Anyone factoring <5M?

[garo]

I am planning to do some exponents from 61 to 62 or 63. They cannot be assigned via PrimeNet so I just wanted to check here first.

[axn]

Originally Posted by garo

I am planning to do some exponents from 61 to 62 or 63. They cannot be assigned via PrimeNet so I just wanted to check here first.

What is the relative CPU cost of getting the exponent from 61->63 vs running a 20-digit level ECM?

[garo]

Honestly, I am not sure. But my guess is that Prime95 is still faster at 61-63. And is guaranteed to find a factor if it exists. But I have some hardware that is good for factoring < 64 bits and with 64 bit exponents in danger of running out I thought I'd put some work towards <5M.

If ECM is more efficient at finding factors, I'd be happy to switch.

[petrw1]

Originally Posted by garo

Honestly, I am not sure. But my guess is that Prime95 is still faster at 61-63. And is guaranteed to find a factor if it exists. But I have some hardware that is good for factoring < 64 bits and with 64 bit exponents in danger of running out I thought I'd put some work towards <5M.

If ECM is more efficient at finding factors, I'd be happy to switch.

We know that the factoring limits are set based on relative time and potential effectiveness vs LL. http://www.mersenne.org/various/math.php

I also know that when I try to assign low exponents (mind you, lower than yours) to higher levels of factoring I get an error message something like: "Invalid assignments use ECM instead". I have ASSUMED from this error that ECM would be more efficient.

Finally, in my experiments with assigning ECM to old hardware it is more INeffecient than TF<64 and even more INeffecient than LL/DC. i.e. Points Per Day (PPD). Mind you, ECM might just be a litle more frugal on points as I found that on every PC I tried ECM the PPD was lower.

[axn]

Originally Posted by garo

If ECM is more efficient at finding factors, I'd be happy to switch.

So I did some preliminary timings on a C2D. It looks like near the 5M range, it may still be worthwhile to TF upto 2^64. Probably not below 3M. Of course, a decent P-1 might be even better.

[petrw1]

I see from http://www.mersenne.org/primenet/ that they are just starting to hand out ECM in the 5M range to 25 digits.

There are exponents up to 8.2M less than 64 bits.
Just a thought: You might be safer at the higher end.

[cheesehead]

Originally Posted by garo

I am planning to do some exponents from 61 to 62 or 63. They cannot be assigned via PrimeNet

Yes, they can (for exponents below 10M, that is) -- use the procedure described in the sticky thread "How to LMH using Prime95 v25.8 and PrimeNet v5" (http://mersenneforum.org/showthread.php?t=11308). Note my recent cautionary post #4 of that thread!

I've been running TFs on exponents < 10M for a while. However, instead of selecting a range, in my case I select individual exponents based on their so-far P-1 bounds. So I'm not doing steps #1 and #2 given in the "How to ..." thread, but instead am accomplishing the same assignment-collision-avoidance by running Exponent Status reports (not the same as the Factoring Effort reports specified in step #3) to see whether any of my exponents of interest are already assigned to someone else, then proceeding with the other steps.

So, what I do (which may not be exactly what you want to do) is:

First, I do step #3 of the "How to ..." thread, in order to get the TF and P-1 limits within a range. Note: check the "Exclude currently assigned exponents" box!!!!

Next, I select a few specific exponents with (relatively) high P-1 bounds but (relatively) low TF limits. This is my own criterion -- substitute your own.

Next, I get an Exponent Status report for each of those selected exponents, and drop any that are already assigned to someone.

Then I proceed with steps #4-end of the "How to ..." thread.

(If I forgot to check Exponent Status reports, or if, between when I got the Exponent Status report and when I manually communicated to PrimeNet, PrimeNet assigned an exponent I specified, then PrimeNet will give me "N/A" as the assignment key. As in my "How to ..." post #4, I always check for "N/A" and delete the worktodo lines that have them, so I don't step on anyone else's assignment.)

