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Old 2004-05-20, 00:26   #111
jinydu
 
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Dec 2003
Hopefully Near M48

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21169397 0x746B874910048A__ curtisc grn16-11
22776563 0xCF3C3B04BD5A10__ curtisc wde3100-028
24036583 0x7EC80125B6DB7E__ jfindley M3
23393483 0xD9BFF123AAE613__ mesirow DellH

Those are the four candidates.
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Old 2004-05-20, 00:49   #112
PrimeCruncher
 
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Quote:
Originally Posted by liqi
What exponent should george`s machine run a month on?
It certainly doesn't look like the verification will take a month. The updates Xyzzy has been posting show fairly rapid progress. I doubt it'll take an entire month to finish that one, but it may take a month to finish ALL of them.
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Old 2004-05-20, 03:57   #113
justinsane
 
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Quote:
Originally Posted by philmoore
Great! If I don't find a factor of M21169397 running stage 2 to 4,200,000, I'll go ahead and run it to 8,400,000.
And I'll start M23393483 stage 1 to 525,000 stage 2 to 8,400,000 tomorrow morning on a rather fast box, should be done quick
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Old 2004-05-20, 04:58   #114
TTn
 

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I have cross referenced my general Mersenne estimations and found that:

2^23393483-1 Should be Prime!

This is my non-encrypted guess, based upon the pre-screened candidates given by Y'all.

 
Old 2004-05-20, 05:29   #115
jinydu
 
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How's the factoring going?
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Old 2004-05-20, 12:16   #116
Xyzzy
 
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9,000,000...
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Old 2004-05-20, 12:57   #117
liqi
 
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Quote:
Originally Posted by Xyzzy
9,000,000...
so quick!!
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Old 2004-05-20, 13:04   #118
jinydu
 
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I estimate that his average per iteration time is about 0.046s, judging by his posts.

In fact, that's about the same per iteration time as my computer when I close down everything and its working on a 20.3M exponent. And I'm using a P4 too!

Last fiddled with by jinydu on 2004-05-20 at 13:08
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Old 2004-05-20, 14:41   #119
Prime95
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Jeff is leading the race in the official different-hardware different-software test. He matches xyzzy at 3,000,000 iterations.
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Old 2004-05-20, 15:20   #120
Lumo
 
May 2004

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Default You are right!

Oh, sure. You are absolutely right. In fact, I know that all divisors of 2^N-1 are of the form 2kN+-1 for an integer k - I forgot the sign, but only one sign is correct... This makes it clear that these numbers are not only odd, but they are not multiple of any small prime.

This makes the numbers 2^N-1 seemingly much more frequent, and I wonder why the original conjecture works so well... Well, let me admit that I believe that the statement with the sqrt(2) limit might still be correct, and therefore what you say - even though it is true - is compensated by something else, so that it is still legitimate to use this statistical reasoning.

OK, let me withdraw the word "theorem". ;-) do you have a different specific idea whether the limit exists, and what it is?

Lubos Motl - I had to change my username because LumĂ­dek can't be logged in (probably a bug with the 8bit characters).
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Old 2004-05-20, 17:22   #121
philmoore
 
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No factor found on M21169397:

[Thu May 20 09:42:36 2004]
M21169397 completed P-1, B1=525000, B2=8400000, WZ1: 234E1D80

Does anyone have an estimate of the chances of finding a factor if I increase B2 again? I suspect it is pretty small, but would be curious to find out.
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