Some Somewhat Easier n^i Sequences Available for Termination - Page 24

gd_barnes · 2022-06-01, 20:31

OK here is my "secret" (lol):

I was partially joking about the formulas, although not entirely. I do apply a score. The main key is that I take a snapshot of your sequences each day in the early afternoon. Then I know what has been added or changed. I then do an (almost) full ECM/factorization (to 30% or t35, whichever is smaller) on all of the ones that have been updated until they hit a "hard" cofactor > C110. I then have a spreadsheet that applies the following score to all of the sequences looking for the lowest lying fruit:

size + 2 * cofactor length - log (smallest factor) + if smallest factor = 3, +5, else 0.

Of course lower score is better. I found that the smallest factor of 3 is hard to break hence the penalty. Smallest factors of 5, 7, 11 don't seem so tough so no adjustment.

This is kind of interesting when there is no factor known. For instance on 60^86 that is a 137/137, as per above I ECM'd it to t35. So I just use 1e35 for the smallest factor size. The doubling of the 137 cofactor length makes it mostly untenable score-wise for me even with the reduction of 35 from the log of the smallest factor.

This only works if you've mostly fully ECM'd the latest iteration on all of the sequences. Otherwise the ones that have not been ECM'd will appear tougher than they really are.

This score is kind of a "difficulty rating" for terminating a sequence. It can probably be improved upon. I have already done a few changes to it. The most recent addition was to add 5 when the lowest factor was 3. That seemed to help quite a bit. I kept getting stuck on tough ones where the factor of 3 would not go away.

So...I just run the ones that have been updated and sometimes that alone with terminate them. With what is left I work top-down from lowest score. It is an iterative process. Many times I'll take one with lowest score and it will hit a larger hard cofactor. If the hard cofactor becomes > C120 I usually stop it because the score has become much greater. I'll then move on to the one with the now lowest score.

gd_barnes · 2022-06-01, 21:27

95^77 terminates

gd_barnes · 2022-06-02, 07:03

85^79 terminates

This was a slog. It quickly dropped into the low 120's making it look like a quick one. It then picked up the factor 3, which remained for ~50 iterations from size 122 to 106. Finally the 3 dropped and it terminated quickly after that.

EdH · 2022-06-02, 12:29

I have a few different things I do to choose which sequences to bring down, as well. I look for those that have no small factors because those will likely fall several digits. And, I look for those bases with one or two sequences left. While the list is lengthy, I will toss in some larger composites or work those last holdouts.And, I have a smaller GPU that I will set up with a second machine (for stage 2 residues) to run through a set of sequences looking for ECM hits, similar to what you're doing,

I'm afraid this thread may have lost some interest since I moved to a threshold of 145 digits, But, there are still many smaller sequences left, so maybe it's due to summer approaching.

gd_barnes · 2022-06-02, 12:31

113^71 terminates

gd_barnes · 2022-06-02, 19:55

151^61 and 1250^42 terminate

gd_barnes · 2022-06-03, 00:51

1152^48 terminates

richs · 2022-06-03, 03:33

Taking 57^85

gd_barnes · 2022-06-03, 04:26

131^71 terminates

richs · 2022-06-03, 14:54

57^85 terminated by me.

Taking 6^200

richs · 2022-06-03, 15:05

Well, that was quick: 6^200 terminated by me.

Taking 53^99

2022-06-01, 20:31	#254
gd_barnes May 2007 Kansas; USA 13·853 Posts	OK here is my "secret" (lol): I was partially joking about the formulas, although not entirely. I do apply a score. The main key is that I take a snapshot of your sequences each day in the early afternoon. Then I know what has been added or changed. I then do an (almost) full ECM/factorization (to 30% or t35, whichever is smaller) on all of the ones that have been updated until they hit a "hard" cofactor > C110. I then have a spreadsheet that applies the following score to all of the sequences looking for the lowest lying fruit: size + 2 * cofactor length - log (smallest factor) + if smallest factor = 3, +5, else 0. Of course lower score is better. I found that the smallest factor of 3 is hard to break hence the penalty. Smallest factors of 5, 7, 11 don't seem so tough so no adjustment. This is kind of interesting when there is no factor known. For instance on 60^86 that is a 137/137, as per above I ECM'd it to t35. So I just use 1e35 for the smallest factor size. The doubling of the 137 cofactor length makes it mostly untenable score-wise for me even with the reduction of 35 from the log of the smallest factor. This only works if you've mostly fully ECM'd the latest iteration on all of the sequences. Otherwise the ones that have not been ECM'd will appear tougher than they really are. This score is kind of a "difficulty rating" for terminating a sequence. It can probably be improved upon. I have already done a few changes to it. The most recent addition was to add 5 when the lowest factor was 3. That seemed to help quite a bit. I kept getting stuck on tough ones where the factor of 3 would not go away. So...I just run the ones that have been updated and sometimes that alone with terminate them. With what is left I work top-down from lowest score. It is an iterative process. Many times I'll take one with lowest score and it will hit a larger hard cofactor. If the hard cofactor becomes > C120 I usually stop it because the score has become much greater. I'll then move on to the one with the now lowest score. Last fiddled with by gd_barnes on 2022-06-01 at 21:25

2022-06-02, 07:03	#256
gd_barnes May 2007 Kansas; USA 13·853 Posts	85^79 terminates This was a slog. It quickly dropped into the low 120's making it look like a quick one. It then picked up the factor 3, which remained for ~50 iterations from size 122 to 106. Finally the 3 dropped and it terminated quickly after that. Last fiddled with by gd_barnes on 2022-06-02 at 07:28

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2022-06-01, 21:27	#255
gd_barnes May 2007 Kansas; USA 13×853 Posts	95^77 terminates

2022-06-02, 12:29	#257
EdH "Ed Hall" Dec 2009 Adirondack Mtns 4,691 Posts	I have a few different things I do to choose which sequences to bring down, as well. I look for those that have no small factors because those will likely fall several digits. And, I look for those bases with one or two sequences left. While the list is lengthy, I will toss in some larger composites or work those last holdouts.And, I have a smaller GPU that I will set up with a second machine (for stage 2 residues) to run through a set of sequences looking for ECM hits, similar to what you're doing, I'm afraid this thread may have lost some interest since I moved to a threshold of 145 digits, But, there are still many smaller sequences left, so maybe it's due to summer approaching.

2022-06-02, 12:31	#258
gd_barnes May 2007 Kansas; USA 2B51₁₆ Posts	113^71 terminates

2022-06-02, 19:55	#259
gd_barnes May 2007 Kansas; USA 13×853 Posts	151^61 and 1250^42 terminate

2022-06-03, 00:51	#260
gd_barnes May 2007 Kansas; USA 25521₈ Posts	1152^48 terminates

2022-06-03, 03:33	#261
richs "Rich" Aug 2002 Benicia, California 1551₁₀ Posts	Taking 57^85

2022-06-03, 04:26	#262
gd_barnes May 2007 Kansas; USA 13·853 Posts	131^71 terminates

2022-06-03, 14:54	#263
richs "Rich" Aug 2002 Benicia, California 3·11·47 Posts	57^85 terminated by me. Taking 6^200

2022-06-03, 15:05	#264
richs "Rich" Aug 2002 Benicia, California 3×11×47 Posts	Well, that was quick: 6^200 terminated by me. Taking 53^99