[QUOTE=EdH;526999]11+7,288 - c153:
[code]
62810859081165879408050227175713686797900754129217
14496198764206105948214556620269595824785190594447578608707582028587996695968320038000452676843664060609
[/code]Found by ECM - B1=11e7.:smile:[/QUOTE]

Thanks. FWIW, running ECM at this level is probably not worth your cycles for a number this easy. Its SNFS difficulty was only 200, so maybe a t45 is about the right level at which to start running NFS. All of the HCNs have had more than that.

[QUOTE=jyb;527001]Thanks. Do your scripts handle Aurifeuillian factors?[/QUOTE]No, I just have scripts that basically run ECM and gnfs across a "farm" of ancient hardware.[QUOTE=jyb;527002]Thanks. FWIW, running ECM at this level is probably not worth your cycles for a number this easy. Its SNFS difficulty was only 200, so maybe a t45 is about the right level at which to start running NFS. All of the HCNs have had more than that.[/QUOTE]The ECM I'm running for these composites is really rather minimal across 128 cores with ecmpi. It does a small count of curves at 3e6, 11e6, 43e6 and 11e7. Then it swaps over to CADO-NFS. It kind of just tries for a lucky hit before GNFS. I still haven't ventured into the SNFS realm.

[QUOTE=EdH;527010]No, I just have scripts that basically run ECM and gnfs across a "farm" of ancient hardware.[/QUOTE]
I meant the part about automatically updating factorDB. Does it just use the full digit representation of the number, or does it identify it to factorDB symbolically (e.g. as "11^288+7^288")? If the latter, then Aurifeuillian factors could be more complicated.

[QUOTE=EdH;527010]The ECM I'm running for these composites is really rather minimal across 128 cores with ecmpi. It does a small count of curves at 3e6, 11e6, 43e6 and 11e7. Then it swaps over to CADO-NFS. It kind of just tries for a lucky hit before GNFS. I still haven't ventured into the SNFS realm.[/QUOTE]
I see. Well you definitely wouldn't have wanted to run 11+7,288 as a GNFS job. It would have been more than twice as much work that way.

[QUOTE=jyb;527015]I meant the part about automatically updating factorDB. Does it just use the full digit representation of the number, or does it identify it to factorDB symbolically (e.g. as "11^288+7^288")? If the latter, then Aurifeuillian factors could be more complicated.[/QUOTE]Everything is done with full digit workings.

[QUOTE=jyb;527015]I see. Well you definitely wouldn't have wanted to run 11+7,288 as a GNFS job. It would have been more than twice as much work that way.[/QUOTE]Now, this is enlightening. I have never studied SNFS at all, so I need to learn some things. I knew that SNFS showed a better solution, but I thought it was a much smaller percentage and was willing to trade that off. But, if it is that much better. I need to learn SNFS and write some more scripts!

First, how can I tell equivalencies between a GNFS value and an SNFS value?

I'm currently using GNFS for 9+7,266 and expect factors in the morning, although it may be afternoon.

Second, where can I learn how to use SNFS from scratch? I know nothing about it.

Thanks,
-Ed

[QUOTE=EdH;527024]
First, how can I tell equivalencies between a GNFS value and an SNFS value?

I'm currently using GNFS for 9+7,266 and expect factors in the morning, although it may be afternoon.
[/quote]

Ed - you can use the relationship

(GNFS-30)*1.8 = SNFS

But Serge has already done the heavy lifting on the [url=http://www.chiark.greenend.org.uk/ucgi/~twomack/homcun.pl]reservation page[/url]. The green values are optimal path. Just sort on GNFS, select a reasonable green GNFS value and factor that composite.

Note that GNFS is not the optimal path for 9+7,266 though by only a few points.

[Quote]
Second, where can I learn how to use SNFS from scratch? I know nothing about it.

Thanks,
-Ed[/QUOTE]

There used to be articles on the process in the wiki but they are gone now AFAIK.

YAFU can do some forms of SNFS. It’s in the documentation.

Thanks! I knew the green showed that SNFS would be better, but I don't understand by how much. I need to post elsewhere about how to use CADO-NFS to run these as SNFS. There is a little info in the README, but I'm too unfamiliar with SNFS.

I had figured I'd just knock out some of these 15x digit hcn's, but I'm up for some new learning. . .

[QUOTE=EdH;527030]Thanks! I knew the green showed that SNFS would be better, but I don't understand by how much. I need to post elsewhere about how to use CADO-NFS to run these as SNFS. There is a little info in the README, but I'm too unfamiliar with SNFS.

I had figured I'd just knock out some of these 15x digit hcn's, but I'm up for some new learning. . .[/QUOTE]

Take a look at [URL="https://mersenneforum.org/showthread.php?p=501186#post501186"]this post[/URL] from earlier in the thread. It points out some of the gotchas with the reservation page. In particular, it's not always true that the green method is better, because SNFS might require using a quartic.

So for example, the reservation page shows 10+3,260 as having 150 digits and an SNFS difficulty of 208. Now a quintic or sextic polynomial for an SNFS difficulty of 208 would be substantially faster than GNFS-150. But this number requires a quartic polynomial to get a difficulty of 208, so GNFS would probably end up being better.

9+7,266:
[code]
4062600630695288281176230800461852647207383901225157793
447321928093355073110101352212660436847260674697753638741781876651688030426747150166261024611553993
[/code]

[QUOTE=jyb;527038]Take a look at [URL="https://mersenneforum.org/showthread.php?p=501186#post501186"]this post[/URL] from earlier in the thread. It points out some of the gotchas with the reservation page. In particular, it's not always true that the green method is better, because SNFS might require using a quartic.

So for example, the reservation page shows 10+3,260 as having 150 digits and an SNFS difficulty of 208. Now a quintic or sextic polynomial for an SNFS difficulty of 208 would be substantially faster than GNFS-150. But this number requires a quartic polynomial to get a difficulty of 208, so GNFS would probably end up being better.[/QUOTE]
Thanks! I had looked over the referenced post, as well as several previous posts in this thread. And, I'm studying a bunch of stuff in the CADO-NFS thread. I'll be trying to get a better understanding of SNFS and then work some of these in that arena.

10+3,259:
[code]
12604017829082881620778655055326425829964313971631
461400869084561443747907270916612504387747744172749737499865196476929306944400628343082321905387388785699
[/code]

8-3,287:
[code]
10293490470942357020585413137950482669911799410000040765048857905299
15960547488593645104335444853915293228699212461367485628209909657720155468832149907075391
[/code]