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-   -   100M digits prefactor project. (

VBCurtis 2005-02-08 15:31

I don't care which I run for fun-- this or the billion-digit search. I picked up a couple weeks' worth of factoring on the Billion site last night, so if you get things updated within 2-3 weeks, I'll be happy to contribute.

I finished the range mentioned yesterday, but I'm not sure where to email it.. yahoo rejected the mail sent to addy on the site.

If your efforts are better spent helping admin the BD search, I'm happy to help there, too, and let this one slide into darkness.

VBCurtis 2005-02-14 16:02

I'll have everything from 333100000 to 333600000 finished to 52 bits by the weekend. Where do I email the results files? Can I get your filtering program, so I can extend the ranges to 54 or 55 bits for exponents without a factor? I have 3 slow (500 or slower) machines working on factoring.


Uncwilly 2005-02-14 17:08

The e-mail address listed on the site is active again. The program is touchy, (it has a quirk or two) and I don't want to have somebody lose data when it gets run. I will try to be more on top of things...

VBCurtis 2005-03-11 06:07

I'll finish the first range (333100-333200K) to 55 bits over the weekend. I built the worktodo file by hand from the 50-bit results.... UncWilly, did you get the other results files? This search seems useful in the nearer future, so I want to run half my classroom's machines on it (they're nearly all on Billion right now); there's joy in finding factors so quickly, too. Maybe the posts will stir a little interest in the project!
I plan to build another worktodo to 56 or 57 bits next week for the same range-- easy to change bit-limits and delete the exponents with factors found during the previous pass.
Any guidance?

ValerieVonck 2005-03-11 07:40

M333700000 to M333799999 from 1 to 50 bits

Peter Nelson 2005-03-11 15:58

Factoring probabilities
Hi, I'm interested in how likely we are to find a factor by trial factoring.

Primenet records a found factor, but regretably (with hindsight) not the number of tests required to find it.

With 100mdpp you have opportunity to record/collate this important stat.

Therefore could the person who has these results please count up for me, and ideally update your project website to include this info.

If you could break it down by bit depth that would be great!

Or raw data would be acceptable and I will collate my own stats.

Something like eg 332,192,831 through nnn nnn nnn tested exhaustively to 50 bits and found fff factors. (followed by next range by someone else).

If you have no idea what I'm talking about say so and I will try to clarify.

Uncwilly 2005-03-11 17:06

I think that I may know what you mean. Later today I will get off my rear and work on the site when I get to the machine that has the data on it.
BTW, do you mean xxx,xxx,xxx to yyy,yyy,yyy have been tested to zz bits and found aaa factors is acceptable to any zz? Cause once I ran groups through a set bit level, I culled all that had factors, then reprocessed the remainders to a higher level.

ValerieVonck 2005-03-12 00:22

M333700000 to M333799999 from 1 to 50 bits => Complete

VBCurtis 2005-03-12 17:57

It seems easy enough to report batches (likely in the 100K increments UncWilly has set up on his page) by number of factors found from xx bits to yy bits.
UncWilly has set up the search to run to 50 bits first, then run the nonfactored numbers to 52 or 53, etc... this seems like the type of data you wish for, in the sense of "if we run one more bit on this batch, how much time per factor does it cost?" My current batch is running 50 to 55 bits, and I'll post number of factors found (and time spent/machine speed) Tuesday when the run finishes.
However, though I have no specific thread in mind, these stats have been run extensively on smaller numbers for GIMPS to determine the most efficient use of time between factoring and LL testing; George has the bit depth set so that when factoring takes more time per expected factor found than LL, Primenet moves the exponent from TF status to LL test status. For exponents around 28 million (the last size I TF'ed for Primenet), that cutoff was 69 bits. For project billion, someone calculated the level as roughly 85 bits (ouch!), but the calculation is heavily dependent on the speed of the code doing the factoring, and the code doing the LL testing, so none of us would really work to 85 bits on a number (not to mention the years it would take!).

ValerieVonck 2005-03-13 01:05

Range: 333600000 333699999
Number of exponents: 5127
from 1 to 50

cheesehead 2005-03-13 01:13

[QUOTE=Peter Nelson]Hi, I'm interested in how likely we are to find a factor by trial factoring.[/QUOTE]
AFAIK we have only the [i]empirical[/i] statement on [url=""][/url] (last paragraph in "Trial Factoring" section) that the chance of finding a factor between 2^x and 2^(x+1) is about 1/x. But note that (a) this was derived from TF on rather smaller exponents and ranges, and (b) it's an [i]approximation[/i] that breaks down when the size of the Mersenne's exponent is too close to the size of the factors being tried (i.e, k in 2kp+1 is small).

See thread "Probability of finding a factor" at [url=""][/url]

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