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-   -   Thinking out loud about getting under 20M unfactored exponents (https://www.mersenneforum.org/showthread.php?t=22476)

petrw1 2017-07-26 04:45

Thinking out loud about getting under 20M unfactored exponents
 
[url]http://www.mersenne.ca/status/tf/0/0/1/0[/url]

Breaking it down I'm thinking if each 100M range has less than 2M unfactored we have the desired end result.
Similarly if each 10M range has less than 200K unfactored...
or each 1M range has less than 20K unfactored...
or each 100K range has less than 2,000 unfactored.

So I did some Excel ciphering looking at:
- how many more factors are required in each range
- how many exponents need to be TF'd at the current bit level to get there (could require several bit levels to complete)
- how many GhzDays each assignment would take.
- I stopped at the 59M range thinking current GPU TF bit levels will factor adequately (most of the time) to get below my limits of interest here.

I did this for the 10M, 1M and 100K ranges.

Then I added it all up and came up with very roughly 250M GhzDays of TF with some ranges requiring up to 10 more bit levels of TF. WOW.

In perspective, my 1,000 per day GPUs would take 250K days: 685 years.

Oh dear; that's way more than I had expected.

Note: I only considered TF.
I understand that in some (many?) cases ECM (on lower exponents) and P-1 could find factors much quicker.

In either case it looks like this will be a very far off milestone.

0PolarBearsHere 2017-07-26 07:48

It just means we need more GPUs.
For instance if we can get 1000 high end GPUs on it, we could get it done in under a year based on your maths. We just need to find an organisation with a spare 800K USD who had a sudden urge to generously donate GPUs to anyone that requests one.

VictordeHolland 2017-07-26 10:43

And what would this accomplisch?

petrw1 2017-07-26 16:03

[QUOTE=VictordeHolland;464195]And what would this accomplisch?[/QUOTE]

Absolutely nothing of consequence.
Nothing more than another milestone of interest to some.

S485122 2017-07-26 19:48

If your best tool is a factoring machine you view everything as as entities to be factored. :-)

Jacob

chalsall 2017-07-26 20:03

[QUOTE=S485122;464237]If your best tool is a factoring machine you view everything as as entities to be factored. :-)[/QUOTE]

Just to reflect Jacob... Sometimes it is worth the effort to think about what other people are thinking about...

In addition to the Philips, are you familiar with the Roberson? The hex?

I have actually watched people slam screws into wood using a hammer, because the Philips screws' heads were stripped with a screw driver which was too small.

I actually learned some new words (containing many symbols, including (!*%$@***!!!)) from men who should have understood the simplicity of the situation.

For what that is worth....

CRGreathouse 2017-07-26 20:35

[QUOTE=VictordeHolland;464195]And what would this accomplisch?[/QUOTE]

I'm not sure what the OP has in mind, but I know that full factorizations of small Mersenne numbers are very useful. For example, they greatly speed up the [url=http://www.janfeitsma.nl/math/psp2/not-sqrt-smooth]non-sqrt-smooth part[/url] (which dominates computationally) of [url=http://www.janfeitsma.nl/math/psp2/index]Feitsma's algorithm[/url] for listing 2-pseudoprimes. I've heard interest in extending his work beyond 2^64 so this isn't just academic.

As for finding individual factors, I don't know... I guess it just gives simpler/shorter certificates of compositeness.

Gordon 2017-07-26 23:01

[QUOTE=VictordeHolland;464195]And what would this accomplisch?[/QUOTE]

because they are there and because we can :-)

science_man_88 2017-07-26 23:25

[QUOTE=VictordeHolland;464195]And what would this accomplisch?[/QUOTE]

if done high enough, in theory, it could deplete the candidate factors for larger mersenne numbers a bit.

chalsall 2017-07-26 23:52

[QUOTE=science_man_88;464251]if done high enough, in theory, it could deplete the candidate factors for larger mersenne numbers a bit.[/QUOTE]

Yeah... In theory....

storm5510 2017-07-27 04:40

1 Attachment(s)
I believe just about everyone here recognizes the image I have attached. This ends at 2[SUP]80[/SUP]. I suppose some here could comfortably TF to this level in a reasonable period of time. Of course, I do not know what most would consider "reasonable."

The last I heard, a computer "generation" was in the area of 18 months. It is probably less now. It would take many generations of tech growth to get to the level the OP was writing about.

[U]Point[/U]: Let us do now what needs to be done now, and not think about the future.

:smile:

petrw1 2017-07-27 05:06

I think I'll start somewhere in this range....some day soon.
This is the current DC range so it can help there too.

[CODE]
100K ToGo 2^N
40.0 2059 72
40.1 2116 72
40.2 2046 72
40.3 2096 72
40.4 2032 72
40.5 2077 72
40.6 2023 72
40.7 2033 72
40.8 2066 72
40.9 2004 72
41.0 2063 72
41.1 2093 72
41.2 2012 72
41.3 2041 72
41.5 2035 72
41.6 2049 72
41.7 2099 72
41.8 2051 72
41.9 2047 72
42.0 2021 72
42.1 2017 72
42.2 2014 72
42.3 2045 72
42.4 2022 72
42.5 2003 72
42.6 2129 72
42.7 2035 72
42.8 2015 72
42.9 2067 72
43.0 2133 72
43.1 2046 72
43.2 2064 72
43.3 2097 72
43.4 2102 72
43.6 2021 72
43.7 2025 72
43.8 2049 72
43.9 2028 72
44.0 2017 72
44.1 2012 72
44.2 2024 72
44.6 2098 72
44.7 2060 72
44.8 2009 72
44.9 2034 72
45.0 2015 72
45.2 2046 72
45.3 2090 72
45.4 2014 72
45.5 2096 72
45.6 2024 72
45.7 2031 72
45.8 2093 72
46.0 2042 72
46.1 2005 72
46.2 2028 72
46.3 2097 72
46.5 2061 72
46.6 2054 72
46.7 2044 72
46.8 2030 72
47.0 2025 72
47.1 2060 72
47.2 2038 72
47.5 2065 72
47.6 2019 72
47.7 2046 72
47.8 2074 72
48.0 2028 72
48.1 2026 72
48.2 2053 72
48.3 2035 72
48.4 2113 72
48.6 2030 72
48.7 2029 72
48.9 2023 72
49.1 2004 72
49.3 2049 72
49.4 2081 72
49.5 2056 72
49.6 2121 72
49.8 2072 72
49.9 2008 72
50.2 2053 73
50.3 2034 73
50.4 2019 73
50.6 2005 73
50.8 2012 73
50.9 2017 73
51.3 2000 73
51.7 2004 73
52.2 2003 73
52.3 2057 73
52.4 2005 73
52.9 2045 73
53.2 2034 73
53.3 2002 73
53.5 2029 73
53.9 2053 73
54.0 2018 73
54.2 2019 73
54.6 2009 73
55.0 2009 73
55.4 2011 73
55.6 2016 73
55.9 2011 73
56.0 2002 73
56.1 2010 73
56.3 2032 73
56.5 2032 73
56.6 2043 73
56.7 2027 73
56.8 2061 73
57.4 2009 73
57.6 2030 73
57.7 2008 73
57.8 2004 73
58.1 2032 73
58.7 2067 73
58.8 2019 73
59.4 2065 73
59.6 2031 73
59.9 2004 73[/CODE]

