Programming and factoring problem

[frmky]

Originally Posted by axn

If anyone has the factor(s) for 10^199+91, could you update it, please?

Done. It was a relatively easy one.

[lavalamp]

Originally Posted by frmky

Unfortunately, this is the last one NFS can solve. 500 digits is much too large.

Ah, a shame. Thank-you for the guide though, I have that bookmarked, I'm sure it will come in handy some time.

Thats a hefty computer you've got there, do you happen to work in a data centre?

[frmky]

Originally Posted by lavalamp

do you happen to work in a data centre?

University physics dept.

[Jens K Andersen]

From a PRP Top Search for (10^x+y)/z:

(10^268207+1)/11, Paul Bourdelais, 02/2010
(10^14118+11)/3, Lelio R Paula, 10/2008
(10^12891+11)/3, Lelio R Paula, 10/2008
(10^10683+11)/3, Lelio R Paula, 10/2008
(10^10044+9)/173, Lelio R Paula, 04/2006

10^10683+7 has no known factor.
239704723397 divides 10^10683+9.
All other smaller numbers have a very small factor.

Based on gigantic prp's this gives:

  d    |  k
 10044 | 9
 10683 | 7, 11
 12891 | 11
 14118 | 11
268207 | 1

[lavalamp]

Finished 4,482 curves with B1=11 million on 10^999+13. Starting 7,557 with B1=43 million.

So, quick question about ECM-GMP (version 6.2.3). Using the -resume switch to run stage2 from prime 95s output requires the B2 value to be set manually. So I ran some tests and found the appropriate B2 value for B1=11 million to be 30,114,149,530. The commands therefore look something like this:

ecm -resume results.txt -nn 1 30114149530 > save.txt

However, from the save file, I see this:

Using B1=1, B2=36007711756, polynomial Dickson(12), sigma=1435085703664580

That's nearly 20% higher than what I specified.

I thought it might just be particular to that level, but it's not, I ran a curve for the next level (stage 1 done by P95 as usual), and the command was:

ecm -resume results-13th.txt -nn 1 198654756318 > save.txt

And in the save file it says:

Using B1=1, B2=251378307196, polynomial Dickson(12), sigma=5940927478065527

That's proportionally even higher than the last level.

Does anyone know why ECM seems to be ignoring the B2 values I specify?

[lavalamp]

To anyone wondering, about 1000 complete curves have been done on 10^999+13 with B1=43e6 and B2=198654756318. The ETA for all 7557 curves done is some time around the 10th May.

Also, I fixed the issue I had in the previous post.

[lavalamp]

Seems I made a mistake earlier, about 1000 curves have not been completed, in fact a handful over 2150 are done now.

[lavalamp]

Here's my progress on 10^999+13.

Finished 7557 curves with B1=43M and B2=198,654,756,318.

Just for kicks I also ran four curves on each of the following B1, B2 values:
110M, 970,090,831,726
260M, 3,134,108,727,766
850M, 15,793,458,981,318
2,600M, 86,489,653,750,516

No factor found, I do not intend to do any more work attempting to factor this number.

[Jens K Andersen]

Originally Posted by lavalamp

Finished 7557 curves with B1=43M and B2=198,654,756,318.

That was an impressive attempt. I hope you post to http://www.shyamsundergupta.com/canyoufind.htm. It can take a long time (many months) before the page is updated.

[lavalamp]

Email sent.

[lavalamp]

I've recently come back to this semiprime problem and put some more work into it, the table now looks like this:

  d   |       k
 100  |  9
 200  |  103
 300  |  59
 400  |  31
 500  |  21, 51, 217, 247, 267
 600  |  19, 109, 939
 700  |  63
 800  |  79, 167
 900  |  69, 153
1000  |  13, 139
1100  |  51
1200  |  211

Here are the new factors:

10^499 + 187 = 8318017179025508261683881403545462119 * c463

10^599 +  81 = 163697520944382449180416421217352133 * c564
10^599 + 631 = 117759052641160151602853649672528225089 * c561

To the best of my knowledge the current progress of all candidates stands like this:

• The 500 and 600 digit candidates have been fully ECM'd at B1=3e6.
• The 800 and 900 digit candidates have been fully ECM'd at B1=1e6.
• The 1000 digit candidate has been fully ECM'd at B1=43e6.

I am currently running 4482 curves on both 600 digit candidates at B1=11e6, should be completed in about 5 days.

I have also confirmed that the information in the table is correct and that all other removed candidates have at least one factor and a composite remainder.

Incidentally, GMP-ECM 6.3 seems to crash after a few seconds of running on the 600 digit candidates, but it's fine for the 500 digit candidates. GMP-ECM 6.2.3 does not crash. Does anyone know why this might be? I was using the exe in ecm63_win64_core2.zip found on this page:
http://gilchrist.ca/jeff/factoring/index.html