Mersenne Digest Wednesday, April 25 2001 Volume 01 : Number 843
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Date: Sun, 22 Apr 2001 20:37:11 -0700
From: Spike Jones <[EMAIL PROTECTED]>
Subject: Re: Mersenne: [slightly OT] Web discussion about distributed computing
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Nathan Russell wrote:
>
>http://www.half-empty.org/servlet/LoadPage?pageID=idea&ideaid=1644&sortmode=3&viewmode=3
>
> I thought the prime community might want to stop by and take a look at
> what's been said.
Nathan I liked your comment about the largest genuine composite:
a number known to be composite but for which none of the factors
are known. I suppose we could set up a computer to arbitrarily
generate a few million 20 digit primes by factoring, then multiply
them all together to get the largest known composite number for
which none of the factors would be "known", eh? spike
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<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
Nathan Russell wrote:
<blockquote TYPE=CITE><a
href="http://www.half-empty.org/servlet/LoadPage?pageID=idea&ideaid=1644&sortmode=3&viewmode=3";>http://www.half-empty.org/servlet/LoadPage?pageID=idea&ideaid=1644&sortmode=3&viewmode=3</a>
<p>I thought the prime community might want to stop by and take a look
at
<br>what's been said.</blockquote>
Nathan I liked your comment about the largest genuine composite:
<br>a number known to be composite but for which none of the factors
<br>are known. I suppose we could set up a computer to arbitrarily
<br>generate a few million 20 digit primes by factoring, then multiply
<br>them all together to get the largest known composite number for
<br>which none of the factors would be "known", eh? spike</html>
- --------------953E7B41754C35108B97B346--
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Date: Mon, 23 Apr 2001 06:40:29 +0200 (MET DST)
From: [EMAIL PROTECTED]
Subject: Re: Mersenne: [slightly OT] Web discussion about distributed computing
Spike Jones <[EMAIL PROTECTED]> comments;
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> Nathan I liked your comment about the largest genuine composite:
> a number known to be composite but for which none of the factors
> are known. I suppose we could set up a computer to arbitrarily
> generate a few million 20 digit primes by factoring, then multiply
> them all together to get the largest known composite number for
> which none of the factors would be "known", eh? spike
Knowing that the product is composed of 20-digit
primes, it can be broken by ECM.
If the product has 100 million decimal digits (330 million bits),
then we need 41 megabytes per residue.
ECM step 1 with homogeneous coordinates needs about 6-10 such residues,
so 1 Gb is more than adequate even with temporaries for FFT code.
The first GCD will reveal several of the factors --
how many depends upon the step 1 limit.
Perhaps one finds an 8-million-digit factor and a 92-million-digit cofactor.
Both of these can be fed back into the algorithm
(recursively) until the original number is completely factored.
This computation can be partially parallelized. Perhaps 30 machines
each get two factors, around 8 million digits and 92 million digits.
Using results from two machines, we get four factors, about
640000, 7360000, 7360000, 84640000 digits.
After incorporating results from all 30 machines,
the largest factor (where all curves were unsuccessful)
will be about 10^8 * (23/25)^20 ~- 8.2 million digits.
Spike's idea, with 50-digit or 100-digit primes rather than
20 digits, will give hard-to-factor numbers using today's
Are there any large known composite numbers c
for which we know a (not necessarily prime) factor of 2^c - 1 but not of c?
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Date: Mon, 23 Apr 2001 11:31:08 -0400
From: Nathan Russell <[EMAIL PROTECTED]>
Subject: Re: Mersenne: [slightly OT] Web discussion about distributed computing
(Sprry Spike, I mistyped the list address the first time on the copy i
sent to you)
On Sun, 22 Apr 2001 20:37:11 -0700, Spike Jones wrote:
>Nathan Russell wrote:
>
>>
>http://www.half-empty.org/servlet/LoadPage?pageID=idea&ideaid=1644&sortmode=3&viewmode=3
>>
>> I thought the prime community might want to stop by and take a look at
>> what's been said.
>
>Nathan I liked your comment about the largest genuine composite:
>a number known to be composite but for which none of the factors
>are known. I suppose we could set up a computer to arbitrarily
>generate a few million 20 digit primes by factoring, then multiply
>them all together to get the largest known composite number for
>which none of the factors would be "known", eh? spike
That's an interesting thought - and perhaps I was speaking too
quickly.