A lot of these will have poor P-1; might be more efficient to start there?

petrw1 2017-08-31 02:54

So here's my plan....
 
I will be starting my little pet project within the next week with 2 GPUs and adding about 30 Cores a few weeks later.

I'll be working in the extremes ranges.
The bigger horses in the 40M and 50M ranges.
The side benefit is that this will reduce the number requiring DC.
The smaller ponies in the 2M range.

For the GPUs there are about 16,000 Assignments in the high 40's factored below the yellow bar: [url]http://www.mersenne.ca/status/tf/0/0/3/4000[/url]
I expect to find about 200 factors there.

For the faster cores with adequate RAM I will be P-1'ing exponents in that same range that were done with B1=B2. These seem to give better odds at finding a factor than doing P-1 where the B1 and B2 bounds were less than adequate.

I'll let a few slower cores dabble at the low end (2M) doing ECM.

=================

If anyone is intrigued you are more than welcome to join in.
Keep me posted so we don't step on each other's toes.

See the first post for the details on this little initiative.

Wayne

chalsall 2017-09-04 14:55

[QUOTE=petrw1;466721]For the GPUs there are about 16,000 Assignments in the high 40's factored below the yellow bar: [url]http://www.mersenne.ca/status/tf/0/0/3/4000[/url] I expect to find about 200 factors there.

If anyone is intrigued you are more than welcome to join in. Keep me posted so we don't step on each other's toes.[/QUOTE]

After conferring with Wayne, I have re-enabled DCTF on GPU72 to take the candidates from 48.8M to 50M up to (at least) 73 bits (the optimal economic cross-over point for contemporary GPUs). This is to help avoid any "toes being stepped on".

If anyone is interested, the DCTF manual assignments page has been re-enabled, and the spiders (MISFIT et al) can simply ask for DCTF work again.

tha 2017-09-07 07:27

For what it is worth, if been redoing P-1 on exponents that had their P-1 done with B1=B2 (usually on machines with no spare memory to do the higher B2 level). Almost all of it in the 10M to 20M range. Mostly with B1=300000 and B2=6000000. About one in 38 candidates yields a new found factor on a previously unfactored exponent.

petrw1 2017-09-07 15:02

[QUOTE=tha;467296]For what it is worth, if been redoing P-1 on exponents that had their P-1 done with B1=B2 (usually on machines with no spare memory to do the higher B2 level). Almost all of it in the 10M to 20M range. Mostly with B1=300000 and B2=6000000. About one in 38 candidates yields a new found factor on a previously unfactored exponent.[/QUOTE]

Thanks....I'll note that and try not to step on your toes.

I realize my little sub-project is actually quite a massive undertaking that I couldn't dream of finishing in my lifetime.

But I understand that there are always people dabbling at factoring in these ranges:
- Some are doing TF in the 20M or 30M ranges; in fact most ranges.
- There is a steady stream of ECM in the 0M - 20M range.
- Others are doing P-1 here and there.

So we'll see where we are at end of 2018.

To compare: since the beginning of 2017 there have been 4,082 exponents newly factored under 60M.
- Over half of these in the 20-30M range.
- And another 30% under 10M

-W-

tha 2017-09-07 21:11

[QUOTE=petrw1;467318]Thanks....I'll note that and try not to step on your toes.

/QUOTE]

Oh, thanks, but I am not claiming any range, do go ahead.

petrw1 2017-09-16 22:21

Almost 8 weeks later...an update.
 
698 (1.25%) exponents factored in the ranges of interest....0 - 59.9M

1 range cleared (now below 2,000): 22.2M
Several with significant progress.

Gordon 2017-09-16 22:43

I am doing a lot of the TF in the under 10m block.

Have already done to 67 bits

3,5,6,7,8 & 9m to 67 bits. Someone else took 9m to 68 bits

2m is 2/3 the way to 67 bits. So about 100k'ish exponents so far.

Did quite a bit in the sub 1m range to lift them to 64 bits, but mfaktc doesn't work below 100k so would need to use the cpu - which is currently tied up doing the ecm stage 1's to keep the deep stage 2's going on M4007.

GP2 2017-09-16 23:54

[QUOTE=Gordon;467921]
Did quite a bit in the sub 1m range to lift them to 64 bits, but mfaktc doesn't work below 100k so would need to use the cpu - which is currently tied up doing the ecm stage 1's to keep the deep stage 2's going on M4007.[/QUOTE]

Below 100k all exponents have already been ECM'd to t=30 (about 100 bits), so only about a 37% chance of finding a factor smaller than 100 bits. So TF to 64 bits would have a very very low probability of finding any new factors.

Below 656k all exponents have already been ECM'd to t=25 (about 83 bits). Poor prospects for finding factors of 64 bits or smaller.

The above is for all exponents, including the ones that already have at least one known factor.

If we consider only exponents with no known factors, then everything below 1M has already been ECM'd to t=25.


Edit: also [URL="http://www.mersenneforum.org/showthread.php?t=19014&p=461679"]user TJAOI has covered everything up to 64 bits[/URL].

petrw1 2017-09-17 04:05

[QUOTE=GP2;467922]... everything below 1M has already been ECM'd to t=25. ...
[/QUOTE]

Good to know...however.

The lowest range of interest to my little subproject (getting all 100K ranges below 2,000 unfactored) is 1.8M

petrw1 2017-09-17 04:59

[QUOTE=Gordon;467921]I am doing a lot of the TF in the under 10m block.

