[QUOTE=RichD;528716]Hint: 957 = 3 * 11 * 29[/QUOTE]

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?

[QUOTE=jyb;528664]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.[/QUOTE]

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.

[QUOTE=jyb;528712]Can you show me that split? More concretely, can you show me the actual polynomial you would use?[/QUOTE]

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.

[QUOTE=R.D. Silverman;528726]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.[/QUOTE]

Yes, the relevant identity can be found [URL="https://www.unshlump.com/hcn/aurif_polys.txt"]here[/URL]. 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.

Funny fact:
[C]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)[/C]
is shorter (281 symbols) to write than
[C]c303[/C] in [url]http://factordb.com/index.php?id=1100000000803053534[/url]
so factordb replaced the description with the polynomial one.

5+2,429 (SNFS):
[code]
174488927704196017427834562121968536581079996293421394919018919940726247
209043091779597774551774686317841540363734596172666574678086496372738995504504719585897383
[/code]

11+10,291 (SNFS):
[code]380266943142329489412928870550360580454015242272929288510561
91914698655355790011195552383112079792954658462237710112670585624673996698462259257559594644719083486385439
[/code]

11+5,291 (SNFS):
[code]
47521634785763411240247359604230285991147693001772703203641404053619418742692777
471929208501024860711796292282895325629782080663188075720839533085043437379187774162028765127369101
[/code]

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.

11+7,291 (SNFS):
[code]
13887041718955084964115299213884823850098058524524459846840021965702131949435080239
189866682981898495174146951771128840200039263317932342660926788811513955895890735130955393913903811863273027
[/code]

11-5,291 (SNFS):
[code]
38570866425429718750632134005994098100226746641653615888603985991302290837706069934854812289201275837244293972913
1382692059052256387858158993319709629363715785078428304443505109860053154824264309912657
[/code]