Factoring humongous Cunningham numbers - Page 148

jyb · 2019-10-23, 19:46

Quote:

Originally Posted by RichD

Hint: 957 = 3 * 11 * 29

I'm afraid I don't find this enlightening. I can use algebraic factors to find a polynomial for this number in several different ways. However, I can find no way to get the difficulty down to 332 without having a degree of at least 20. Are you saying you have found such a way?

swellman · 2019-10-23, 20:06

Quote:

Originally Posted by jyb

Good luck!

FWIW, it's probably not necessary to reserve a number for which you're just planning to run ECM. Unless there's a high likelihood of success, we don't need to worry too much about duplicating effort, since every extra ECM curve run by anyone else will still be helpful. However, if you really, really want to make sure that you're the only one looking at this number, then there's no real harm in making the reservation. Just know that the ECMnet server may still be handing it out.

No worries on ECMnet, I was just guarding against the unlikely scenario of someone else picking it out for individual ECM effort. Won’t make a habit of reserving HCNs for individual ECM efforts going forward.

R.D. Silverman · 2019-10-23, 20:23

Quote:

Originally Posted by jyb

Can you show me that split? More concretely, can you show me the actual polynomial you would use?

It's a mess. I have no computer algebra system to do the manipulations. It may well
be that the final polynomial has a Hamming weight that is too large to be useful.

The base 11 Aurifeuillians have a LOT of terms.

jyb · 2019-10-23, 21:06

Quote:

Originally Posted by R.D. Silverman

It's a mess. I have no computer algebra system to do the manipulations. It may well
be that the final polynomial has a Hamming weight that is too large to be useful.

The base 11 Aurifeuillians have a LOT of terms.

Yes, the relevant identity can be found here. Note that using this will automatically use both the algebraic factors given by the 3 and the 11, so it actually gets the difficulty down to 302.

But its natural degree is 20. We can halve that to get a 10th-degree polynomial, but I see no way to do better than that.

Batalov · 2019-10-23, 22:07

Funny fact:
11^290+16*11^261*3^29+37*11^232*3^58+19*11^203*3^87-32*11^174*3^116-59*11^145*3^145-32*11^116*3^174+19*11^87*3^203+37*11^58*3^232+16*11^29*3^261+3^290+33^15*(11^261+5*11^232*3^29+6*11^203*3^58-11^174*3^87-9*11^145*3^116-9*11^116*3^145-11^87*3^174+6*11^58*3^203+5*11^29*3^232+3^261)
is shorter (281 symbols) to write than
c303 in http://factordb.com/index.php?id=1100000000803053534
so factordb replaced the description with the polynomial one.

EdH · 2019-10-24, 03:11

5+2,429 (SNFS):

Code:

174488927704196017427834562121968536581079996293421394919018919940726247
209043091779597774551774686317841540363734596172666574678086496372738995504504719585897383

EdH · 2019-10-25, 14:22

11+10,291 (SNFS):

Code:

380266943142329489412928870550360580454015242272929288510561
91914698655355790011195552383112079792954658462237710112670585624673996698462259257559594644719083486385439

EdH · 2019-10-26, 02:23

11+5,291 (SNFS):

Code:

47521634785763411240247359604230285991147693001772703203641404053619418742692777
471929208501024860711796292282895325629782080663188075720839533085043437379187774162028765127369101

pinhodecarlos · 2019-10-26, 07:10

Looking forward to seeing next stats update. Also is it possible to show like on the GCW page the contributions breakdown per user (with all combinations)? Thank you.

EdH · 2019-10-26, 15:31

11+7,291 (SNFS):

Code:

13887041718955084964115299213884823850098058524524459846840021965702131949435080239
189866682981898495174146951771128840200039263317932342660926788811513955895890735130955393913903811863273027

EdH · 2019-10-27, 02:14

11-5,291 (SNFS):

Code:

38570866425429718750632134005994098100226746641653615888603985991302290837706069934854812289201275837244293972913
1382692059052256387858158993319709629363715785078428304443505109860053154824264309912657

2019-10-24, 03:11	#1623
EdH "Ed Hall" Dec 2009 Adirondack Mtns 2⁸×3×5 Posts	5+2,429 (SNFS): Code: 174488927704196017427834562121968536581079996293421394919018919940726247 209043091779597774551774686317841540363734596172666574678086496372738995504504719585897383

2019-10-25, 14:22	#1624
EdH "Ed Hall" Dec 2009 Adirondack Mtns 111100000000₂ Posts	11+10,291 (SNFS): Code: 380266943142329489412928870550360580454015242272929288510561 91914698655355790011195552383112079792954658462237710112670585624673996698462259257559594644719083486385439

2019-10-26, 02:23	#1625
EdH "Ed Hall" Dec 2009 Adirondack Mtns 2⁸×3×5 Posts	11+5,291 (SNFS): Code: 47521634785763411240247359604230285991147693001772703203641404053619418742692777 471929208501024860711796292282895325629782080663188075720839533085043437379187774162028765127369101

2019-10-26, 15:31	#1627
EdH "Ed Hall" Dec 2009 Adirondack Mtns 7400₈ Posts	11+7,291 (SNFS): Code: 13887041718955084964115299213884823850098058524524459846840021965702131949435080239 189866682981898495174146951771128840200039263317932342660926788811513955895890735130955393913903811863273027

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2019-10-23, 22:07	#1622
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,497 Posts	Funny fact: 11^290+1611^2613^29+3711^2323^58+1911^2033^87-3211^1743^116-5911^1453^145-3211^1163^174+1911^873^203+3711^583^232+1611^293^261+3^290+33^15(11^261+511^2323^29+611^2033^58-11^1743^87-911^1453^116-911^1163^145-11^873^174+611^583^203+511^29*3^232+3^261) is shorter (281 symbols) to write than c303 in http://factordb.com/index.php?id=1100000000803053534 so factordb replaced the description with the polynomial one.

2019-10-26, 07:10	#1626
pinhodecarlos "Carlos Pinho" Oct 2011 Milton Keynes, UK 3·17·97 Posts	Looking forward to seeing next stats update. Also is it possible to show like on the GCW page the contributions breakdown per user (with all combinations)? Thank you.