Have already done to 67 bits

3,5,6,7,8 & 9m to 67 bits. Someone else took 9m to 68 bits

2m is 2/3 the way to 67 bits. So about 100k'ish exponents so far.

Did quite a bit in the sub 1m range to lift them to 64 bits, but mfaktc doesn't work below 100k so would need to use the cpu - which is currently tied up doing the ecm stage 1's to keep the deep stage 2's going on M4007.[/QUOTE]

Thanks....

retina 2017-09-17 08:28

The plural of "guess" is not "fact"
 
[QUOTE=GP2;467922]also [URL="http://www.mersenneforum.org/showthread.php?t=19014&p=461679"]user TJAOI has covered everything up to 64 bits[/URL].[/QUOTE]It is my understanding that we don't know this for certain. It is merely an assumption that people seem to take as a known truth.

Mark Rose 2017-09-17 17:53

[QUOTE=retina;467936]It is my understanding that we don't know this for certain. It is merely an assumption that people seem to take as a known truth.[/QUOTE]

It's no different than trusting all the other "no factor" TF results.

retina 2017-09-17 17:58

[QUOTE=Mark Rose;467963]It's no different than trusting all the other "no factor" TF results.[/QUOTE]Maybe. But there is a difference in that we can audit results from users doing TF to compare the expected vs discovered factors. It isn't a perfect test of course. However, there is no equivalent test we can apply to the results from TJAOI.

GP2 2017-09-18 00:42

[QUOTE=retina;467964]Maybe. But there is a difference in that we can audit results from users doing TF to compare the expected vs discovered factors. It isn't a perfect test of course. However, there is no equivalent test we can apply to the results from TJAOI.[/QUOTE]

See [URL="http://www.mersenneforum.org/showthread.php?p=467989"]my post in the "User TJAOI" thread[/URL], where I look at the datestamps for factor discoveries in the PrimeNet database to check how systematic TJAOI's searches are.

Spoiler: from the empirical evidence, it is very systematic. Apart from one glitch almost three years ago, which was quickly fixed, it is indeed true that when TJAOI finishes with a given bit-size range, no new factors of that bit size are ever discovered, by him or by anyone else.

Doing TF for 64-bits or smaller will not find any new factors. Even 65 bits would probably just be a duplication of effort, since we can expect TJAOI to systematically complete that range sometime in 2018.

ATH 2017-09-26 04:08

Here is a graph of the number of factored exponents (at least 1 factor) since November 2008 based on the summary files.

[URL="http://hoegge.dk/mersenne/factored.png"]factored.png[/URL]

The top of the chart 30,850,000 is roughly at 20M unfactored exponents (19,997,534).

Unfortunately the slope has gone down during 2017, the averate rate in the last 6 months is 436 exponents per day, which will give 10.1 years to reach 20M unfactored exponents.

ATH 2017-09-26 07:04

Number of newly factored exponents per day, average over 30 days:

[URL="http://hoegge.dk/mersenne/factoredspeed.png"]factoredspeed.png[/URL]

petrw1 2017-09-26 14:46

Yeah I know its a long way away....but I think it will be done before all exponents are tested up to 100M ... or before we find our find a 100M digit prime.

I just find it interesting to watch.
And if I can knock off a couple dozen ranges over the next year it will be fun.

TeeHeeHee

And thanks for the data.

petrw1 2017-10-15 03:56

Oct 15, 2017 Update; 1 month later
 
643 more exponents factored in the ranges of interest....0 - 59.9M
(In ranges where there are still more than 1,999 unfactored.

2 more ranges cleared (now below 2,000): 48.9M and 49.1M

petrw1 2017-11-17 05:08

November 16, 2017 - 1 month later
 
800 more exponents factored in the ranges of interest....0 - 59.9M
(In ranges where there are still more than 1,999 unfactored.

2 more ranges cleared (now below 2,000): 46.1M and 49.9M

petrw1 2017-12-14 23:26

100 days...100 factors for me.
 
...

petrw1 2017-12-17 22:01

December 17,2017 - Monthly Update
 
841 more exponents factored in the ranges of interest....0 - 59.9M
(In ranges where there are still more than 1,999 unfactored.

6 more ranges cleared (now below 2,000): 1.8M, 2.1M, 45.4M, 47.0M, 47.6M and 48.0M

petrw1 2018-01-15 00:29

UPDATE - January 14, 2018
 
1,547 !!! more exponents factored in the ranges of interest...0 - 59.9M GREAT PROGRESS
(In ranges where there are still more than 1,999 unfactored.

4 more ranges cleared (now below 2,000): 45.0M, 48.1M, 51.3M, and 59.9M

11 ranges within 5 or less to go.

Good news (HAHA): There will be no February update (Vacation)

petrw1 2018-03-06 02:29

6 months
 
And I've found 200 factors for this little subproject so far.

VictordeHolland 2018-03-06 14:54

You got some work to do
 
There remain 21,535,921 unfactored exponents below 1G, so even if GIMPS keeps up with the current pace of ~160,000 new factors per year, you're looking at another 10 years to get that number below 20,000,000 :unsure:.

I haven't even factored in that is gets increasingly harder to find factors...

ET_ 2018-03-06 16:01

I am doing some heavy ECM on a few candidates between M100000 and M220000 chosen from [url]https://www.mersenne.org/report_ecm/[/url] but I don't want to step over someone else's work...

petrw1 2018-03-06 18:46

[QUOTE=VictordeHolland;481690]There remain 21,535,921 unfactored exponents below 1G, so even if GIMPS keeps up with the current pace of ~160,000 new factors per year, you're looking at another 10 years to get that number below 20,000,000 :unsure:.

I haven't even factored in that is gets increasingly harder to find factors...[/QUOTE]

Agreed. But Moore's law is our friend.

I'm focused on exponents under 60M. Those higher (with a few exceptions) will happen naturally with the given TF limits.
We need about 40,000. Last year over 10,000 were found.
Granted this range even more so will take progressively longer but likely much less than 10 years.

lycorn 2018-03-06 22:59

Since the 1st of February 2013 we have found nearly 1,400,000 new factors. I am pretty confident it will take no longer than 6-7 years to get to under 20M unfactored.

petrw1 2018-03-17 04:13

2 Months later and great progress - March 16,2018
 
2,759 !!! more exponents factored in the ranges of interest...0 - 59.9M
GREAT PROGRESS (In ranges where there are still more than 1,999 unfactored.