For that matter, pick fifty of the top hundred numbers on the Prime
Pages and then multiply them together using calc, maple or some such
software (and plenty of swap space!). There's no way you'll remember
which numbers you originally chose.
Perhaps I should have said something like "have ever been known"? Of
course, then we get into a debate over whether a computer can 'know'
something....
Nathan
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------------------------------
Date: Mon, 23 Apr 2001 18:25:40 -0000
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: [slightly OT] Web discussion about distributed computing
On 22 Apr 2001, at 20:37, Spike Jones wrote:
> Nathan I liked your comment about the largest genuine composite:
> a number known to be composite but for which none of the factors
> are known. I suppose we could set up a computer to arbitrarily
> generate a few million 20 digit primes by factoring, then multiply
> them all together to get the largest known composite number for which
> none of the factors would be "known", eh? spike
If you allow a construction like that then, whatever number you
suggest, I'll nominate a bigger one.
AFAIK the largest number currently known to be composite but with no
known factors is 2^33219281-1, the only 10 million digit Mersenne
number which has been LL tested twice with matching final residual.
(Rick Pali, 2000 & Brian Beesley, 2001) This number has been trial
factored up to 2^68 and subjected to P-1 with B1=495000.
Naturally I am happy to give up this claim to "fame" should a factor
of this number be discovered, or when a larger number is eventually
subjected to a definitive test for compositeness and cross-checked
against the possibility of error.
Regards
Brian Beesley
1775*2^332181+1 is prime! (100000 digits) Discovered 22-Apr-2001
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Date: Tue, 24 Apr 2001 08:28:47 +0100
From: "Andy Hedges" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: [slightly OT] Web discussion about distributed computing
>1775*2^332181+1 is prime! (100000 digits) Discovered 22-Apr-2001
How was is found?
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Date: Tue, 24 Apr 2001 19:48:53 -0500
From: Ken Kriesel <[EMAIL PROTECTED]>
Subject: Re: Mersenne: [slightly OT] Web discussion about distributed computing
Brian is likely to break his own record in about 5 months, with an LLtest of
2^40250087 -1 proceeding rapidly, with Stephan Grupp's simultaneous
test of the same number trailing by 11 days at the moment, both as
part of the continuing mersenne QA effort.
This candidate was P-1 tested by Brian, B1=360000, B2=1800000
after being trial factored by Nathan Russell last summer.
There are still some QA exponents available in the upper stratosphere
ranges for various forms of factoring, or LLtest. (These mostly require
cpu speeds above 500Mhz to complete LLtest in less than 5 years. Each.)
Ken
At 06:25 PM 4/23/2001 -0000, Brian J. Beesley wrote:
>
>If you allow a construction like that then, whatever number you
>suggest, I'll nominate a bigger one.
>
>AFAIK the largest number currently known to be composite but with no
>known factors is 2^33219281-1, the only 10 million digit Mersenne
>number which has been LL tested twice with matching final residual.
>(Rick Pali, 2000 & Brian Beesley, 2001) This number has been trial
>factored up to 2^68 and subjected to P-1 with B1=495000.
>
>Naturally I am happy to give up this claim to "fame" should a factor
>of this number be discovered, or when a larger number is eventually
>subjected to a definitive test for compositeness and cross-checked
>against the possibility of error.
>
>
>Regards
>Brian Beesley
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------------------------------
Date: Wed, 25 Apr 2001 23:33:34 -0400
From: George Woltman <[EMAIL PROTECTED]>
Subject: Mersenne: More P4 timings
Hi all,
I just completed my first 512K FFT using the new SSE2 instructions!
The 512K FFT handles exponents up to 10.3 million.
Timings are as follows:
1.4GHz P4, old code: 0.126 sec.
1.4GHz P4, new code: 0.048 sec.
1.2GHz Athlon, 133MHz DDR: 0.084 sec.
I have a few more optimizations up my sleeve. I think my goal
of 0.040 seconds is achievable.
Having fun,
George
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End of Mersenne Digest V1 #843
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