, Allan G. Schrum wrote:
> Next, there are several independant programs already that work on
> several architectures for independant verification. Namely, Richard
> Crandall's lucdwt code is portable and works. The algorithm is used by
> George's Prime95 but is completely in C so it works on many
> architectures. Certainly a good starting point. I'm sure there are
> others.
I'll offer my ARMprime program as another if desired. It has some advantages
namely that it is an integer based DWT over GF(2^64-2^32+1) so is quite
different and uses no floating point. It runs on StrongARM so the processor
is different too. It isn't very quick though, about equivalent to a P66 on a
200 Mhz StrongARM. It has been validated against Prime95's internal test
sequences amongst others.
- --
Nick Craig-Wood
[EMAIL PROTECTED]
http://www.axis.demon.co.uk/
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Date: Wed, 07 Apr 1999 14:07:53 -0500
From: "Chris K. Caldwell" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: 2^n-3
At 02:49 AM 4/7/99 -0400, lrwiman wrote:
At 02:49 AM 4/7/99 -0400, you wrote:
>In the function, 2^n-3, in [3,94] the following values for n yield a prime
>result: 3,4,5,6,9,10,12,14,20,24,29, and 94 seems like a likely canidate
as well,
>my computer ran for about 3 hours trying to find a factor, but didn't
>suceed.
What about 22? Let me add the proven primes for
n = 94, 116, 122, 150, 174, 213, 221, 233, 266, 336, 452, 545,
689, 694
and the probable primes for
n = 850, 1736, 2321, 3237 (stopped at 3294 to do other stuff)
The primality proofs for these would be fairly quick using say UBASIC &
APRT-CL (the first should take
less than an hour, for the last you might use CYCLOPROVE, both UBASIC and
CYCLOPROVE are
in the public domain). The proof for n=94 was about 1 second.
Chris
[EMAIL PROTECTED]
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Date: Wed, 7 Apr 1999 20:46:37 +0100
From: Tony Forbes <[EMAIL PROTECTED]>
Subject: Re: Mersenne: 2^n-3
"Chris K. Caldwell" <[EMAIL PROTECTED]> writes
>At 02:49 AM 4/7/99 -0400, lrwiman wrote:
>At 02:49 AM 4/7/99 -0400, you wrote:
>>In the function, 2^n-3, in [3,94] the following values for n yield a prime
>>result: 3,4,5,6,9,10,12,14,20,24,29, and 94 seems like a likely canidate
>as well,
>>my computer ran for about 3 hours trying to find a factor, but didn't
>>suceed.
>
>What about 22? Let me add the proven primes for
>
> n = 94, 116, 122, 150, 174, 213, 221, 233, 266, 336, 452,
>545,
>689, 694
>
>and the probable primes for
>
> n = 850, 1736, 2321, 3237 (stopped at 3294 to do other stuff)
>
And let me add
3954, 5630, 6756, 8770, 10572, 14114, 14400, 16460, 16680
of which 3954, 5630 and 14114 are proven.
See NMBRTHRY archives
http://listserv.nodak.edu/archives/nmbrthry.html : May 1996.
- --
Tony
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Date: Wed, 07 Apr 1999 10:09:06 -0400
From: George Woltman <[EMAIL PROTECTED]>
Subject: Mersenne: NFSNet
Hi all,
Does anyone know if NFSNet is still operational and if they
have a web site? I've had two people ask in the last week.
Best regards,
George
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Date: Wed, 07 Apr 1999 10:14:14 -0400
From: George Woltman <[EMAIL PROTECTED]>
Subject: Re: Mersenne: 1050 people?
Hi,
At 02:30 AM 4/7/99 -0400, lrwiman wrote:
>1050 people in 7 days?!?!?
>Sounds like, maybe when some people upgraded they accidentally created an
>extra username...
It could be partly that, but I'd guess it's interest generated by EFF
announcing a $50,000 prize.
Regards,
George
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Date: Wed, 07 Apr 1999 17:32:43 -0700
From: Gordon Irlam <[EMAIL PROTECTED]>
Subject: Mersenne: Censored for you by SurfWatch
Hi,
I recently dicovered all of the web sites I host are blocked by
SurfWatch.
I've placed a little censored stamp on top of the base.com homepage:
http://www.base.com/
to indicate this.
What is blocked:
- The Political Writings of George Orwell (ironic that they
choose to censor someone who dedicated his life to speaking
the truth and writing against the dangers of censorship).
- An interviewing I conducted with a homeless person in
Mountain View.