13 more ranges cleared (now below 2,000):
2.0M
35.6M
40.9M
42.5M
44.8M
45.6M
45.7M
46.2M
46.8M
51.7M (51.xM is now complete)
55.0M
56.0M
57.8M

6 ranges within 5 or less to go.

petrw1 2018-04-16 05:14

April 15 Update
 
3 Ranges cleared: 44.1M, 54.6M, 57.7M
910 Exponents Factored

5 ranges within 5 or less factors to go.
And 6 more with 10 or less factors to go.

petrw1 2018-05-15 21:24

May 15 Update
 
3 Ranges cleared: 44.0M, 44.2M, 57.4M (34/497 Cleared since Sept 24, 2017)
601 Exponents Factored (8,770 since Sept 24, 2017)

6 ranges within 5 or less factors to go.
And 6 more with 10 or less factors to go.

petrw1 2018-05-20 03:22

50M Range Update
 
This has been my current focus though others have certainly helped in this range too.

As of today all 10 5xM Ranges have under 20,000 un-factored.

69 5x.x Ranges have under 2,000 un-factored.

Of the 31 remaining ranges I hope to get 20 of them under 2,000 over time.

The last 10 ranges, which for some reason have more than expected un-factored, may have to remain. :(

petrw1 2018-05-20 05:25

[QUOTE=petrw1;488036]Of the 31 remaining ranges I hope to get 20 of them under 2,000 over time.

The last 10 ranges, which for some reason have more than expected un-factored, may have to remain. :([/QUOTE]

I am doing fine getting the P-1 done; if anyone wants to participate the TF to higher bits is lagging; I am behind getting my new GPU thanks to BITCOIN!!!

ATH 2018-05-20 06:24

Some historical data on 50M-60M:


[CODE] Factored Unfactored
2008-11-20 10:00 UTC 327315 233666
2009-05-20 00:00 UTC 336948 224033
2010-05-20 00:00 UTC 341827 219154
2011-05-20 00:00 UTC 346016 214965
2012-05-20 00:00 UTC 354917 206064
2013-05-20 00:00 UTC 359500 201481
2014-05-20 00:00 UTC 359592 201389
2015-05-20 00:00 UTC 360076 200905
2016-05-20 00:00 UTC 362262 198719
2017-05-20 01:00 UTC 362269 198712
2018-05-20 00:00 UTC 362510 198471
[/CODE]

petrw1 2018-05-21 00:57

[QUOTE=ATH;488041]Some historical data on 50M-60M:


[CODE] Factored Unfactored
2008-11-20 10:00 UTC 327315 233666
2009-05-20 00:00 UTC 336948 224033
2010-05-20 00:00 UTC 341827 219154
2011-05-20 00:00 UTC 346016 214965
2012-05-20 00:00 UTC 354917 206064
2013-05-20 00:00 UTC 359500 201481
2014-05-20 00:00 UTC 359592 201389
2015-05-20 00:00 UTC 360076 200905
2016-05-20 00:00 UTC 362262 198719
2017-05-20 01:00 UTC 362269 198712
2018-05-20 00:00 UTC 362510 198471
[/CODE][/QUOTE]

Interesting 35,000 in 10 years.

petrw1 2018-05-30 16:33

As of a couple days ago all 100Million ranges have less than 2.2Million unfactored.

[url]http://www.mersenne.ca/status/tf/0/0/1/0[/url]

ixfd64 2018-05-30 19:29

I recently started rerunning P-1 on some really old exponents with only stage 1 done. I'm aware that this won't help us find a new Mersenne prime or even progress towards milestones, but at least I can do several hundred P-1 jobs for the cost of a single LL test at the current wavefront.

petrw1 2018-05-30 22:04

[QUOTE=ixfd64;488652]I recently started rerunning P-1 on some really old exponents with only stage 1 done. I'm aware that this won't help us find a new Mersenne prime or even progress towards milestones, but at least I can do several hundred P-1 jobs for the cost of a single LL test at the current wavefront.[/QUOTE]

Cool.

I'm doing so in the 50M range at least until October.
Then I will move down to 40M.

petrw1 2018-06-04 16:25

5xM progress since September 2017
 
I have now completed 5,000 PM-1 in the 5xM Range since September 2017.
And found 151 Factors for just over a 3% success rate.
There are all redo's of PM-1 that only had a Stage 1 done previously.

I've also found 27 factors with TF in this same range.
Others have found 48 more factors in this same range.

We now have 11 more 5x.x ranges with less than 2,000 un-factored.
29 ranges to go; granted about 10 are not cooperating and may have to be left.

And that is 226 less DC's required.

petrw1 2018-06-15 04:28

June 15 Update
 
4 Ranges cleared: 37.2M, 37.9M, 52.2M, 58.8M (38/497 Cleared since Sept 24, 2017)
491 Exponents Factored (9,251 since Sept 24, 2017)

5 ranges within 5 or less factors to go.
And 8 more with 10 or less factors to go.

petrw1 2018-07-25 05:29

July 24, 2018 ... 1 years since I started tracking
 
Total of 43 ranges cleared (out of a total of 497) = 8.65%
4 more ranges with less than 5 exponents to go.
11 ranges with less than 10 to go.
43 ranges with less than 25 to go.

9,918 exponents of interest factored (out of a total of 55,228) = 17.96%

I understand we are NOT 17.96% done or even 8.65% done because in general the easiest ranges fall first.

BUT....we have made great progress.

GO, TEAM GO!!!!!

(REMINDER: My lofty goal is to get all 0.1Million ranges under 60Million to under 2,000 unfactored. With the deeper factoring for ranges over 60Million I expect virtually all these ranges to be cleared in this way).

petrw1 2018-09-05 05:50

September 5 ... 1 year since I started work on this
 
A very good 6 weeks.

Total of 55 ranges cleared (out of a total of 497) = 11.07%
13 new ranges this month: 2.5, 39.2, 41.2, 42.2, 43.6, 43.7, 43.9, 50.6, 53.3, 54.0, 54.2, 55.4, 55.9

This got the entire 54M range complete.
And the 55M range is REALLY close....just 2 more factors.

3 more ranges with less than 5 exponents to go.
4 ranges with less than 10 to go.
36 ranges with less than 25 to go.

