Missed small factors - Page 3

GP2 · 2003-11-18, 23:07

I just noticed these exponents in dswanson's previously cut-and-pasted messages:

> 5977297 53 DF 6726544627832489
> 6019603 57 DF 137024179940485697

Seems like confirmation of sorts.

By contrast, there don't seem to be too few large factors around 7 M (anymore, anyways).

GP2 · 2003-11-18, 23:37

I just started a factoring run to 53 bits for all 512 exponents:

M5980519 has a factor: 5940298383023833

Looks confirmed.

Maybe the Lone Mersenne Hunters might want to take a crack at it, it's their traditional area.

GP2 · 2003-11-19, 00:47

Two more 53-bit factors so far:

UID: GP2/G8, M5986889 has a factor: 6992859337170767
UID: GP2/G8, M5990147 has a factor: 5484105191882591

Here's a graph:

[Edit: the graph title was wrong, so a new graph has been attached.

The title should read "factors of 16 decimal digits or more", not "factors larger than 16 decimal digits".]

dswanson · 2003-11-19, 03:07

GP2,

The cut-and-paste's above included an exponent outside of the 5.98 - 6.02M range:

> 5977297 53 DF 6726544627832489

Do you intend to add a set for the Mersenne-aries covering the range a little under 5.98M?

BTW, excellent analysis! I wish I had the time to dig into the numbers like you do.

GP2 · 2003-11-19, 03:29

I redid 5.97 - 5.98 M and 6.00 - 6.01 M to 53 bits without finding factors. I'll probably add sets of these after we see how the 5.98 - 6.00 M goes.

dswanson · 2003-11-19, 03:37

10,000+10,000 is a rather narrow range. It wouldn't surprise me if there simply weren't any factors up to 2^53. After all, you only found 3 in the 20,000 range you did post. I suspect that some will turn up when trial-factored a little deeper.

But you're right, the 20,000 range should be interesting, and should keep people busy for a little while. I look forward to the results. I'm seriously tempted to put one of my machines on it. But they're all P4's, so that would be a terribly inefficient use of resources.

dswanson · 2003-11-19, 03:40

Given the fuzziness on the start and end of the range, you might want to ease into the edges one block of 50 or so at a time, and let that block finish before posting the next block.

When a block finishes with no factors found, I think you can declare that the end of the misfactored range.

garo · 2003-11-19, 09:03

GP2,
great work. one more thing. Would it be useful to break the number of factors up on a per bit basis? And maybe increase the bin size?

GP2 · 2003-11-19, 15:59

I experimented with different histogram bin sizes. Larger ones reduce the noise, but they also diminish the size of the dip at 5.98M by averaging it out with other nearby data.

Calculating the number of factors of each bit size sounds like an interesting suggestion, I'll try that. Although it might decrease the statistics and make them even noisier...

PS,
For what it's worth, no additional factors of 53 bits in 5.94-5.9799M or 6.00-6.0199M.

garo · 2003-11-19, 18:35

I found one in the 5.99 range!! :) I'll report the results when I'm finmished to 58 bits.I may decide to take it higher as well.

GP2 · 2003-11-19, 19:05

I added a script that compares the weekly data files with previous versions and looks for new factors found with equal or fewer bits than the previously claimed trial-factoring bit depth.

[Clarification: these are factors newly found for exponents that previously did not have any known factors.]

Then I ran it against some historical data (thanks garo and others).

