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Old 2005-09-13, 10:20   #1
MoZ
 
Feb 2004
Paris

38 Posts
Default Some news about Home Prime ?

Hello

On http://www.worldofnumbers.com/topic1.htm, it seems nothing new.

Has anyone any info about this ?

It seems that the work has ended on January 3, 2004 (by Alex Kruppa and Paul Leyland)

Looks like the c204 which is
34636914551761683256158051843633814787706289345767962219592\
92066545246725876130493435583943733963381945857837752697856\
75210636696425094776859733305947996048061499249566197147212\
934512427988113420226762897
could be GMP-ECM-able even if 5500 curves at B1=11M, and 9000 curves at B1=44M has already been done.

Any more results about this ?

Cheers

MoZ
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Old 2005-09-13, 12:20   #2
Mystwalker
 
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Jul 2004
Potsdam, Germany

33F16 Posts
Smile

Chances are that there exists a factor < ~60 digits, which can be found by ECM, given enough computing power (over time).
But for most, the benefit/effort ratio is not high enough to continue this factorization attempt. For example, a lot of Cunningham numbers have obtained way less effort, but are generally considered "more valuable" (AFAIK, the Home Primes are merely a recreational project with no further use).

Having said that, I don't want to dictate where people have to put their efforts on. I think that everyone should choose their own favorites, based on their individual preferences. So please, only take this posting as decision support.
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Old 2005-09-13, 12:33   #3
akruppa
 
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"Nancy"
Aug 2002
Alexandria

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>Chances are that there exists a factor < ~60 digits

I'm not too sure about that...

Alex
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Old 2005-09-13, 13:09   #4
Mystwalker
 
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Jul 2004
Potsdam, Germany

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Well, I planned to add "but are not very high", but forgot to do it lateron.
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Old 2005-09-13, 14:16   #5
R.D. Silverman
 
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Nov 2003

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Quote:
Originally Posted by Mystwalker
Well, I planned to add "but are not very high", but forgot to do it lateron.
Actually, the probability can be computed if we have reasonably accurate
ECM curve counts. My paper "A Practical Analysis of ECM" shows how to do
this.

Suppose the number we are trying to factor is a randomly chosen integer
[i.e. chosen uniformly at random from all odd numbers of the same size]

Dickman's function tells us the distribution (in terms of size) of its prime
factors. This gives a Bayesian prior. Then, the ECM failures yield further
information [a sample]. We then use Bayes' Theorem to derive a posterior
distribution, from which we can compute an expected value.
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Old 2006-02-20, 20:20   #6
jasong
 
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"Jason Goatcher"
Mar 2005

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Quote:
Originally Posted by R.D. Silverman
We then use Bayes' Theorem to derive a posterior
distribution, from which we can compute an expected value.
My mom worries constantly about her posterior distribution, maybe you could help her?

Just kidding. :D
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Old 2006-02-28, 12:02   #7
[Leo_01]
 
May 2005
Lyon

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Hello,

For information:
hp49:
i have run 2280 @ b1=11e7 on hp49(100).c204 (with ecm 5.0.3) I had done them in 2004 and at the beginning of 2005. Sean Irvine 100 * B1= 11e7
Details:
- http://euclide.euclide.free.fr/hp49/ (it is same the link that I had already posted a few months ago, it didn't evolve
- http://www.angelfire.com/falcon2/hom...oendprime.html

hp146/273:
7704 @ B1=43e6
3 @ B1 = 11e7
p+1 1 @ B1 = 10^9
p-1 3 @ B1 = 10^9

hp242:

p+1 1 @ B1 = 10^9
p-1 3 @ B1 = 2*10^9

hp300:
p+1 1 @ B1 = 10^9
p-1 3 @ B1 = 2*10^9

hp312:
4402 @ B1 = 11e6
7779 @ B1= 43e6
370 @ B1 = 11e7
p+1 1 @ B1 = 10^9
p-1 3 @ B1 = 10^9

hp495:
p+1 1 @ B1 = 10^9
p-1 3 @ B1 = 2*10^9

hp858:
p+1 1 @ B1 = 10^9
p-1 3 @ B1 = 2*10^9

All without results :-(

Alex

p.s : Sorry for my so bad english :-(

Last fiddled with by [Leo_01] on 2006-02-28 at 12:03
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