10,761 exponents of interest factored (out of a total of 55,228) = 19.48%

As well the 44Million range is now under 20,000 un-factored.
We have made great progress.

GO, TEAM GO!!!!!

A big thanks to Chris and his GPU72 support; and to everyone else willingly helping out.

……………………… Personally (not to brag because my contribution is small relative to the entire team) ……………..

In 365 days I ran over 20,000 assignments and have found 383 factors; just a little over 1 per day.
91 factors from TF with just slightly better than a 1% success rate.
263 factors from P1 with a 3.15% success rate.
29 factors from ECM with a little less than a 1% success rate (though I often ran 30-60 curves per assignment)

lycorn 2018-09-06 10:03

Looking at it from a slightly different point of vue:

157 [B]0.1M[/B] ranges cleared, out of 600 ([B]26.17%)[/B]

13 [B]1M[/B] ranges cleared, out of 60 ([B]21.67%)[/B]

1 [B]10M[/B] range cleared, out of 6 ([B]16.67%)[/B]

ET_ 2018-09-06 10:35

:tu:

Nice project!

petrw1 2018-09-13 04:57

Not only lightning strikes twice....
 
A couple months ago I was patiently waiting for the last 2 Factors to get range 50.6 under 2,000.
I had a decent 2-core laptop (LAP-A) going full-steam but having a bad streak (over 100 consecutive NF-PM1 results).
The assignments I am doing should statistically succeed 3 times in 100 attempts.
So I added a second 2-core laptop (LAP-B) and about a week later LAP-B found 1 factor so with only 1 remaining I chose to let LAP-A finish the work.
About another week later LAP-A found the remaining factor (YAY) but by the time I could get to LAP-A to give it new work it was nearly complete another P-1;
so I let it finish...and it found another factor: That is 2 in a row after 100 failures.

So this week LAP-A is once again in charge of completing the 50.4 range and again has 2 to go and I am again letting LAP-B help out.
Except this time LAP-A finds the penultimate factor first
… AND … over night it finds another (2 in a row again)
… AND … again by the time I get to it is almost finished another P-1 which I let complete and if finds a third factor
… YUP: 3 factors in a row (with no intervening NF).

chalsall 2018-09-13 18:43

[QUOTE=petrw1;495985]… YUP: 3 factors in a row (with no intervening NF).[/QUOTE]

Congrats. And, yup... Statistics has no memory.... :wink:

petrw1 2018-09-25 23:41

1 year in and 5xMillion P-1 is almost done...4xM next
 
I am about a week away from completing all the P-1 I can do in he 5xM range.
I took every exponent in the ranges of interest that had B1=B2 to B1=1000000, B2=20000000 ...
Then a few hundred more that had B1 and B2 low enough that they still had a 1.5% chance of finding a factor with the same new B1,B2.
When all my P-1 is done I will have done almost 8,000 and found about 240 P-1 factors in this range.

There is still quite a bit of TF to do, though.
I didn't have the GPUs I counted on for the last year for a couple reasons.
But I had great help from many others here....THANKS

I started with 40 ranges needing work.
As of today we are half done (20 to go).
I expect that TF will clear about half the remaining.
The last 10 or so ranges are being stubborn and may have to left behind for a while.

---------------------------------------------------------

Shortly I will be starting P-1 in the 4xM ranges; starting with those already at 73 TF bits (43.5M +) with lower remaining.
I will avoid any ranges I detect others working on (like 44.9 and 46.3).
Let me know if you have or want dibs on any ranges and I will respect them.

I plan to start with these ranges: Any conflicts?
48.6, 48.7, 46.7, 48.3, 47.2, 47.7, 43.8, 46.0, 45.2

petrw1 2018-10-13 04:53

Oct 12, 2018...I've completed P-1 in the 5xM range
 
I've done 8,161 P-1 in the 5xM range; the last 350 or so had B2>B1 but low values.
244 factors for a 3% success rate.

Personally I will move my P-1 effort to 4xM while working my GPUs in the remaining 5xM ranges.

23 of the 40 5xM ranges I started with are now "cleared" (under 2,000 unfactored).
Ranges 51M, 54M and 55M are complete; have all ranges "cleared"
Of the 17 ranges remaining 8 or 9 will be tough to complete.

This month the project completed 8 more ranges:
31.1; 33.6; 44.9; 50.4; 50.8; 55.6; 56.1; 56.3
for a total of 64 out of 497 or 12.88%
557 factors found in ranges of interest.

Thanks for all the help and interest.
Go Team Go!!!!

ET_ 2018-10-13 09:16

[QUOTE=petrw1;497975]I've done 8,161 P-1 in the 5xM range; the last 350 or so had B2>B1 but low values.
244 factors for a 3% success rate.

Personally I will move my P-1 effort to 4xM while working my GPUs in the remaining 5xM ranges.

23 of the 40 5xM ranges I started with are now "cleared" (under 2,000 unfactored).
Ranges 51M, 54M and 55M are complete; have all ranges "cleared"
Of the 17 ranges remaining 8 or 9 will be tough to complete.

This month the project completed 8 more ranges:
31.1; 33.6; 44.9; 50.4; 50.8; 55.6; 56.1; 56.3
for a total of 64 out of 497 or 12.88%
557 factors found in ranges of interest.

Thanks for all the help and interest.
Go Team Go!!!![/QUOTE]

I had grabbed and reserved 43 P-1 in the 5xM range for the project... Should I complete them, or you had zeroed the whole range? :-O

petrw1 2018-10-13 16:07

[QUOTE=ET_;497978]I had grabbed and reserved 43 P-1 in the 5xM range for the project... Should I complete them, or you had zeroed the whole range? :-O[/QUOTE]

Feel free to work on whatever you like...

Specifically for my project I am working on 0.1 Million ranges with 2000+ unfactored.
In my opinion I have done all the P-1 of value in the 5xMillions in those 2000+ ranges.
There is lots of P-1 left in other ranges with B1=B2 but not much in my ranges.

Any extra P-1 would have less than a 1.5% chance of finding a factor with P-1 to B1=1000000,B2=20000000 over what P-1 has already been done.

Mind you 1.5% is better than nothing but I think GPU TFing might be the best choice to continue there.

That is why I have chosen to move my P-1 efforts to the 4xMillions and let GPUs work in 5xMillion.

Thanks for your help and interest

ET_ 2018-10-13 16:24

[QUOTE=petrw1;497993]Feel free to work on whatever you like...