- A list of things I eat for dinner (it is true that I
misspelled potato the same way as Dan Quayle, and perhaps
they are concerned I could also permanently damage the minds
of young children).
- Resources for shy people (which a lot of high school and
college students that don't have SurfWatch make use of and
find helpful).
- A web site devoted to the music of Jonathan Richman (known
for his song "I'm a little airplane" that appears on Sesame
Street, and his appearances on Space Ghost Coast to Coast).
- And a lot of other useful material I try to make available
to the net.
What to do:
- Please oppose over-broad attempts at net censorship.
- Please boycott the use of SurfWatch products.
- If you have purchased SurfWatch products in the past please
return them to the place of purchase and seek a refund.
- Please oppose the use of SurfWatch in schools, libraries,
homes, and offices.
Please see:
http://www.base.com/gordoni/thoughts/surfwatch.html
for further details.
thanks,
gordoni (list admin)
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Date: Wed, 7 Apr 1999 21:21:38 -0400
From: "Paul Missman" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: 1050 people?
From: George Woltman <[EMAIL PROTECTED]>
>
> It could be partly that, but I'd guess it's interest generated by EFF
> announcing a $50,000 prize.
>
> Regards,
> George
>
>
I can only hope that the newbies enjoy what we're doing, and aren't
viewing this as they would going to pick up a lottery ticket.
Paul
P.S. Anybody win the 190 million last night in Virginia? ;-)
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Date: Wed, 7 Apr 1999 22:33:25 -0400
From: "Rick Pali" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: 1050 people?
From: Paul Missman
> > It could be partly that, but I'd guess it's interest
> > generated by EFF announcing a $50,000 prize.
>
> I can only hope that the newbies enjoy what we're doing,
> and aren't viewing this as they would going to pick up
> a lottery ticket.
Those won't last long, I'm sure. I got about eight people to join and less
than half are still crunching for primenet. Oh well, even one is a good
thing.
Rick.
- -----
[EMAIL PROTECTED]
http://www.alienshore.com/
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Date: Wed, 7 Apr 1999 23:33:57 -0400
From: Joth Tupper <[EMAIL PROTECTED]>
Subject: Re: Mersenne: 1050 people?
Message text written by "Paul Missman"
>
From: George Woltman <[EMAIL PROTECTED]>
>
> It could be partly that, but I'd guess it's interest generated by EFF
> announcing a $50,000 prize.
>
> Regards,
> George
>
>
I can only hope that the newbies enjoy what we're doing, and aren't
viewing this as they would going to pick up a lottery ticket.
Paul
P.S. Anybody win the 190 million last night in Virginia? ;-)
<
An interesting point. I can think of few lotteries (for any significant
prize, i.e., >=$1,000) that
1) cost less out of pocket, and
2) offer ANY tangible reward other than a tiny chance of winning
than searching for a Mersenne prime.
I know I did not sign up for GIMPS with the idea of winning a prize (I
would not be shy
about accepting!) but that is still a fine reason. "Nothing succeeds like
success."
Joth Tupper
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Date: Thu, 08 Apr 1999 16:21:18 -0700
From: Rudy Ruiz <[EMAIL PROTECTED]>
Subject: Mersenne: Re: Need Clarafication
The SHORT answer to your question is no. The contrary is true. Almost all of
those numbers (a mathematical term) are composite.
I suggest you try the Prime pages of Chris Caldwell which hold a wealth of
information.
Try this link for more on those numbers which are called "primordial +1
primes" or "prime factorial".
These are the only numbers of that form that have been discovered for
2>p>35000....p#+1 is prime for the primes p=2, 3, 5, 7, 11, 31, 379, 1019,
1021, 2657, 3229, 4547, 4787, 11549, 13649, 18523, 23801,
and 24029
> http://www.utm.edu/research/primes/glossary/PrimeFactorial.html
>
[EMAIL PROTECTED] wrote:
> Hello,
>
> Just wondering if someone can give me a yes or no on a simple concept.
>
> Given {1, 2, 3, 5, 7, ..., Xn-1, Xn}, where each Xn is prime and there are
> no prime numbers between each Xn-1 and Xn, is the following always prime:
>
> (1*2*3*5*7*...*Xn-1*Xn) + 1
>
> Thank you!
>
> --
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> : WWW: http://www.silverlink.net/poke : Boycott Microsoft :
> : E-Mail: [EMAIL PROTECTED] : http://www.vcnet.com/bms :
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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End of Mersenne Digest V1 #542
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