Mersenne Digest Tuesday, 2 February 1999 Volume 01 : Number 504
----------------------------------------------------------------------
From: Allan Menezes <[EMAIL PROTECTED]>
Date: Sun, 31 Jan 1999 17:03:21 -0500
Subject: Mersenne: Altered definition of Mersenne numbers.
Hi,
I was wondering if we could be looser in the definition of mersenne
numbers allowing it also to be defined as (-2)^n-1 for n >=2 and n a
natural number and n odd.
For example using +/-2 and n=3 yields 2^3-1=7 a mersenne prime.
abs[(-2)^3-1]=9=3^2 which would make the alternative definition of
mersenne numbers (looser definition ) not square free!
What does this suggest to you?
Regards,
Allan Menezes
------------------------------
From: Allan Menezes <[EMAIL PROTECTED]>
Date: Sun, 31 Jan 1999 17:28:06 -0500
Subject: Mersenne: Altered definition of Mersenne numbers.Coreection!
This is a multi-part message in MIME format.
- --------------E5D396C028ECB7BE0EBC4E73
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
Ofcourse all these abs[(-2)^n-1] numbers where n >=3 n odd and n an
integer will be composite and divisible by +/-3.(-2-1). So divide out
the common 3 factor and one does get primes. I found this out using a
program written in Mathematica 3.0.1.
Regards,
Allan Menezes
P.S. I do not know whether the resulting composite numbers are all
square free.
- --------------E5D396C028ECB7BE0EBC4E73
Content-Type: message/rfc822
Content-Transfer-Encoding: 7bit
Content-Disposition: inline
X-Mozilla-Status2: 00000000
Message-ID: <[EMAIL PROTECTED]>
Date: Sun, 31 Jan 1999 17:03:21 -0500
From: Allan Menezes <[EMAIL PROTECTED]>
X-Mailer: Mozilla 4.5 [en] (WinNT; I)
X-Accept-Language: en
MIME-Version: 1.0
To: [EMAIL PROTECTED], [EMAIL PROTECTED]
Subject: Altered definition of Mersenne numbers.
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
Hi,
I was wondering if we could be looser in the definition of mersenne
numbers allowing it also to be defined as (-2)^n-1 for n >=2 and n a
natural number and n odd.
For example using +/-2 and n=3 yields 2^3-1=7 a mersenne prime.
abs[(-2)^3-1]=9=3^2 which would make the alternative definition of
mersenne numbers (looser definition ) not square free!
What does this suggest to you?
Regards,
Allan Menezes
- --------------E5D396C028ECB7BE0EBC4E73--
------------------------------
From: [EMAIL PROTECTED]
Date: Mon, 1 Feb 1999 09:16:58 -0800 (PST)
Subject: Re: Mersenne: Problems with ATI graphics
On Fri, 29 Jan 1999, John R Pierce wrote:
> > > 3) The on-board ATI graphics chip is about 2 cm away from the Slot1,
> > > directly underneath the CPU's big heat sink.
> >
> > Hmmm, sounds pretty suspicious to me. I would move it down a slot or
> > two...
>
>
> "ON-BOARD" ATI graphics. its a all-in-one motherboard. can't move it.
EEEEEWWWWWWWW, that sounds like a poor design. I would notify the
manufacturer and solicit advice on creating some shielding.
> re: emf radiation, I heavily doubt that a CPU could radiate any significant
> EMF thru a heatsink, which after all is a large mass of aluminum, presumably
> grounded.
>
> I'd be more likely to suspect power transients coming through the +5VDC.
'tis possible, however there is a way to determine if and what is
emanating EMF. Take a length of fine wire preferably with shellac
insulation and coil it up about 1 inch in diameter(Probably 10-15 loops
should do) and connect the two ends to the probes on an oscilliscope (a
multimeter should do in a pinch). Replicate the problem on your monitor
and wave the coil over various components on your motherboard. You should
be able to "see" what is pumping out excessive EMF. Be careful you don't
touch the board with your coil :-)
>
> > > 4) The distributed.net client does not cause this behavior. My
> > > understanding is that it does not use either FPU or cache.