Specifically for my project I am working on 0.1 Million ranges with 2000+ unfactored.
In my opinion I have done all the P-1 of value in the 5xMillions in those 2000+ ranges.
There is lots of P-1 left in other ranges with B1=B2 but not much in my ranges.

Any extra P-1 would have less than a 1.5% chance of finding a factor with P-1 to B1=1000000,B2=20000000 over what P-1 has already been done.

Mind you 1.5% is better than nothing but I think GPU TFing might be the best choice to continue there.

That is why I have chosen to move my P-1 efforts to the 4xMillions and let GPUs work in 5xMillion.

Thanks for your help and interest[/QUOTE]

No problem, I will look for something else :smile:

chalsall 2018-10-13 16:53

[QUOTE=ET_;497995]No problem, I will look for something else :smile:[/QUOTE]

I think you guys are missing each other's points... Redoing P-1 (where only Stage 1 was done) in 5xM /would/ help the GIMPS DC'ing effort. It just wouldn't be of interest for Wayne's "to below 2,000" sub-sub-project.

petrw1 2018-10-13 17:07

[QUOTE=chalsall;497997]I think you guys are missing each other's points... Redoing P-1 (where only Stage 1 was done) in 5xM /would/ help the GIMPS DC'ing effort. It just wouldn't be of interest for Wayne's "to below 2,000" sub-sub-project.[/QUOTE]

Exactly... :)

ET_ 2018-10-13 19:14

[QUOTE=chalsall;497997]I think you guys are missing each other's points... Redoing P-1 (where only Stage 1 was done) in 5xM /would/ help the GIMPS DC'ing effort. It just wouldn't be of interest for Wayne's "to below 2,000" sub-sub-project.[/QUOTE]

:davieddy::picard:

petrw1 2018-11-01 16:55

As of today the 50M range is 50% complete.
 
I started tracking for this project 14 months ago (2017/09/01).
At that time it required 981 factors in the 40 ranges of interest.
Today the 491st factor was found.

Granted most of the "easy" work is done so the next 490 will certainly be more difficult.

lycorn 2018-11-01 21:59

As per James´s site there are just 475 to go. Not that it makes a big difference, but still...
I know, I know: "just" is more appropriate than just... :smile:

petrw1 2018-11-01 22:56

[QUOTE=lycorn;499297]As per James´s site there are just 475 to go. Not that it makes a big difference, but still...
I know, I know: "just" is more appropriate than just... :smile:[/QUOTE]

Hmmmm I better check my math.

petrw1 2018-12-03 04:40

December 2, 2018 Update
 
7 more cleared: 11.5, 38.1, 42.0, 42.1, 42.4, 48.7, 56.5
71 total cleared or 14.29%

12 Ranges with less than 20 to go.
551 more factored.

I've moved all my P1'ers (32 of them) to the 4xM Ranges.

My GPUs (4500GhzDays) continue to work in the 5xM Ranges...15 to go.

Thanks again for everyone contributing.

petrw1 2018-12-03 20:28

10,000 P-1 assignments later...
 
In just over 14 months and I have surpassed 10,000 P-1 attempts in the 4x and 5x Million ranges for exponents that had B1=B2 (and a few hundred more with low bounds).

The assignments were taken to: B1=0.8M to 1M, B2=16M to 20M.

I have found 293 P-1 factors for a 2.93% success rate.

Also, 69 TF factors out of almost 6,900 attempts for a 1% success rate.

--------------------------------------------------------------------------------------------------

This may seem like a lot but everyone else has contributed a lot more to this project.

Thanks

lycorn 2018-12-14 23:21

How´s your new GPU doing?

petrw1 2018-12-14 23:50

[QUOTE=lycorn;502813]How´s your new GPU doing?[/QUOTE]

Whoop whoop.

4,000 GhzDays/Day.

59.6M 74-75 in 23 minutes.

Mark Rose 2018-12-15 02:12

[QUOTE=petrw1;502817]Whoop whoop.

4,000 GhzDays/Day.

59.6M 74-75 in 23 minutes.[/QUOTE]

I'd have to run 5 of my GTX 1070s to match that. The RTX series are crazy good at TF.

lycorn 2018-12-15 18:58

[QUOTE=petrw1;502817]Whoop whoop.

4,000 GhzDays/Day.

59.6M 74-75 in 23 minutes.[/QUOTE]

Geee...
That´s great, man! :bow:

A nice push towards your "personal goal" :smile:

On another note, it would be interesting that you run TF on a small (read 900k or lower) exponent just to compare performance. My GTX1060 does about 470 GHz-d/day while running TF on 300M (69->70 bits) exponents, and around 700Ghz-d/day on 900K (66-> 67 bits).

petrw1 2018-12-15 19:37

[QUOTE=lycorn;502908]Geee...
That´s great, man! :bow:

A nice push towards your "personal goal" :smile:

On another note, it would be interesting that you run TF on a small (read 900k or lower) exponent just to compare performance. My GTX1060 does about 470 GHz-d/day while running TF on 300M (69->70 bits) exponents, and around 700Ghz-d/day on 900K (66-> 67 bits).[/QUOTE]

My lower limit is just over 1Million without changing some config parms.
1,155,xxx from 67 to 68 runs at almost 5,000GD

lycorn 2018-12-15 19:48

[QUOTE=petrw1;502913]My lower limit is just over 1Million without changing some config parms.
1,155,xxx from 67 to 68 runs at almost 5,000GD[/QUOTE]

Yes, I see, the GPUSievePrimes isn´t it? I have to tweak it as well, whenever I change from high to low ranges. It also makes a fair difference in your rig.

Gordon 2018-12-16 02:18

[QUOTE=lycorn;502908]Geee...
That´s great, man! :bow:

A nice push towards your "personal goal" :smile:

On another note, it would be interesting that you run TF on a small (read 900k or lower) exponent just to compare performance. My GTX1060 does about 470 GHz-d/day while running TF on 300M (69->70 bits) exponents, and around 700Ghz-d/day on 900K (66-> 67 bits).[/QUOTE]

Come down to the *low* side - under 5k...

lycorn 2018-12-16 09:21

[QUOTE=Gordon;502951]Come down to the *low* side - under 5k...[/QUOTE]

That´s too low for the GPU TF programs we have available. Or did you want to mean 5[B]M[/B]?