Output is:
Exponent,
Previously claimed trial-factoring bit-depth,
Number of bits of the new factor,
The new factor

Jan 2002 - June 2002

865121,57,54,14212193461596241
881899,57,56,60897762538747129
889481,57,56,39950486299000577
889769,57,55,20219205733502137
1056823,57,55,19455109680160177
1131421,57,55,22563829039691809
1168249,57,55,24984521700809617
2101259,58,57,77848777227162841
2101903,58,55,21174976606985569
7045427,62,61,1453789862361107809
7057123,62,57,104515436827218233
14722831,65,60,697340345368815937

June 2002 - Sept 2002

1507889,57,57,78465904916463751
1510913,57,56,50424735576000449
1604147,59,58,243033130949911417
1630243,57,55,28901095930064401
2262461,59,58,258344106658630943
16233187,65,53,6662303184301241

Sept 2002 - Jan 2003

1502801,57,55,23767608714397193
1776839,57,57,133653567034269361
1781863,57,57,78005860736839751
1783553,57,56,56932126024035433
5993719,62,53,6807510023694431
6001991,62,60,1036390398570018343
16692337,65,65,18479898164720462161
16761923,65,65,21031410033480320161
16956883,65,65,25935990321804878551
17364989,65,60,635193685179906751
17365199,65,64,12807992157020885777
17821381,65,65,33854132584011567089

Jan 2003 - Sept 2003

9329521,64,62,2742715083753727079
18066317,66,60,1146015834795539233
18445681,66,66,37654786733671555367

September 2003

1173883,58,55,20527759345537817
1403453,58,55,25655917922710633
1404257,58,55,22737663478729673
2351641,58,58,148389237767555137
38016527,60,59,451198075592116441

October 2003

2441083,59,57,75649430225324231
2448961,59,57,95075864569432231
2623141,59,55,23522191782267041

November 2003

268813,57,50,1017111715779881
2596589,59,55,25067922220213121
19327019,66,62,3082263328775126129

The 3 factors in October and the small 268813 exponent were found by user k5gj,
which is what prompted this whole thread. He found them doing P-1. But P-1 won't find all small factors, just some with certain properties.

2003-11-19, 00:47	#25
GP2 Sep 2003 3²×7×41 Posts	Two more 53-bit factors so far: UID: GP2/G8, M5986889 has a factor: 6992859337170767 UID: GP2/G8, M5990147 has a factor: 5484105191882591 Here's a graph: [Edit: the graph title was wrong, so a new graph has been attached. The title should read "factors of 16 decimal digits or more", not "factors larger than 16 decimal digits".] Attached Thumbnails Last fiddled with by GP2 on 2003-11-19 at 01:35

2003-11-19, 03:07	#26
dswanson Aug 2002 310₈ Posts	GP2, The cut-and-paste's above included an exponent outside of the 5.98 - 6.02M range: > 5977297 53 DF 6726544627832489 Do you intend to add a set for the Mersenne-aries covering the range a little under 5.98M? BTW, excellent analysis! I wish I had the time to dig into the numbers like you do. Last fiddled with by dswanson on 2003-11-19 at 03:08

2003-11-19, 19:05	#33
GP2 Sep 2003 101000010111₂ Posts	I added a script that compares the weekly data files with previous versions and looks for new factors found with equal or fewer bits than the previously claimed trial-factoring bit depth. [Clarification: these are factors newly found for exponents that previously did not have any known factors.] Then I ran it against some historical data (thanks garo and others). Output is: Exponent, Previously claimed trial-factoring bit-depth, Number of bits of the new factor, The new factor Jan 2002 - June 2002 865121,57,54,14212193461596241 881899,57,56,60897762538747129 889481,57,56,39950486299000577 889769,57,55,20219205733502137 1056823,57,55,19455109680160177 1131421,57,55,22563829039691809 1168249,57,55,24984521700809617 2101259,58,57,77848777227162841 2101903,58,55,21174976606985569 7045427,62,61,1453789862361107809 7057123,62,57,104515436827218233 14722831,65,60,697340345368815937 June 2002 - Sept 2002 1507889,57,57,78465904916463751 1510913,57,56,50424735576000449 1604147,59,58,243033130949911417 1630243,57,55,28901095930064401 2262461,59,58,258344106658630943 16233187,65,53,6662303184301241 Sept 2002 - Jan 2003 1502801,57,55,23767608714397193 1776839,57,57,133653567034269361 1781863,57,57,78005860736839751 1783553,57,56,56932126024035433 5993719,62,53,6807510023694431 6001991,62,60,1036390398570018343 16692337,65,65,18479898164720462161 16761923,65,65,21031410033480320161 16956883,65,65,25935990321804878551 17364989,65,60,635193685179906751 17365199,65,64,12807992157020885777 17821381,65,65,33854132584011567089 Jan 2003 - Sept 2003 9329521,64,62,2742715083753727079 18066317,66,60,1146015834795539233 18445681,66,66,37654786733671555367 September 2003 1173883,58,55,20527759345537817 1403453,58,55,25655917922710633 1404257,58,55,22737663478729673 2351641,58,58,148389237767555137 38016527,60,59,451198075592116441 October 2003 2441083,59,57,75649430225324231 2448961,59,57,95075864569432231 2623141,59,55,23522191782267041 November 2003 268813,57,50,1017111715779881 2596589,59,55,25067922220213121 19327019,66,62,3082263328775126129 The 3 factors in October and the small 268813 exponent were found by user k5gj, which is what prompted this whole thread. He found them doing P-1. But P-1 won't find all small factors, just some with certain properties. Last fiddled with by GP2 on 2003-11-19 at 22:04