> >
> > Huh? If you are LL testing you are using FPU and cache. I'm almost as sure
> > that applies if you are factoring as well.
>
> he meant the distributed.net client does not use FPU or cache. In fact, it
> does use some cache, but not nearly as heavily as the LL tests do. The
> distributed.net client is that RC-5 encryption thing, its all integer math.
>
> -jrp
>
>
>
--
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
: WWW: http://www.silverlink.net/poke : Boycott Microsot :
: E-Mail: [EMAIL PROTECTED] : http://www.vcnet.com/bms :
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
------------------------------
From: Don Moss <[EMAIL PROTECTED]>
Date: Mon, 1 Feb 1999 11:58:13 -0600 (CST)
Subject: Re: Mersenne: Rewards for prime stuff??
On Fri, 29 Jan 1999 Jonathan A Zylstra wrote:
> Also, what about imaginary numbers as factors?
> - -3i and 5i are factors of 15
> (i = square root of -1)
>
> Jonathan Zylstra
> [EMAIL PROTECTED]
True, but they're not smaller (or larger) than 3. They're on a different
number line!
- Don
* * * * * * * * * * * * * * * * *
* Don Moss <[EMAIL PROTECTED]> *
* * * * * * * * * * * * * * * * *
* Timing has a lot to do with *
* the outcome of a rain dance. *
* * * * * * * * * * * * * * * * *
------------------------------
From: Blake Stacey <[EMAIL PROTECTED]>
Date: Mon, 01 Feb 1999 16:52:34 -0600
Subject: Re: Mersenne: Rewards for prime stuff?
Hi.
Just to continue the delightfully irrelevant string of almost-off-topic
posts, I note that -3i (where i is the square root of -1) has the same
absolute value as 3, so it IS as small a factor, by some definition.
- --
Blake Stacey
Executive Director of Programming
HyperSphere Software
[EMAIL PROTECTED] :: http://fly.hiwaay.net/~bstacey
Some chairs are ergonomic.
No junk bond is ergonomic.
Therefore, some chairs are not junk bonds.
------------------------------
From: [EMAIL PROTECTED]
Date: Mon, 1 Feb 1999 20:52:02 EST
Subject: Re: Mersenne: Rewards for prime stuff?
In a message dated 2/1/99 6:38:53 PM Eastern Standard Time, [EMAIL PROTECTED]
writes:
> Hi.
> Just to continue the delightfully irrelevant string of almost-off-topic
> posts, I note that -3i (where i is the square root of -1) has the same
> absolute value as 3, so it IS as small a factor, by some definition.
I have seen definitions of factoring that define 1, -1, i, -i as "units", and
prove that every integer can be factored uniquely into the product of positive
prime integers and one "unit". So yes, -3i is a factor, but it should be
considered "composite."
------------------------------
From: David L Nicol <[EMAIL PROTECTED]>
Date: Mon, 01 Feb 1999 23:28:41 -0600
Subject: Re: Mersenne: Rewards for prime stuff?
[EMAIL PROTECTED] wrote:
> every integer can be factored uniquely into the product of positive
> prime integers and one "unit".
Negative numbers? Euclid didn't need no negative numbers.
------------------------------
From: Paul Derbyshire <[EMAIL PROTECTED]>
Date: Tue, 02 Feb 1999 02:00:27 -0500
Subject: Re: Mersenne: Rewards for prime stuff?
At 11:28 PM 2/1/99 -0600, you wrote:
>[EMAIL PROTECTED] wrote:
>
>> every integer can be factored uniquely into the product of positive
>> prime integers and one "unit".
>
>Negative numbers? Euclid didn't need no negative numbers.
He didn't have to deal with quantum mechanics either.
- --
.*. "Clouds are not spheres, mountains are not cones, coastlines are not
- -() < circles, and bark is not smooth, nor does lightning travel in a
`*' straight line." -------------------------------------------------
-- B. Mandelbrot |http://surf.to/pgd.net
_____________________ ____|________ Paul Derbyshire [EMAIL PROTECTED]
Programmer & Humanist|ICQ: 10423848|
------------------------------
End of Mersenne Digest V1 #504
******************************