VictordeHolland 2018-12-16 15:56

[QUOTE=Gordon;502951]Come down to the *low* side - under 5k...[/QUOTE]
Exponents <5000 all have had at least a t40 of ECM done, most of them even t50 or more. Please don't use TF in that region, it's a complete waste of time/resources.

LaurV 2018-12-17 02:21

[QUOTE=lycorn;502968]That´s too low for the GPU TF programs we have available. Or did you want to mean 5[B]M[/B]?[/QUOTE]

[QUOTE=VictordeHolland;502989] Please don't use TF in that region, it's a complete waste of time/resources.[/QUOTE]
There are modified versions of mfaktc that allow factoring "over 2k", but we agree with Victor that TF there is a totally waste of time and resources. They had tons of ECM and P-1 done, so the chance a factor under 100 bits escaped is smaller than any epsilon...

Gordon 2018-12-17 17:06

[QUOTE=VictordeHolland;502989]Exponents <5000 all have had at least a t40 of ECM done, most of them even t50 or more. Please don't use TF in that region, it's a complete waste of time/resources.[/QUOTE]

Sorry, I didn't make that clear, it's ECM that I'm doing...

snme2pm1 2019-01-03 06:53

[QUOTE=petrw1;492437](REMINDER: My lofty goal is to get all 0.1Million ranges under 60Million to under 2,000 unfactored. With the deeper factoring for ranges over 60Million I expect virtually all these ranges to be cleared in this way).[/QUOTE]

What was the basis for reliance on the notion of unfactored <2000 per 100k goal for below 60M or any other range for that matter?
Perhaps there is a graph somewhere that supports the accompanying notion that the goal posts might be shifted for different, particularly higher, exponent million zones?

By the way I didn't notice mention of what grand GPU equipment you apparently now have enslaved, perhaps that was highlighted in a different thread slightly off topic from here!

Uncwilly 2019-01-03 07:00

[QUOTE=snme2pm1;504737]By the way I didn't notice mention of what grand GPU equipment you apparently now have enslaved, perhaps that was highlighted in a different thread slightly off topic from here![/QUOTE]Enough that during the winter in central Canada he must needs keep a window open in a room where the beasts reside.
[url]https://mersenneforum.org/showthread.php?p=502902[/url]

petrw1 2019-01-03 17:07

[QUOTE=snme2pm1;504737]What was the basis for reliance on the notion of unfactored <2000 per 100k goal for below 60M or any other range for that matter?
Perhaps there is a graph somewhere that supports the accompanying notion that the goal posts might be shifted for different, particularly higher, exponent million zones?

By the way I didn't notice mention of what grand GPU equipment you apparently now have enslaved, perhaps that was highlighted in a different thread slightly off topic from here![/QUOTE]

GIMPS as a whole has well defined standards of how deep to factor all ranges; though GPUs have increased these somewhat. I am not trying to undermine that in any way. I see my interest as more custodial; cleaning up behind them.

Some time back someone, on the topic of milestones, noted that having less than 20,000,000 unfactored exponents would be monumental though admittedly a LONG way off.
See unfactored total at the bottom of this (just over 21.3 Million): [url]https://www.mersenne.ca/status/tf/0/0/1/0[/url]

That got me to thinking as I noted in the first post of this Thread:
[QUOTE]
Thinking out loud about getting under 20M unfactored exponents
Breaking it down I'm thinking if each 100M range has less than 2M unfactored we have the desired end result.
Similarly if each 10M range has less than 200K unfactored...
or each 1M range has less than 20K unfactored...
or each 100K range has less than 2,000 unfactored.[/QUOTE]

So I decided to make it a sub-project of focus for me.
Happily several others found it interesting as well and have been helping out.
A huge thanks to Chris for volunteering to let GPUto72 spider the TF work assignments.

When I drilled down into the same link above I noticed that ranges 60M and above would mostly end up with less than 2,000 on their own due to the deep factoring going on at GPUto72.
There are a few exceptions but not many. Some day I may look there too.
So my main focus and tracking has been under 60M though I do occasionally "spy" on the larger ranges.

Still I wanted to work on this project in a way that would benefit GIMPS as a whole if I could.
I noted that the current DC wave-front is in the 40M area so I realized that factoring there would reduce the DC workload at the same time.
Hence my main focus that last couple years has been in the 40M and 50M ranges.

My 3-pronged approach has been to find ranges with 2000+ unfactored. Then:
1. Find exponents with poor P1 bounds (mainly with B1=B2) and redo them with CPUs. I am going beyond the default bounds set by Prime95. Mostly B1=1000000; B2=20000000 in the 50M ranges. This has cleared several ranges; as in <2000.
2. Use the GPUs to factor remaining ranges deeper. This cleared many more.
3. For CPUs with slower processors or less RAM run P1 or ECM in the very low ranges; i.e. under 5M. I have cleared about half a dozen ranges there. Granted normal ECM work would probably have done so itself over the next few years.

I would recommend the same approach for anyone interesting in helping out. We only ask that there is some communication to ensure no toe-stepping.

In the 50M range I started with 40 ranges (out of 100) with 2000+ unfactored. I am a few weeks away from getting that count down to 9 and factoring over 600 exponents; thereby eliminating a DC for these.

Most of my effort has now shifted to the 40M ranges. It had over 60 ranges to go when I started this sub-project. It is now under 50 ranges to go and dropping.

Others are working in lower ranges; mostly 30M with great progress.

I started tracking about 16 months ago. At that time for the ranges under 60M there were almost 500 ranges over 2000 unfactored (out of 600 total). We are now closing in on 400.

Thanks again to all contributors and to those showing an interest.

petrw1 2019-01-03 17:24

[QUOTE=snme2pm1;504737]By the way I didn't notice mention of what grand GPU equipment you apparently now have enslaved, perhaps that was highlighted in a different thread slightly off topic from here![/QUOTE]

I took a risk and bought one of the newly announced RTX 2080Ti GPUs in the fall. The first was faulty and had to be replaced.
I also bought an 8-core i7-7820x CPU and put in it 32GB of DDR4-3600 RAM.
These were my personal reward for taking one more contract at work when I would rather have been retired.

In total I have 2 GPUs:
GTX-980 at about 560 GhzDays/Day of TF
RTX-2080Ti at about 4,000 GhzDays/Day of TF

And the following CPUs. Only the 3570K (5 years ago) and the 7820X (this year) were bought new.
Collectively they complete over 200GhzDays/Day (45 assignments) of P1.
All 4 core except the 3 noted differently.
All but 2 are in my house....I think the only people with higher power bills have a grow-op in the basement.