This does require that you personally select and specify each exponent you want to TF, instead of having PrimeNet do that part, and it does require you to regularly and systematically perform assignment-collision-avoidance activities.

If the consensus is that I should post the exponents I intend to test here: okay, but I'll warn you that I'd be posting every day or so and they'd be lists of scattered individual exponents, not simple contiguous ranges.

[WVU Mersenneer]

Originally Posted by axn

What is the relative CPU cost of getting the exponent from 61->63 vs running a 20-digit level ECM?

Forgive me forposting here even though I am a vast novice at all of this, but I felt a discovery by one of my computers this morning dove-tails nicely with this thread.

I have almost half of my computers doing small ECM factoring work, and this morning one of my machines found 29,166,507,389,557,009 is a factor of 2 ^ 1,620,989 -1.

However, that factor < 2^55, but the V5 server reports show all exponents of this size have no factors up to 2^60.

I am wondering how this happened. Have all exponents truly been factored up to 2^60?

Similar to this is a find I made just over one year ago that 22,049,255,272,665,169 is a factor of 2^ 1,104,409 - 1. It also struck me as odd to get 17-digit factors via ECM, but again, I know very little about all of this.

As to speed, my computer can factor 1,620,989 from 2^50 to 2^59 in 19 minutes whereas 3 ECM curves at B1=50,000 and B2=B1*100 takes one hour.

I thank everyone for their input and assistance.

Edit: here's the results file:
[Fri Apr 16 04:50:08 2010]
ECM found a factor in curve #2, stage #2
Sigma=7080176765941688, B1=50000, B2=5000000.
UID: /ryan, M1620989 has a factor: 29166507389557009, AID: C2A31C6E0062425DE48C2058D89018B1

[cheesehead]

Originally Posted by WVU Mersenneer

Forgive me forposting here even though I am a vast novice at all of this

We're very glad you posted!

I have almost half of my computers doing small ECM factoring work, and this morning one of my machines found 29,166,507,389,557,009 is a factor of 2 ^ 1,620,989 -1.

However, that factor < 2^55, but the V5 server reports show all exponents of this size have no factors up to 2^60.

There have been other such reports a few times over the years.

I am wondering how this happened.

Apparently, since we've occasionally had other reports such as yours, either:

a) one or more of the trial factoring (TF) programs used in the past had some bug that caused it/them to miss some factors,

or (the following is much more likely, in my opinion):

b) when TF was performed on that exponent in the past, someone made a mistake when specifying which "bit levels" (powers of 2) were to be searched, and the range from 2^54 to 2^55 was skipped somehow.

Unfortunately, though we have a database that records all reported TF results, there has not always been a guarantee that no power-of-2 was skipped AFAIK.

Have all exponents truly been factored up to 2^60?

The database indicates that it was truly "thought" that that exponent had been TFed up to 2^60. But as I explained, we don't yet have foolproof verification that all TF ranges were properly scanned.

Similar to this is a find I made just over one year ago that 22,049,255,272,665,169 is a factor of 2^ 1,104,409 - 1. It also struck me as odd to get 17-digit factors via ECM, but again, I know very little about all of this.

The more reports of such discrepancies, the sooner we'll get the cause investigated and cured.

[markr]

Originally Posted by cheesehead

There have been other such reports a few times over the years.

Here's a thread from a long, long time back:
http://www.mersenneforum.org/showthread.php?t=1425

[markr]

Originally Posted by garo

Anyone factoring <5M?

I am planning to do some exponents from 61 to 62 or 63. They cannot be assigned via PrimeNet so I just wanted to check here first.

I'm doing TF from 61 to 62, currently in the 48xxxxx range. Using the LMH method to have them assigned in PrimeNet, I simply take the highest currently unassigned, queuing up a few days work at a time.

Ahead of that effort I do P-1 to fairly high bounds on the few exponents that haven't had "enough" P-1. This actually finds more factors than the TF effort, measured by success rate.