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Old 2011-08-02, 18:46   #1
Dubslow
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Default Factoring bit depth?

Hey guys,
I read somewhere that the bit depth listings for exponents was on the wiki, but I couldn't find it. Anybody have a list, or point me to one?
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Old 2011-08-02, 19:30   #2
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Here is a list from september 2009:
http://www.mersenne.org/various/math.php

but I think they were recalculated more recent somewhere in the forum but can't find it.
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Old 2011-08-02, 19:38   #3
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I agree, because I know now that the low/mid 50,000,000's are being taken up to 71. (Saw P95 mention that in a GPU thread, but haven't seen a complete revised table since.)
Although, we could assume the same boundaries, and then just add two bits to the table there. Sound reasonable?
Also, what depth are the LMH/100 million factorings going to?

Last fiddled with by Dubslow on 2011-08-02 at 19:41
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Old 2011-08-02, 23:37   #4
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Try James's calculator: http://mersenne-aries.sili.net/factorbits.php

I don't know if it has been updated recently. 100M digit numbers are taken to 77. But those with GPU's have taken many to higher levels. From: 332192831 to 332599999 there are currently 444 at 79 bits or higher.
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Old 2011-08-02, 23:56   #5
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Quote:
Originally Posted by ATH View Post
Here is a list from september 2009:
http://www.mersenne.org/various/math.php

but I think they were recalculated more recent somewhere in the forum but can't find it.
You might mean this:
Quote:
Originally Posted by davieddy View Post
TF from 2^(69+x) to 2^(70+x) takes
119.566*2^x/(exponent/10^6) GHz-days.
LL takes ~ .036*(exponent/10^6)^2 Ghz-days.

I'll take the probability of a finding a factor to be 1/100 to take
account of past or future P-1 work.

The "break-even point" for TF on a CPU is given by:

119.566*2^x/(exponent/10^6) = .00072*(exponent/10^6)^2
(assuming finding a factor saves 2 LL tests)

exponent/10^6 = 55 * 1.26^x

So TF (by CPU) to:
68 bits for exponent < 43M
69 bits for exponent < 55M
70 bits for exponent < 69M
71 bits for exponent < 87M

For the DC range,
simply halve the exponent and subtract 4 from the bit level.
But this is a bit academic now GPUs are so much faster at TF than CPUs.
The concensus is that they should be able to do 3 more bits without
breaking sweat.
Early days I know, but I would like to see this borne out in practice!

David

Last fiddled with by davieddy on 2011-08-03 at 00:12
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Old 2011-08-03, 00:42   #6
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Quote:
Originally Posted by Uncwilly View Post
Try James's calculator: http://mersenne-aries.sili.net/factorbits.php

I don't know if it has been updated recently. 100M digit numbers are taken to 77. But those with GPU's have taken many to higher levels. From: 332192831 to 332599999 there are currently 444 at 79 bits or higher.
How good is P-1 in this range?

And how many exponents could those GPUs have raised to 72 bits in the
50M-60M exponent range in the same time?
(Yes I can work it out!)

David
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Old 2011-08-03, 01:09   #7
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I'm asking because I just got my GTX 460 up and running. Does 70-71 in 1.5 hrs, takes a couple of days on my CPU. The calculator isn't correct, it says 69 for 60,000,000 which I know isn't correct.
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Old 2011-08-03, 06:23   #8
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Quote:
Originally Posted by Dubslow View Post
I'm asking because I just got my GTX 460 up and running. Does 70-71 in 1.5 hrs, takes a couple of days on my CPU.
About 200 LLs are assigned per day (exponent 53M).
So it seems that it takes a mere 12 GTX460s (24/7) to dish them out
factored to 71 bits.
My guess is that each of these 12 GPUs would reserve 16 exponents
a day (at least).
Say there are actually 40 GPUs doing TF for imminent LL tests.
If they all reserved just 5 a day, they could TF the daily LL assignments
from 70 to 72 bits.

Doesn't this make good sense?
Remember the CPU doing the LL test can't sensibly TF to 72 bits.

David

Last fiddled with by davieddy on 2011-08-03 at 06:30
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Old 2011-08-03, 13:46   #9
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Quote:
Originally Posted by Dubslow View Post
I agree, because I know now that the low/mid 50,000,000's are being taken up to 71. (Saw P95 mention that in a GPU thread, but haven't seen a complete revised table since.)
Although, we could assume the same boundaries, and then just add two bits to the table there. Sound reasonable?
Also, what depth are the LMH/100 million factorings going to?
I see no discussion of mathematics in this thread.

May I suggest that a different forum would be more appropriate?
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Old 2011-08-03, 15:47   #10
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Quote:
Originally Posted by R.D. Silverman View Post
I see no discussion of mathematics in this thread.

May I suggest that a different forum would be more appropriate?
Sounds like a good idea to me. Either that, or start including some maths.

Any suggestions as to a more appropriate place?

Paul
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Old 2011-08-03, 16:08   #11
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Information and answer seem appropriate
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