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-   -   Factoring humongous Cunningham numbers (https://www.mersenneforum.org/showthread.php?t=5722)

pinhodecarlos 2016-04-05 05:05

Input number is 176648521095254757695831572017874418458831244642790650826091193431673766367336763489498160619901783806447404240317078462752799029 (129 digits)
Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1:308916830
Step 1 took 65926ms
Step 2 took 27644ms
********** Factor found in step 2: 1280728140217088011740794602021286161592377441
Found prime factor of 46 digits: 1280728140217088011740794602021286161592377441
Prime cofactor 137928195335281849907271729444618846169208007815817801433599225868254496324250851669 has 84 digits

xilman 2016-04-05 17:56

[QUOTE=pinhodecarlos;430777]Input number is 176648521095254757695831572017874418458831244642790650826091193431673766367336763489498160619901783806447404240317078462752799029 (129 digits)
Using B1=43000000, B2=240490660426, polynomial Dickson(12), sigma=1:308916830
Step 1 took 65926ms
Step 2 took 27644ms
********** Factor found in step 2: 1280728140217088011740794602021286161592377441
Found prime factor of 46 digits: 1280728140217088011740794602021286161592377441
Prime cofactor 137928195335281849907271729444618846169208007815817801433599225868254496324250851669 has 84 digits[/QUOTE]Thanks. Good find by ECM.

Paul

Batalov 2016-04-06 01:34

Here are the remaining super-easy snfs candidates for anyone to grab:
[CODE]#____the expos are divisible by 15: use quartic____
#Expression Length Starts Difficulty
11 285 + 10 285 139 5005... 158.2
11 285 - 5 285 140 1832... 158.2
11 285 - 6 285 117 2320... 158.2
11 285 + 6 285 135 6794... 158.2
9 315 - 2 315 126 1819... 160.3
9 315 + 5 315 125 7408... 160.3
[strike]5 435 + 2 435 157 2847... 162.1[/strike]
[strike]7 360 + 2 360 158 9001... 162.2[/strike]
7 360 + 5 360 137 1191... 162.2
12 285 - 11 285 147 9019... 164.0
12 285 + 11 285 149 2677... 164.0
#____the expos are divisible by 21: use sextic____
7 336 + 5 336 145 5369... 162.2
7 336 + 6 336 141 3195... 162.2
11 273 - 10 273 140 5600... 162.4
11 273 + 10 273 145 3526... 162.4
11 273 - 3 273 135 3394... 162.4
11 273 + 5 273 128 2484... 162.4
11 273 - 5 273 151 1510... 162.4
11 273 + 6 273 142 5344... 162.4
11 273 + 9 273 125 4620... 162.4
3 609 - 2 609 149 8354... 166.0
3 609 + 2 609 151 5277... 166.0
6 378 + 5 378 143 8121... 168.0
7 357 + 5 357 159 4439... 172.4
11 294 + 2 294 124 1461... 174.9
11 294 + 3 294 140 2949... 174.9
[strike]11 294 + 9 294 114 8709... 174.9[/strike] /--gnfs!
5 441 - 2 441 164 6161... 176.1
5 441 + 3 441 152 6398... 176.1[/CODE]

debrouxl 2016-04-06 06:07

The site is not reachable for me at the moment, from two very different network environments. The Web server accepts connections, but doesn't reply to HTTP requests :wink:

Reviving an ECMNet server for HCN composites would probably speed up splitting 40-50 digit prime factors.

frmky 2016-04-06 16:39

Input number is 135208777652707551627613394323172349287658234884006214941830419038629271216360971380190458698241219665584896965795899 (117 digits)
Using B1=11000000, B2=5714965630, sigma=3:3291808790-3:3291809621 (832 curves)
GPU: Block: 16x32x1 Grid: 26x1x1 (832 parallel curves)
Computing 832 Step 1 took 70619ms of CPU time / 1919508ms of GPU time
GPU: factor 1259183377997512211834207021579593490689 found in Step 2 with curve 809 (-sigma 3:3291809599)
Computing 832 Step 2 on CPU took 1562272ms
********** Factor found in step 2: 1259183377997512211834207021579593490689
Found prime factor of 40 digits: 1259183377997512211834207021579593490689
Prime cofactor 107378146833331757743843198866359402606798797253252448208276600932366296728891 has 78 digits

