Mersenne: Online proof of Lucas-Lehmer

[Joth Tupper]

The Lucas-Lehmer test seems pretty magical to me and I have wanted to see a
full proof of the theorem for some time.

For a long time, there has been a proof online that M(p) divides the term in
the LL sequence means that M(p) is prime but
I had still never seen the other half.  So I worked out the rest of a proof.

If interested, please take a look at http://www.jt-actuary.com/lucas-le.htm.
I see one "typo" where the "less than" symbol () displays incorrectly
online.
There may be other typos and even errors.  (Well, I can hope not...)

If this seems readable, would anyone want it linked in to a FAQ?
(Not my call.  I just wanted a proof.)

Trivial note:  back in the summer of 1968, I was one of a bunch of high
school kids who met
DH Lehmer (son of the Lehmer of LL fame, also a UC Berkeley math professor)
in the basement of
one of the engineering buildings at Berkeley.  (It may have been a math
building then, but the location
is now an engineering building and the math buildings were in three other
spots even then.)

He showed us his "DLS-127" (Delay Line Sieve).  This was one of the best
prime-crunchers of the 1960's.
As I recall, it was an ANALOG computer based on very precise inductors.

Thanks,

Joth


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Mersenne: From elsewhere, on network protocols being readable

[David L. Nicol]

Harrumph. 
___
   David Nicol 816.235.1187 [EMAIL PROTECTED]
   ./configure  make  make test


Grant Edwards [EMAIL PROTECTED]:
 I'm sure most people on this list already realize it, but whoever
 first decided to implement things like this using ASCII line-oriented
 protocols on telnettable TCP/IP ports deserves free doughnuts for the
 rest of his/her life.
 
 Being able to implement/test servers and clients with expect, telnet,
 etc. has undoubtedly save thousands of hours of development time..

You speak truly indeed.  I have a good bit to say about this in my next
book, "The Art Of Unix Programming".
-- 
a href="http://www.tuxedo.org/~esr"Eric S. Raymond/a

The IRS has become morally corrupted by the enormous power which we in
Congress have unwisely entrusted to it. Too often it acts like a
Gestapo preying upon defenseless citizens.
-- Senator Edward V. Long

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Mersenne: forgot my password

[Darxus]

Okay, the one machine I had set up the gimps client on is currently..
well, the hard drive is in the mail :(

I'm setting it up on another computer,  I have no idea what password was
assigned to me.  I'm used to being able to click an "I forgot my password,
please email it to me" button.

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[EMAIL PROTECTED] / http://www.op.net/~darxus
  Join the Great Internet Mersenne Prime Search
http://www.mersenne.org/prime.htm


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Mersenne Digest V1 #637

[Mersenne Digest]

Mersenne DigestTuesday, October 5 1999Volume 01 : Number 637




--

Date: Sun, 3 Oct 1999 14:33:51 -0400
From: "Matthew Smith" [EMAIL PROTECTED]
Subject: Mersenne: Mprime

This is a multi-part message in MIME format.

- --=_NextPart_000_000D_01BF0DAC.4FC96D40
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

I really want to run the Linux prime search software when I'm in Red Hat =
5.2 (I'm usually in Windows 98), but the program seems to have no =
documentation or information once it's running.  I ran it for 4 hours =
once and had no idea how to close it.  I had to use "kill," the only =
command I could think of to close it.  When I got back to Windows, I saw =
that my work had not been saved.  I had set the option in Windows for =
disk saves every 15 minutes.  Mprime and Prime95 shared the same data =
files, like they are supposed to.  What's going on?  I'd vote for an =
mprime on an X-server.  I want to see SOMETHING while the thing's going. =
 At least show me the iteration #, iteration % of total, and seconds / =
iteration.

- -

"The brave do not fear the grave."

--Battle Square, Final Fantasy VII

- 

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charset="iso-8859-1"
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DIVFONT face=3DArial size=3D2I really want to run the Linux prime =
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software when I'm in Red Hat 5.2 (I'm usually in Windows 98), but the =
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seems to have no documentation or information once it's running.nbsp; I =
ran it=20
for 4 hours once and had no idea how to close it.nbsp; I had to use =
"kill," the=20
only command I could think of to close it.nbsp; When I got back to =
Windows, I=20
saw that my work had not been saved.nbsp; I had set the option in =
Windows for=20
disk saves every 15 minutes.nbsp; Mprime and Prime95 shared the same =
data=20
files, like they are supposed to.nbsp; What's going on?nbsp; I'd vote =
for an=20
mprime on an X-server.nbsp; I want to see SOMETHING while the thing's=20
going.nbsp; At least show me the iteration #, iteration % of total, and =
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DIVFONT face=3DArial size=3D2"The brave do not fear the =
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Square, Final Fantasy VII/FONT/DIV
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NT/DIV/BODY/HTML

- --=_NextPart_000_000D_01BF0DAC.4FC96D40--

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--

Date: Sun, 3 Oct 1999 15:39:53 -0400 (EDT)
From: Lucas Wiman  [EMAIL PROTECTED]
Subject: Re: Mersenne: Mprime

 I really want to run the Linux prime search software when I'm in Red Hat 5.2 (I'm 
usually in Windows 98), but the program seems to have no documentation or information 
once it's running.  I ran it for 4 hours once and had no idea how to close it.  I had 
to use "kill," the only command I could think of to close it.  When I got back to 
Windows, I saw that my work had not been saved.  I had set the option in Windows for 
disk saves every 15 minutes.  Mprime and Prime95 shared the same data files, like 
they are supposed to.  What's going on?  I'd vote for an mprime on an X-server.  I 
want to see SOMETHING while the thing's going.  At least show me the iteration #, 
iteration % of total, and seconds / iteration.

(could everyone please set their mailer to wrap at 80 charactors)

Try mprime -m 
then choose 6.  Test/Continue

It seems a bit odd that it didn't save work when it was killed.
I thought it was supposed to.  What signal did you send the process?
Try CTRL+C if kill continually keeps it from saving.

- -Lucas
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--

Date: Sun, 03 Oct 1999 21:35:49 GMT
From: [EMAIL PROTECTED] (Michael Oates)
Subject: Re: Mersenne: Mprime

On Sun, 3 Oct 1999 15:39:53 -0400 (EDT), you wrote:

 I really want to run the Linux prime search software when I'm in Red Hat 5.2 (I'm 
usually in Windows 98), but