Large small factor
 

I just found my first decent sized factor using ECM. It's a 44 digit probable prime factor coming from 16651^13-1. (It's one of the composites on the OPN website.)

Just wanted to share my joy. :)

[QUOTE=Zeta-Flux]I just found my first decent sized factor using ECM. It's a 44 digit probable prime factor coming from 16651^13-1. (It's one of the composites on the OPN website.)

Just wanted to share my joy. :)[/QUOTE]


Huh???? :question: :question: :question:

(16651^13 -1)/16650 is itself only 51 digits......

It is divisible by 30187, leaving a composite of only 47 digits...

Perhaps you wrote the wrong number?

The exponent should have been written 31, not 13. The composite factor he was working on is listed at [url]www.oddperfect.org[/url] as having 110 digits.

Congratulations!

R. D. Silverman,

Woops! Yeah, Philmoore got it. 31 is right. :)

(Oh, and I hope there are no bad feelings about the religion thread.)

Best,
Pace

[QUOTE=Zeta-Flux]I just found my first decent sized factor using ECM. It's a 44 digit probable prime factor coming from 16651^13-1. (It's one of the composites on the OPN website.)
[/QUOTE]
Well done! A p44 by ECM usually represents a fair bit of work, and it is easy to become discouraged as the count of unsuccessful curves mounts up. A nice factor makes it all worthwhile.

[QUOTE=geoff]A p44 by ECM usually represents a fair bit of work[/QUOTE]

A don't want to sound ungrateful for the factor, but people should realize that these composites are better suited for SNFS than ECM.

The SNFS difficulty was 131 digits. The rule of thumb is ECM for 2/9 the size then SNFS. So SNFS would probably have been a better choice than ECM once the 30 digit level was passed.

wblipp,

First, thanks for your comments. Know that if there was an easy way to do SNFS I would probably take a crack at it. From what I've read on this forum, to do SNFS takes quite a bit of effort. Unlike ECM, you can't just plug in the number into a program and let it run. I'm smart enough to probably figure it out one day, but for now I'm just having fun with ECM. :)

Second, know that there are an quite a few other unclaimed composite numbers on the site that SNFS people can have fun with, and I just felt like giving ECM a try for a while. Fortunately, I found a factor after only a few days. So, by sheer luck, I didn't have to watch the number of tried curves mount up.

geoff,

Thanks! Fortunately (and surprisingly) it only took a few curves!

[QUOTE=Zeta-Flux]Second, know that there are an quite a few other unclaimed composite numbers on the site that SNFS people can have fun with
[/QUOTE]

On the other hand, there are several numbers that aren't as easy for SNFS as 16651^31-1 was, for example 1213^59-1, 379^67-1, 55829^37-1 and the last five on the current composites list. These would take several days to a few weeks to sieve, more ECM effort would be welcome here. With difficulty 131, 16651^31-1 would have taken SNFS less than a day, so the ECM discovery didn't save us nearly as much work.

Alex

[QUOTE=Zeta-Flux]I'm smart enough to probably figure it out one day, but for now I'm just having fun with ECM. :)[/QUOTE]
I appreciate being the beneficiary of your fun! I want all participants at OddPerfect.org to have fun. Many people are choosing the same path as you - many composites suddenly transition to "DONE" without ever having been reserved - most of these are ECM factors.

I also want to urge people towards the most efficient methods. I haven't figured out how to do that without coming across as a churlish ungrateful troll. Maybe when the work situation calms down a bit I can put together some web pages of guidelines for which method and how to set it up. For now, thanks for the factors and I'm glad you are having fun.

I didn't realize that some of the numbers were better suited to ECM. Wblipp, go ahead and de-reserve the C112 for me, and instead I'll work on the C135 (which looks to be the least fitted to SNFS).

Hope that cheers everyone up! :D

Yep, at difficulty 200, 547^73-1 c135 is a worthwhile target for ECM. By the 2/9 rule of thumb, ECM to 45 digits would suffice to justify switching to SNFS, but as NFS sievers are in notoriously short supply, going a little further and running a couple of curves at B1=44M as well wouldn't hurt...

Good luck!

Alex