Records in January

wblipp · 2003-12-16, 18:15

I’m preparing for January, when Paul Zimmerman’s list of the Top Ten Factors Found by GMP-ECM This Year will reset. Forty digit factors will be sufficient to make the list, at least for a while. ElevenSmooth has twenty-three numbers testing in this range, so we have a rich pool of opportunity to make the list.

To further increase this pool, I’ve been concentrating on numbers that are almost finished testing at the 35 digit level. Today I also adjusted the public ecm server to this task. It looks like we will have more than a dozen additional numbers ready by January. This will make at least three dozen numbers suitable for the list, with many numbers nearly untested at 40 digits.

wblipp · 2004-01-03, 19:38

We're off and running.

The ElevenSmooth ECM Server has three dozen numbers testing for at least 40 digit factors, including a dozen with no previous work at this level. All factors found are likely to qualify for the Top Ten Factors found by GMP-ECM in 2004, at least for a while. Through January, all ECM assignments will be in this record-setting range.

William

wblipp · 2004-01-05, 03:26

I've been asked about the chances that a particular individual will find a record factor in January. Here's how to make a rough estimate for yourself.

From the ElevenSmooth FAQ, the probabilty that any one of the numbers in the ECM Server actually has a factor in the 40 digit range is about one in eight. Also, the probability of finding a 40 digit factor, if it exists, is one in 2900.

Next you need to know how many curves you will complete. You can look in the ecmclient.log file and see how many curves you completed in the last 12 or 24 hours. Much shorter than this is probably misleading because the size of the numbers being tested varies from under 200 to over 1000 digits, and you may see an unrepresentative average over short times.

The person who asked is completing about 100 curves per day, so over the course of January he should complete something close to 2900 curves, so his chances of finding a record size factor are about one in eight.

wblipp · 2004-01-05, 03:35

I've also been asked if it is better to work on the Special Project or look for a record size factor in the ECM Server. This depends on your goals. The Special Project will not qualify for the Top 10 Factors found with GMP-ECM this year because it doesn't use GMP-ECM and because it is looking for smaller factors. However, it is more likely to find a factor, mostly because it is looking for smaller factors. So you are more likely to get listed on the ElevenSmooth Factors Page with the Special Project, but at the cost of missing out on the Top 10 page.

wblipp · 2004-01-26, 03:26

The P40 that Gipe found today should qualify for the "bubble" position on Paul Zimmerman's Top Ten list. There were already 9 factors for 2004 ranging from 41 to 47 digits, so this should make position 10, sitting on the bubble and ready to burst as soon as anyone finds a larger factor. I'm hoping the next larger factor will also come from ElevenSmooth.

William

wblipp · 2004-01-27, 19:16

Today the bubble burst, dropping us off the Top10 This Year list. With 10 factors in 25 days, I expected it to be only 2 or 3 days until another factor was found, pushing us off the list. There were 2 days between our factor on Jan 25 and two new factors Jan 27th.

I've trimmed the numbers with low ECM work from the active list. My rationale is that small factors are likely to show up sooner than large factors, so I intend to trim based on the fraction of work completed as the threshold for making the list increases. That is, when 43 digit factors are necessary, I intend to only work on numbers that have already completed 3/5 of the work from 40 to 45 digits. This policy gives the right answer at big milestones like requiring 45 digits, and moves continuously towards that. I'll keep my own machines working just below this threshold, trying to bring numbers to the active threshold.

wblipp · 2004-02-02, 02:47

Unless other people have also found factors, ElevenSmooth should return to Paul Zimmerman's Top Ten List at position 9 with a P42 from M(5280) that I found this weekend.

William

xilman · 2004-02-02, 11:23

Quote:

Originally Posted by wblipp

Unless other people have also found factors, ElevenSmooth should return to Paul Zimmerman's Top Ten List at position 9 with a P42 from M(5280) that I found this weekend.

William

Well, I found a P43 factor at the weekend, but you should still be safe for at least a little while at number 10.

Paul

wblipp · 2004-02-02, 15:00

Quote:

Originally Posted by xilman

Well, I found a P43 factor at the weekend, but you should still be safe for at least a little while at number 10.

Paul

That's only fair, since the number I pushed off the list was yours. With 10 numbers of my size of more having been found in the first 32 days of 2004, I don't expect to last the week, though.

wblipp · 2004-02-06, 14:55

Quote:

Originally Posted by wblipp

I don't expect to last the week, though.

We were pushed off the list on Friday morning by a 48 digit factor, the largest found so far this year with GMP-ECM. I'm tightening the active list in the ECM Server again.

wblipp · 2004-03-22, 01:26

Today ElevenSmooth returned to a broad search strategy. When Paul Zimmermann's Top Ten This Year list opened in January, we started with 36 numbers that were searching for the list-minimum 40 digit factors. As the minimum advanced, our supply of suitable candidates dwindled, but a week ago we still had 22 viable candidates. However, a recent flurry of factors has advanced the threshold to the point where ElevenSmooth has only three suitable candidates.

It was a surprise that we were competitive for so long; I had expected the cutoff to outrun our ability in January. However, a short term boost of about twenty machines was enough to keep us in the running for much longer. We didn't have much luck actually finding factors though - we found two factors that each stayed on the list for less than a week.

