20190515, 21:29  #1 
"James Heinrich"
May 2004
exNorthern Ontario
3,851 Posts 
Software to factor arbitrary ~410bit number
I need to obtain the prime factorization of a number such as this
Code:
5272703229220007874811133810104969405477368739513286723394714036551930163895517204360421097050187418157101219550018359697836 Code:
6349584074128565251579621474009238287623563015787101780061041692025765962232486337920863526534965038592191721 I did try PARI/GP using factor(<number) but that's only using one core, and sadly gives no progress output until it comes up with the final answer. Maybe I'm using it wrong. Other suggestions very much welcome. 
20190515, 21:35  #2 
"Luke Richards"
Jan 2018
Birmingham, UK
2^{5}·3^{2} Posts 

20190515, 22:01  #3 
"James Heinrich"
May 2004
exNorthern Ontario
111100001011_{2} Posts 
Useful, yes, but I need more handholding than that.
I've gotten as far as something like Code:
ecm inp worktodo.txt one c 1000 100000 ... Run 1000 out of 1000: Using B1=100000, B2=40868532, polynomial x^2, sigma=1:187039342 Step 1 took 109ms Step 2 took 94ms It also seems to only use one core, unless there's something I missed to specify number of threads? 
20190515, 22:11  #4 
Jul 2003
Behind BB
787_{16} Posts 

20190515, 23:34  #5 
"James Heinrich"
May 2004
exNorthern Ontario
3,851 Posts 
Thanks, but not for my purposes. I don't want to pick bounds, I want to feed it a number and get an answer, that's all.
Sounds like I'll stick with Dario's ECM site since that works exactly as I want, I'll just need to let it run for some hours/days until it comes up with an answer. 
20190516, 00:28  #6 
"Curtis"
Feb 2005
Riverside, CA
3×1,831 Posts 
If you're on linux, CADO will do what you wish without fuss. Google CADONFS and follow the git download instructions from the official page.
command line would be ./cadonfs.py {input number} If you want to use less than the full number of hyperthreads available on your machine, append the flag serverthreads=4 (change 4 to number of hyperthreads you wish to use). Or, if you don't mind waiting a day or so, I can feed it to my CADO install and have factors for you posted to this thread. EDIT: I just noticed the cofactor is much smaller than 410 bits; I'll have factors posted here in about an hour. Last fiddled with by VBCurtis on 20190516 at 00:31 
20190516, 01:02  #7  
"James Heinrich"
May 2004
exNorthern Ontario
3,851 Posts 
Quote:
edit: after a quick test it didn't compile nicely for me, apparently I don't have a Python interpreter either installed or configured. The SIQS running on Dario's site estimates completion in 3.5 days, although if you want to get me a factorization before then I'm grateful (but it's not urgent). The cofactor is 362 bits which is somewhat smaller than 410 but still not that small. Last fiddled with by James Heinrich on 20190516 at 01:03 

20190516, 01:23  #8 
"Curtis"
Feb 2005
Riverside, CA
5493_{10} Posts 
NFS factoring difficulty doubles about every 5 digits, so 48 bits smaller is about 8x faster to factor than the original 410bit number.
Here are your factors: Code:
80372772078870023311028629526527251806209541 79001680667399413021755551127728881024073264821649477463074552981 
20190516, 01:26  #9 
"James Heinrich"
May 2004
exNorthern Ontario
7413_{8} Posts 
Wow, amazing, thank you. Sure wish I had that compiled for Windows :)

20190516, 02:44  #10 
Jun 2003
1010100011111_{2} Posts 
1. Get yafu, GGNFS sievers, gmpecm binary
2. "Tune" yafu 3. Call yafu "factor(<your number>)" It will take care of all the steps. 
20190516, 03:09  #11  
"James Heinrich"
May 2004
exNorthern Ontario
3,851 Posts 
Quote:
Code:
yafux64 "factor(5272703229220007874811133810104969405477368739513286723394714036551930163895517204360421097050187418157101219550018359697836)" p threads 12 

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