ET_ 2016-04-06 16:54

[QUOTE=frmky;430865]Input number is 135208777652707551627613394323172349287658234884006214941830419038629271216360971380190458698241219665584896965795899 (117 digits)
Using B1=11000000, B2=5714965630, sigma=3:3291808790-3:3291809621 (832 curves)
GPU: Block: 16x32x1 Grid: 26x1x1 (832 parallel curves)
Computing 832 Step 1 took 70619ms of CPU time / 1919508ms of GPU time
GPU: factor 1259183377997512211834207021579593490689 found in Step 2 with curve 809 (-sigma 3:3291809599)
Computing 832 Step 2 on CPU took 1562272ms
********** Factor found in step 2: 1259183377997512211834207021579593490689
Found prime factor of 40 digits: 1259183377997512211834207021579593490689
Prime cofactor 107378146833331757743843198866359402606798797253252448208276600932366296728891 has 78 digits[/QUOTE]

I didn't know that the bug that prevented a factor from Step 2 to be discovered by a GPU had been squashed! :smile: :bow:
What SVN should I download?

Luigi

xilman 2016-04-06 17:02

[QUOTE=ET_;430868]I didn't know that the bug that prevented a factor from Step 2 to be discovered by a GPU had been squashed! :smile: :bow:
What SVN should I download?

Luigi[/QUOTE]The latest, of course.

There was great rejoicing on the [email]ecm-discuss@lists.gforge.inria.fr[/email] list (by me, if no-one else) when the other Paul found the bug and corrected it.

Paul

jyb 2016-04-06 17:06

[QUOTE=Batalov;430828]Here are the remaining super-easy snfs candidates for anyone to grab:
[CODE]#____the expos are divisible by 15: use quartic____

[snip]

#____the expos are divisible by 21: use sextic____

[snip]

[/CODE][/QUOTE]

In case anyone needs help with generating the correct polynomials for these, you can use the "phi" program. Latest version can be found [URL="http://mersenneforum.org/showthread.php?p=372732#post372732"]here[/URL].

wombatman 2016-04-06 17:34

[QUOTE=ET_;430868]I didn't know that the bug that prevented a factor from Step 2 to be discovered by a GPU had been squashed! :smile: :bow:
What SVN should I download?

Luigi[/QUOTE]

Agreed! That is very exciting!

Batalov 2016-04-06 18:05

[QUOTE=debrouxl;430838]The site is not reachable for me at the moment, from two very different network environments. The Web server accepts connections, but doesn't reply to HTTP requests ...[/QUOTE]
The site still appears down ([URL="http://isup.me/http://leyland.vispa.com"]was then and still is[/URL])

bsquared 2016-04-06 19:39

[QUOTE=frmky;430865]Input number is 135208777652707551627613394323172349287658234884006214941830419038629271216360971380190458698241219665584896965795899 (117 digits)
Using B1=11000000, B2=5714965630, sigma=3:3291808790-3:3291809621 (832 curves)
GPU: Block: 16x32x1 Grid: 26x1x1 (832 parallel curves)
Computing 832 Step 1 took 70619ms of CPU time / 1919508ms of GPU time
GPU: factor 1259183377997512211834207021579593490689 found in Step 2 with curve 809 (-sigma 3:3291809599)
Computing 832 Step 2 on CPU took 1562272ms
********** Factor found in step 2: 1259183377997512211834207021579593490689
Found prime factor of 40 digits: 1259183377997512211834207021579593490689
Prime cofactor 107378146833331757743843198866359402606798797253252448208276600932366296728891 has 78 digits[/QUOTE]

Nice!
Out of curiosity, can you say what NVidia card was used to do this? Also, I'm ignorant of how the program works... does the 70-some seconds of CPU usage occur concurrent to the GPU time? i.e., does the GPU operation consume some CPU cycles as well? Or it is up-front CPU initialization or something? I assume the program stops in step 2 after a factor is found, so that the timing there is for 809 curves instead of 832?


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