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2003-11-18, 23:07	#23
GP2 Sep 2003 2583₁₀ Posts	I just noticed these exponents in dswanson's previously cut-and-pasted messages: > 5977297 53 DF 6726544627832489 > 6019603 57 DF 137024179940485697 Seems like confirmation of sorts. By contrast, there don't seem to be too few large factors around 7 M (anymore, anyways).

2003-11-18, 23:37	#24
GP2 Sep 2003 3²×7×41 Posts	I just started a factoring run to 53 bits for all 512 exponents: M5980519 has a factor: 5940298383023833 Looks confirmed. Maybe the Lone Mersenne Hunters might want to take a crack at it, it's their traditional area.

2003-11-19, 03:29	#27
GP2 Sep 2003 101000010111₂ Posts	I redid 5.97 - 5.98 M and 6.00 - 6.01 M to 53 bits without finding factors. I'll probably add sets of these after we see how the 5.98 - 6.00 M goes.

2003-11-19, 03:37	#28
dswanson Aug 2002 310₈ Posts	10,000+10,000 is a rather narrow range. It wouldn't surprise me if there simply weren't any factors up to 2^53. After all, you only found 3 in the 20,000 range you did post. I suspect that some will turn up when trial-factored a little deeper. But you're right, the 20,000 range should be interesting, and should keep people busy for a little while. I look forward to the results. I'm seriously tempted to put one of my machines on it. But they're all P4's, so that would be a terribly inefficient use of resources.

2003-11-19, 03:40	#29
dswanson Aug 2002 2³·5² Posts	Given the fuzziness on the start and end of the range, you might want to ease into the edges one block of 50 or so at a time, and let that block finish before posting the next block. When a block finishes with no factors found, I think you can declare that the end of the misfactored range.

2003-11-19, 09:03	#30
garo Aug 2002 Termonfeckin, IE 3×919 Posts	GP2, great work. one more thing. Would it be useful to break the number of factors up on a per bit basis? And maybe increase the bin size?

2003-11-19, 15:59	#31
GP2 Sep 2003 3²·7·41 Posts	I experimented with different histogram bin sizes. Larger ones reduce the noise, but they also diminish the size of the dip at 5.98M by averaging it out with other nearby data. Calculating the number of factors of each bit size sounds like an interesting suggestion, I'll try that. Although it might decrease the statistics and make them even noisier... PS, For what it's worth, no additional factors of 53 bits in 5.94-5.9799M or 6.00-6.0199M.

2003-11-19, 18:35	#32
garo Aug 2002 Termonfeckin, IE 3·919 Posts	I found one in the 5.99 range!! :) I'll report the results when I'm finmished to 58 bits.I may decide to take it higher as well.