20080604, 21:09  #1 
(loop (#_fork))
Feb 2006
Cambridge, England
14466_{8} Posts 
5^4211 polynomial search
This will be quite a lot of work, I suspect several CPUyears; we're in territory where only the German Information Security Service admits to having gone before.
Pick a number between zero and 1000 which hasn't been picked before, and post saying which you've picked; as far as I know, you're no more likely to find a good polynomial in any range than in any other. I will use '389' as the example number. Put the line Code:
N 856747567165509732120757534754047466186338557004916269612235956443230634437193149247989845404816349224130750819510131856088353227722964229252203600736528648205287332264407802189199 Obtain (from http://www.mersenneforum.org/showpos...10&postcount=2) the pol51m0b and pol51opt executables. Run Code:
pol51m0b b 5421.389 p 8 n 1e27 a 38900000 A 39000000 which will take about 36 hours on one core2/2400 core and produce a file 5421.389.51.m with several thousand lines. Run Code:
pol51opt n 3e26 N 5e23 b 5421.389 e 4.0e14 Code:
BEGIN POLY #skewness 896878.58 norm 5.48e+24 alpha 5.10 Murphy_E 5.67e14 X5 2494474680 X4 60025243754288938 X3 3373062207827200423874 X2 35057246057064976169265284946 X1 4645652748792665336283343904631161 X0 2514680780127600312183202859318919091241 Y1 76567071105830565601 Y0 12798962554719076778809278463492440 M 771275635317927246367346585552260695115076213417404129525820216452123918976984444801245585894710751022186339999038527519003784741579483346878475693401519268671947976948572997457615 END POLY Repeat the whole process until July 19th or until you're fed up. I suspect there's a polynomial with a score better than 7.0e14 to be found, and every 0.01e14 improvement in the score will save us something like a hundred CPUhours at the sieving stage; we'll start sieving with the best polynomial that's been found by July 19th Reservations frmky *000027(6.72) *029041 (6.29) *066099(6.33) andi47 *028 *047 *048059(6.93) *104(6.31) *105(5.47) *106(5.67) *109(5.77) *110(5.59) *111(5.10) *114(5.22) *125(4.89) *126(5.26) *129(5.34) *132(5.36) *133139+(5.73) *142(5.51) *315(5.39) *777 batalov *042046 *060065(6.21) *115124(6.33) *200201(5.87) *420429(5.81) bsquared *100101 (5.82) *102103(5.42) *107108(5.58) *112113(5.62) *127128(5.57) *130131(5.53) *140141(6.01) 143144 *150199(6.36) *450499(6.21; maybe more) *500599(6.41) fivemack *350359(6.40) *360369(6.13) *370379(6.15) *380388(5.99) *389(5.46) *390(5.63) *391(5.77) *392(5.70) *393(5.43) *394(6.05) *395(5.62) *396399(5.98) *part of 970979 (6.09) *980989(6.12) *990999(5.86) Incremental records 4 June 5.67e14 by fivemack at X5=2494474680 (and different parameters  I'm running 03e7 at p9, best was 5.81e14) 5 June 6.35e14 by andi47 at X5=4701325920 6 June 6.38e14 by frmky at X5=1525027200 7 June 6.51e14 by Batalov at X5=4329163800 7 June 6.72e14 by frmky at X5=2676189720 30 June 6.93e014 by andi47 at X5=5767280580 Last fiddled with by fivemack on 20080721 at 08:52 Reason: results and reservations 
20080605, 05:58  #2  
Oct 2004
Austria
2482_{10} Posts 
Quote:
I will increase n and N to run pol51opt in parallel to pol51m0b, I hope n 3.5e26 N 5.5e26 is sufficient. (further testing will be necessary.) 

20080605, 06:50  #3 
Jul 2003
So Cal
3·881 Posts 
Usually, but not always. I'm splitting my range across 20 processor cores with each running a range of 200 a's at a time. pol51m0b takes up to a few minutes. pol51opt runs as fast or faster on most batches but pol51opt ran an hour on one batch, 45 minutes on another, and up to 30 minutes on a number of others. This is on 2GHz Opteron Barcelonas.
Greg 
20080605, 07:16  #4 
Oct 2004
Austria
2×17×73 Posts 
reserving 28
edit: and increasing n and N to n 4.5e26 N 6.5e23 for pol51opt (I don't want it to outspeed pol51m0b when running parallelly.) Last fiddled with by Andi47 on 20080605 at 07:20 
20080605, 11:40  #5  
Tribal Bullet
Oct 2004
5×23×31 Posts 
Quote:


20080605, 12:12  #6  
"Bob Silverman"
Nov 2003
North of Boston
2^{2}·1,889 Posts 
Quote:
Allow me to ask: Why was this number chosen? If the goal is to tackle a ~180 digit number by GNFS, then allow me to suggest that there are better (IMO) candidates. There are a number of numbers in this range from the 1st edition of the Cunningham book that are still unfactored. From an historical viewpoint, I would have to say that they are 'better' candidates. Also, since this is the Mersenne forum, allow me to point out that there is even a Mersenne number in this range: 2,877. 

20080605, 15:46  #7 
(loop (#_fork))
Feb 2006
Cambridge, England
2·7·461 Posts 
I picked 5^4211 as the smallest Cunningham number satisfying
2^8771 seems perfectly suited to Childer/Dodson's resources; it's a bit smaller than 7^313+1 which they have already reserved, though I suppose the large alreadyknown factor makes it less exciting than the biggest numbers they're working on. 
20080605, 16:00  #8 
(loop (#_fork))
Feb 2006
Cambridge, England
2×7×461 Posts 
I've had a look at the Cunningham Tables book, but I can't find a clear indication of what the search limits were in the first, second and third editions, apart from 'All numbers from the base 3 to base 12 tables in our first and second editions have been factored'.
Has the base2 table always run up to 2^1200? 
20080605, 16:12  #9  
"Bob Silverman"
Nov 2003
North of Boston
16604_{8} Posts 
Quote:
Brillhart et.al. extended it to 1200. 

20080605, 16:41  #10  
"Bob Silverman"
Nov 2003
North of Boston
2^{2}×1,889 Posts 
Quote:
Just out of curiosity: How do you plan on doing the LA? I estimate the matrix will have about 30M rows.... 

20080605, 17:10  #11 
Oct 2004
Austria
9B2_{16} Posts 
My best poly so far:
Code:
BEGIN POLY #skewness 519405.61 norm 2.35e+024 alpha 4.88 Murphy_E 6.35e014 X5 4701325920 X4 47150964287659101 X3 15102466789075255601152 X2 10132984676580634566197564310 X1 125328000147380591200834426263986 X0 7806931538168072994169841533113060580 Y1 14205489745441387613 Y0 11275258440050778971199095630546963 M 436601395614430864948853751861763166776593289656180372438832903491529854736236398131551339033730420628551770162585375025235916031559028217830446395115153882860149542060790848576097 END POLY 
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