Intel Core i5-2520M @ 2.50GHz (2-Core Laptop)
Intel Core i5-4310U @ 2.00GHz (2-Core Laptop)
Intel Core i5-2500 @ 3.30GHz
Intel Core i5-3570 @ 3.40GHz
Intel Core i5-3570 @ 3.40GHz
Intel Core i5-3570K @ 3.40GHz
Intel Core i7-6700 @ 3.40GHz
Intel Core i7-7820X @ 3.60GHz (8-core)

snme2pm1 2019-01-05 01:50

[QUOTE=petrw1;504780]When I drilled down into the same link above I noticed that ranges 60M and above would mostly end up with less than 2,000 on their own due to the deep factoring going on at GPUto72.
[/QUOTE]

Don't let folk misunderstand, Wayne and I are friends that have collaborated previously.

I am yet to find an estimate analysis of probability for the composite of tests out to James's yellow marker, or some other criteria, that would leave unfactored candidates within a 100k exponent region at something near [B]2000[/B].
It seems to be somehow close to a likely outcome for some regions, but I suspect, as Wayne seems to acknowledge, that different regions might have different probability of survival of a candidate, again based on some criteria.

I feel somewhat awkward about reliance on such an arbitrary number, and that perhaps there might be a corresponding interpretation of an exercise to chase down exponents within localized 100k regions that didn't achieve the expected probability of finding a factor.
I suspect that the arithmetic has been done before this time, so is there a suitable link that can be cited?

ATH 2019-01-05 12:50

The fastest way to get under 20M unfactored exponents, if you skip your 2nd goal of 2,000 unfactored every 100k, is probably to use GPU to trial factor the range 100M-1000M. There are probably enough factors hidden there without doing very deep factoring.
But this way you contribute more immediately to DC instead of contributing to future LL and DC.


Right now there are 29,544,903 of 50,847,534 exponents with at least 1 factor, so 30,847,534-29,544,903 = 1,302,631 left until 20M unfactored.

Last 365 days that number of factored exponents went up with +267,160, so if that speed is kept it will take just under 5 years:

[url]http://hoegge.dk/mersenne/GIMPSstats.html[/url]

lycorn 2019-01-05 20:49

Over the last 3 or 4 months we have had a very large contributor (sometimes over 1500 factors in a day), but it's apparently cooling down :(
Let's see how it goes.

petrw1 2019-01-06 06:42

What are the odds....
 
I don't mean it literally but I know several of you can tell me:
Same computer; 2 cores both found a P-1 factor in the same minute.
AND...Day; Hour and Minute are all 06.

[CODE]Magic_8_Ball
47728897
F-PM1
2019-01-06 06:06
Factor: 120869547910518815929399 / (P-1, B1=1000000, B2=20000000, E=12)
5.0266

Magic_8_Ball
47704099
F-PM1
2019-01-06 06:06
Factor: 176334906978053159315473649 / (P-1, B1=1000000, B2=20000000, E=12)
5.0266[/CODE]

axn 2019-01-06 10:31

[QUOTE=petrw1;505084]I don't mean it literally but I know several of you can tell me:
Same computer; 2 cores both found a P-1 factor in the same minute.[/QUOTE]

Since the bounds are same, and presumably the FFTs are the same, if you start the computation at the same time, it has a very high probability of finishing on the same time. So it is just a matter of multiplying the odds of individual P-1 success.

As for the 6/6/6 bit, since you haven't specified what kind of date/time combination are "interesting", we can't estimate a probability (for eg:-, if it was 20190106 05:04, would you have noted the 6/5/4 and asked for the odds?) I would crudely estimate that 1% of all date/time combinations are interesting. Whatever be the value, multiply that probability as well.

PhilF 2019-01-06 16:07

Can someone tell me what the E value represents?

LaurV 2019-01-06 16:25

Do you mean the Brent-Suyama extension and stuff related to P-1 stage 2 ? (E=2, or 6, 12, etc)

PhilF 2019-01-06 16:28

[QUOTE=LaurV;505107]Do you mean the Brent-Suyama extension and stuff related to P-1 stage 2 ? (E=2, or 6, 12, etc)[/QUOTE]

Yes, assuming the E= value is applicable only to P-1 tests. The Brent-Suyama extension is something I have never heard of.

petrw1 2019-01-14 03:24

January 13, 2019 Update
 
10 more ranges cleared: 34.8, 42.7, 42.8, 46.7, 47.2, 50.3, 50.9, 56.7, 57.6, 59.6
81 total ranges cleared or 16.30%
57M Range is now complete.

11 Ranges with less than 20 to go.
540 more factored.

Thanks again for everyone contributing.

Personally I just surpassed 30,000 total factoring attempts in just under 500 days and found 574 factors.
14,066 TF with a 1.00% success rate
13,056 P1 with a 3.09% success rate
3,095 ECM with a 0.94% success rate.

petrw1 2019-03-09 04:47

March 8, 2019 Update
 
9 more ranges cleared: 37.7, 40.6, 46.0, 47.7, 48.3, 48.6, 53.5, 581.
Plus bonus ranges cleared in the 6xM series: 68.8, 69.5 (62.8 is 1 away)

90 total ranges cleared or 18.11%
47M Range is now complete.

6 Ranges with less than 20 to go.
530 more factored.

Thanks again for everyone contributing.

petrw1 2019-04-26 23:02

April 26, 2019 Update
 
more ranges cleared: 32.8, 33.9, 43.8, 47.1.
Plus bonus ranges cleared in the 6xM series: 62.8, 64.1

94 total ranges cleared or 18.91%

9 Ranges with less than 20 to go.
411 more factored.

Personally, I found my 800th factor in this sub-project.
And expended just slightly under 1Million GhzDays to date.

Thanks again for everyone contributing.

[B][U]More help is always gratefully appreciated.[/U][/B]

LaurV 2019-04-27 04:55

[QUOTE=PhilF;505108]Yes, assuming the E= value is applicable only to P-1 tests. The Brent-Suyama extension is something I have never heard of.[/QUOTE]
[URL="https://www.rieselprime.de/ziki/Brent-Suyama_extension"]Here[/URL] (most probably you found it long time ago, but I didn't see this thread till petrw1 woke it up by posting)


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