mersenneforum.org 100M digits prefactor project.
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2006-01-13, 16:09   #254
fetofs

Aug 2005
Brazil

2×181 Posts

Quote:
 Originally Posted by gribozavr You should use this thread (But only after TFing it to 2^76-2^78, maybe higher, see post by VBCurtis above): http://mersenneforum.org/showthread.php?t=3175
And you should you should set UsePrimenet=0 in your prime.ini.

 2006-01-18, 15:01 #255 M0CZY     May 2005 Brutal Police State, UK 3·41 Posts Prime 95 for100M digits prefactor project? Is it OK to use Prime 95 v 24.14 for factoring 332M exponents on this project, as Factor_4 doesn't work for me, I just get a stack dump.
 2006-01-19, 18:43 #256 gribozavr     Mar 2005 Internet; Ukraine, Kiev 6278 Posts Did you download the correct version of factor4 for your CPU (SSE2 vs. normal)? What does the stack dump say?
 2006-01-20, 03:00 #257 Prime95 P90 years forever!     Aug 2002 Yeehaw, FL 2·5·7·107 Posts The current Prime95 client would factor these numbers to 2^76. The next prime95 client will factor to 2^74 then try P-1 factoring then factor to 2^76. Whether the prime95 client in use at the time these huge numbers are LL tested will have the same breakeven points is an open issue.
2006-01-20, 15:40   #258
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

34×59 Posts

Quote:
 You should use this thread (But only after TFing it to 2^76-2^78, maybe higher, see post by VBCurtis above): http://mersenneforum.org/showthread.php?t=3175
A slightly more accurate guide for trial-factoring bitdepth:
LL testing time rises roughly with the square of the exponent, so a power twice as long takes roughly 4 times longer to test. Thus, we should spend 4 times longer trial-factoring a number whose exponent is twice as large as some reference point; 4 times longer is the same as 2 bits higher.

GIMPS moves to 68-bit factoring at n=28 million. Extrapolating, n=56 million should take 70 bits, 112 million should take 72 (thus the 100M exponent above falls into the 71 "for sure", 72 if you feel like it area), 225 million 74 bits, and our 100M digit project 75 bits. I overestimated in my first post.

Project billion, at 10 times larger, would take 81 or 82 bits (as Prime95 pointed out, exact depth depends on the efficiency of the CPU in use/algorithm efficiency at the time an LL test is under consideration for such a number). If we round down slightly in the hopes of more efficient code in the future/wanting to make sure we don't waste work done, we should stop 100M at 75 bits, project billion at 81 bits.
Note that Prime95's observation about P-1 factoring should give us pause in the 75-bit range-- at that depth, trial factoring may not be most efficient. P-1 is beyond the scope of our project, so perhaps a 74-bit ceiling for trial factoring should be established?

Last fiddled with by VBCurtis on 2006-01-20 at 15:41

2006-01-20, 19:25   #259
gribozavr

Mar 2005
Internet; Ukraine, Kiev

11×37 Posts

Quote:
 Originally Posted by VBCurtis Optimal bit depth can be extended from Prime's bit depth for smaller numbers-- the idea is that we should factor to a depth that has LL testing eliminating candidates at the same rate as trial-factoring.
Quote:
 Originally Posted by VBCurtis LL testing time rises roughly with the square of the exponent, so a power twice as long takes roughly 4 times longer to test. Thus, we should spend 4 times longer trial-factoring a number whose exponent is twice as large as some reference point; 4 times longer is the same as 2 bits higher.
I may be wrong, but I will ask anyway. Do you take into account the rate at which TF removes exponents? As Ernst wrote above:

Quote:
 ewmayerYou're much less likely to find a factor between 70 and 71 bits than (say) 1-64 bits or 64-70, even though testing 70-71 is roughly as expensive as sieving from scratch up to 70 bits
As I understood, you assumed that factors are equally distributed.

 2006-01-21, 10:14 #260 M0CZY     May 2005 Brutal Police State, UK 3×41 Posts My computer is a rather slow Pentium 233 MMX, with 256 MB of RAM. It is running Windows 2000 Professional Service Pack 4. The version I have downloaded is factor4_02. As a test, I entered exponent 332193457. The program stopped immediately, and created a file called factor4.exe.stackdump, which says: Exception: STATUS_ILLEGAL_INSTRUCTION at eip=10013A27 eax=53E5645C ebx=00000001 ecx=10030224 edx=10030228 esi=13CCDEB1 edi=52FD071A ebp=C0CFD797 esp=00040774 program=C:\Documents and Settings\Administrator\My Documents\unzipped\factor4_02\factor4.exe, pid 980, thread main cs=001B ds=0023 es=0023 fs=0038 gs=0000 ss=0023 Stack trace: Frame Function Args 67010 [main] factor4 980 handle_exceptions: Exception: STATUS_ACCESS_VIOLATION 77804 [main] factor4 980 handle_exceptions: Error while dumping state (probably corrupted stack) ------------------------------------------------------------------------------------------------------------------------ Prime 95, Thank you for your information.
 2006-01-22, 17:55 #261 gribozavr     Mar 2005 Internet; Ukraine, Kiev 6278 Posts How to use Prime95/mprime for 100Mdpp: http://ohmdpp.5gigs.com/prime95.shtml
 2006-01-23, 09:44 #262 Footmaster     Mar 2004 3·13 Posts I'd like to continue my current reservation and also reserve 332193431 and 332193457 Thanks Footmaster Last fiddled with by Footmaster on 2006-01-23 at 09:51
 2006-01-23, 17:03 #263 Footmaster     Mar 2004 3×13 Posts M332193937 no factor to 2^66, Wc1: 745BA2A7 M332193887 no factor to 2^66, Wc1: 7463A2A1 M332193913 no factor to 2^66, Wc1: 7460A2A5 I ran these through Prime95 and i plan to take all of the exponents up to at least ^66 Regards Footmaster
2006-01-23, 19:44   #264
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

34·59 Posts

Quote:
 Originally Posted by gribozavr I may be wrong, but I will ask anyway. Do you take into account the rate at which TF removes exponents? As Ernst wrote above: As I understood, you assumed that factors are equally distributed.
The chance of finding a factor in a single bit-level is roughly 1/n, where n is the level you are searching. Thus, you have about a 1/69 chance of finding a factor from 2^68 to 2^69, and 1/70 chance of finding a factor from 2^69 to 2^70. Since my suggestions are very rough estimates, I considered this to be an equal chance per bit. Ernst's quote points out that going from 69 to 70 costs about as much CPU time as going from start to 69, yet has a very small relative chance of success (compared to the first 69 bit-searching).

Another way to say it is each bit has about the same chance of success, but takes twice as long as the bit that came before.
-Curtis

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