Hey, all;

How would you go about factoring this number?

5006 * 6^250 + 1 (No factor immediately found via ECM.)

[QUOTE=3.14159;232645]Hey, all;

How would you go about factoring this number?

5006 * 6^250 + 1 (No factor immediately found via ECM.)[/QUOTE]

199 digit number. Do 45-digit optimal ECM. Then use SNFS to factor it.

Well, I could do that, if there were any available implementations of it. So far, the only judgment I can make is that it has no factors smaller than 25 digits.

I'll run a few curves for a 30-digit factor. Hopefully, I get lucky and find one.

P plus 1 splits it:
[FONT=Arial Narrow]GMP-ECM 6.2.3 [powered by GMP 4.3.0] [B][P+1][/B]
Input number is 5006*6^250+1 (199 digits)
Using B1=100000000, B2=6083968236318, polynomial x^1, x0=4191628584
Step 1 took 67168ms
Step 2 took 40778ms
********** Factor found in step 2: 4768931962549207720191642703
Found probable prime factor of 28 digits: 4768931962549207720191642703
Composite cofactor (5006*6^250+1)/4768931962549207720191642703 has 171 digits[/FONT]

Found something;

********** Factor found in step 2: 4768931962549207720191642703
Found probable prime factor of 28 digits: 4768931962549207720191642703
Composite cofactor (5006*6^250+1)/4768931962549207720191642703 has 171 digits

Batalov beat me to it.

Alright, (5006*6^250+1)/4768931962549207720191642703 still has 171 digits, and is still composite. I guess I can go no further than there.

Perhaps one of you can split that into a nice p60 * p111, or perhaps a p85 * p86.

Prime found: (240067107876469912*6^9580+1)/69330188139647 (7459 digits)

Well, anything on the 171-digit cofactor of 5006 * 6^250 + 1?

[QUOTE=3.14159;232650]Well, I could do that, if there were any available implementations of it. So far, the only judgment I can make is that it has no factors smaller than 25 digits.[/QUOTE]
Actually, there is a readily available implementation of SNFS. :smile: It's a program called GGNFS, which does both GNFS (numbers of no special form) and SNFS (special form only, but rather faster than GNFS). For your number, you'll want to use SNFS.

A very good guide for getting set up with and running GGNFS can be found at [URL]http://gilchrist.ca/jeff/factoring/nfs_beginners_guide.html[/URL]. GNFS is used in the example, but for SNFS, you just need to construct the polynomial according to specific rules and then feed factmsieve.py your polynomial file on the command line.

Constructing the SNFS polynomial is the tricky part. Read through [url=http://www.mersenneforum.org/showthread.php?t=12962]this thread[/url] (started by yours truly asking for help on a similar problem a while back) to get some pointers on how to do so.

Well.. I'll have a submission; But it is not a special-form prime; It is a factor of a special-form number;

********** Factor found in step 1: 781082703983734893069019
Found probable prime factor of 24 digits: 781082703983734893069019
Composite cofactor (15027*396^56+1)/781082703983734893069019 has 126 digits.

********** Factor found in step 2: 4581671498357
Found probable prime factor of 13 digits: 4581671498357
Composite cofactor (15040*396^56+1)/4581671498357 has 137 digits

SNFS candidates, so far;

(5006 * 6^250 + 1)/4768931962549207720191642703, (GNFS)

8005 * 2^420 + 1 (The judgment I can make is that it has no factors ≤ 30 digits, 704 curves with no luck on B1 = 400K, B2 = 40M. I'll try one last time using B1 = 2M.)