The standard server, on port 8194, will return to using mostly the allocation method of Sum-of-B1 times Length Squared, with a small amount of Random and tiny bit of Smallest Composite. Ports 8195 and 8196 will be a mix of Record Sized Factors and Preparation for Records. Port 8200 is presently in an experiment of sharing ElevenSmooth numbers and Cunningham numbers.

William

2003-12-16, 18:15	#1
wblipp "William" May 2003 Near Grandkid 2·1,187 Posts	Records in January I’m preparing for January, when Paul Zimmerman’s list of the Top Ten Factors Found by GMP-ECM This Year will reset. Forty digit factors will be sufficient to make the list, at least for a while. ElevenSmooth has twenty-three numbers testing in this range, so we have a rich pool of opportunity to make the list. To further increase this pool, I’ve been concentrating on numbers that are almost finished testing at the 35 digit level. Today I also adjusted the public ecm server to this task. It looks like we will have more than a dozen additional numbers ready by January. This will make at least three dozen numbers suitable for the list, with many numbers nearly untested at 40 digits.

2004-01-26, 03:26	#5
wblipp "William" May 2003 Near Grandkid 2·1,187 Posts	Gipe puts a P40 on the Bubble The P40 that Gipe found today should qualify for the "bubble" position on Paul Zimmerman's Top Ten list. There were already 9 factors for 2004 ranging from 41 to 47 digits, so this should make position 10, sitting on the bubble and ready to burst as soon as anyone finds a larger factor. I'm hoping the next larger factor will also come from ElevenSmooth. William

2004-01-27, 19:16	#6
wblipp "William" May 2003 Near Grandkid 4506₈ Posts	Bubble Bursts Today the bubble burst, dropping us off the Top10 This Year list. With 10 factors in 25 days, I expected it to be only 2 or 3 days until another factor was found, pushing us off the list. There were 2 days between our factor on Jan 25 and two new factors Jan 27th. I've trimmed the numbers with low ECM work from the active list. My rationale is that small factors are likely to show up sooner than large factors, so I intend to trim based on the fraction of work completed as the threshold for making the list increases. That is, when 43 digit factors are necessary, I intend to only work on numbers that have already completed 3/5 of the work from 40 to 45 digits. This policy gives the right answer at big milestones like requiring 45 digits, and moves continuously towards that. I'll keep my own machines working just below this threshold, trying to bring numbers to the active threshold.

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2004-01-03, 19:38	#2
wblipp "William" May 2003 Near Grandkid 2×1,187 Posts	We're off and running. The ElevenSmooth ECM Server has three dozen numbers testing for at least 40 digit factors, including a dozen with no previous work at this level. All factors found are likely to qualify for the Top Ten Factors found by GMP-ECM in 2004, at least for a while. Through January, all ECM assignments will be in this record-setting range. William

2004-01-05, 03:26	#3
wblipp "William" May 2003 Near Grandkid 946₁₆ Posts	I've been asked about the chances that a particular individual will find a record factor in January. Here's how to make a rough estimate for yourself. From the ElevenSmooth FAQ, the probabilty that any one of the numbers in the ECM Server actually has a factor in the 40 digit range is about one in eight. Also, the probability of finding a 40 digit factor, if it exists, is one in 2900. Next you need to know how many curves you will complete. You can look in the ecmclient.log file and see how many curves you completed in the last 12 or 24 hours. Much shorter than this is probably misleading because the size of the numbers being tested varies from under 200 to over 1000 digits, and you may see an unrepresentative average over short times. The person who asked is completing about 100 curves per day, so over the course of January he should complete something close to 2900 curves, so his chances of finding a record size factor are about one in eight.

2004-01-05, 03:35	#4
wblipp "William" May 2003 Near Grandkid 4506₈ Posts	I've also been asked if it is better to work on the Special Project or look for a record size factor in the ECM Server. This depends on your goals. The Special Project will not qualify for the Top 10 Factors found with GMP-ECM this year because it doesn't use GMP-ECM and because it is looking for smaller factors. However, it is more likely to find a factor, mostly because it is looking for smaller factors. So you are more likely to get listed on the ElevenSmooth Factors Page with the Special Project, but at the cost of missing out on the Top 10 page.

2004-02-02, 02:47	#7
wblipp "William" May 2003 Near Grandkid 2×1,187 Posts	Unless other people have also found factors, ElevenSmooth should return to Paul Zimmerman's Top Ten List at position 9 with a P42 from M(5280) that I found this weekend. William

2004-03-22, 01:26	#11
wblipp "William" May 2003 Near Grandkid 4506₈ Posts	Today ElevenSmooth returned to a broad search strategy. When Paul Zimmermann's Top Ten This Year list opened in January, we started with 36 numbers that were searching for the list-minimum 40 digit factors. As the minimum advanced, our supply of suitable candidates dwindled, but a week ago we still had 22 viable candidates. However, a recent flurry of factors has advanced the threshold to the point where ElevenSmooth has only three suitable candidates. It was a surprise that we were competitive for so long; I had expected the cutoff to outrun our ability in January. However, a short term boost of about twenty machines was enough to keep us in the running for much longer. We didn't have much luck actually finding factors though - we found two factors that each stayed on the list for less than a week. The standard server, on port 8194, will return to using mostly the allocation method of Sum-of-B1 times Length Squared, with a small amount of Random and tiny bit of Smallest Composite. Ports 8195 and 8196 will be a mix of Record Sized Factors and Preparation for Records. Port 8200 is presently in an experiment of sharing ElevenSmooth numbers and Cunningham numbers. William