20210611, 22:25  #221  
"Max"
Jun 2016
Toronto
19·47 Posts 
Thank you!
After a week of hard work and 220 posts in this thread, we have 95 lines done!
82 of these lines were never calculated before (after completing 85 much easier lines producing 85*2=170 points on the plot, 13 plot points remained not shown on the Figure 3 of the preprint). You have completed 9513=82 much harder lines! And more are coming. The full plot now has (85+82)*2=334 plot points. I was dreaming about ~250 a week ago. Thank you all a lot for this factoring effort! Please don't hesitate to send me a PM with the donation suggestions for any of the upcoming projects. On top of that, as a result of this project, I'll probably write and share a version of the nonstandard SNFS spinner for everybody's future use. If someone wants to rewrite my Maple/msieve/cownoise GNFS spin procedure into one piece of Python/Magma/SageMath/PARI/GP/etc code, please let me know. And these huge GCD factors and swishzzz's Python script are pure genius! I bet we'll get more record level rank 6 Z2xZ6 elliptic curves just because of that p26 that was already posted before, and was noticed after midnight. Quote:
I am still planning to add more factorable lines to the sheet, just need some sleep and rest. 

20210611, 22:37  #222 
(loop (#_fork))
Feb 2006
Cambridge, England
7^{2}×131 Posts 
Code:
x^4  96*x^3 + 2232*x^2  17280*x + 32400 x^4  24*x^3 + 288*x^2  4320*x + 32400 x^4 + 192*x^3  5544*x^2 + 34560*x + 32400 
20210612, 01:06  #223  
"Max"
Jun 2016
Toronto
893_{10} Posts 
Quote:
With GNFS polys, I can predict how high the E score will be just by looking at the log(c1*c2*...*c6*Y1*Y0), or simply the length of the string listing all signless coefficients  in general, the lower the log/length, the higher the E score. With SNFS polys, especially when some of the Ci=0, the log measure is useless, it will most probably return negative infinity. Then you are stuck with the sum c1+c2+...+c6. You can't even include Y0+Y1 into it as they are huge and will definitely sway your estimate. Which is why I need Shi Bai's paper to implement the proper calculation of the E score with the precalculated value of skew, take 10 best and run them through cownoise to optimize the skew and E. If swishzzz steps in with his impressive Python skills, the last step could be automated as well. His script will send any number of polys we want (not just our best 10) to cownoise, receive the cownoise rating, and output the best. 

20210612, 02:06  #224  
"Ben"
Feb 2007
2^{2}·3·293 Posts 
Quote:
This thread led me to improve yafu's ability to work with snfs polynomials, so I thank you for that opportunity. 

20210612, 02:09  #225 
"Max"
Jun 2016
Toronto
19·47 Posts 
L^2norm in Shi Bai's paper
Found the paper: https://hal.inria.fr/hal01089507/fi...t20140905.pdf
I was wrong. How could I forget? The whole point of writing that paper was to introduce the L^2norm as an alternative (and better) predictor of how good the GNFS poly is after the size and root optimization. Formula (2.2) on page 2, where d is a poly degree (d = 4 for us now), s is the skew (could be taken as a standard estimate from c0 and c4 for each poly during the spin). We can drop (1/2)log and pi/7168, and set c5=c6=0. Nine simple terms before simplification (it will simplify when s is given explicitly, and all ci~=ci*s^(i2) are set). The lower the L^2norm, the better the poly. Will code and report the results during the weekend. 
20210612, 02:33  #226  
"Max"
Jun 2016
Toronto
19·47 Posts 
Quote:
Anybody who has input on the topic or preferences for the numbers/polys to spin, please share in this thread. Now I need to ask swishzzz nicely to rewrite my final product (a page of Maple code) into something free and readily available to everybody. If not, I start thinking about Magma Calculator. The code and the output are short and fast, should be no problem. Maybe fivemack will help there. 

20210612, 03:25  #227  
Romulan Interpreter
Jun 2011
Thailand
9631_{10} Posts 
Quote:
Edit, PS: till then, you can donate me a poly for aliquot 814848 C156, this is freaking unlucky, it takes my yafu about 16 hours to get a poly, in theory, but after about 24 hours, 10 of 18 cores are still searching and I can't stop it because there is no way to resume. In this munsoonic season here the electricity stops few times per week for few minutes (or more, depending on the damage caused by rain, lightning, etc) and I am already at the forth or fifth tentative, which means I already spent over 5 days for this f'king poly and I still have no result. Sorry for hacking the thread, you don't need to answer here, if you decide to spin a poly for me than send me a PM. If not, no problem. My GPUs are now busy doing P1 in 35M, and anyhow, I never managed to run poly selection on GPU. Last fiddled with by LaurV on 20210612 at 03:35 

20210612, 03:39  #228  
"Max"
Jun 2016
Toronto
19×47 Posts 
Anyone is good at patterns?
Quote:
Let's compare what we see please. The level of math is pretty high to write a paper like that, I definitely miss something (most probably a lot), and have too many question so far. Code:
polinomi:=[ x  4, 2*x  7, x, x^2  12*x + 28, x^2  6*x + 7, x^4  24*x^3 + 152*x^2  336*x + 196, 2*x^4  30*x^3 + 169*x^2  420*x + 196*2, x^4  12*x^3 + 62*x^2  168*x + 196, x^4  6*x^3 + 17*x^2  84*x + 196 ]; We know that two GCDs for pairs of point (n1,m), (n,m) and (n,m), (n+1,m) always split the number generated by x^4  24*x^3 + 152*x^2  336*x + 196, where x=a. This means that the value of a produced by the Magma script always has the form of a = a(z) for some z that depends on point coordinates (n,m), and if we sub a(z) into a^4  24*a^3 + 152*a^2  336*a + 196, we would always be able to factor it in terms of z, most probably very close to (a^2+...)(a^2+...), as the factors are always roughly the same size. Question. What is the explicit formula for a(z)? (I know it's out there somewhere). Can it be obtained somehow? My ballpark suggestion is that a(z) is not more complex than Code:
Any ideas are welcome here. 

20210612, 04:42  #229 
"Max"
Jun 2016
Toronto
893_{10} Posts 

20210612, 05:38  #230 
Aug 2020
2^{2}×3×5^{2} Posts 
Quick update to the c165:
Initial relations wanted was 17032060, after filtering cado decided it needs 17820319. ETA is about 34 hours. I hope this won't repeat too often... :D There were about 10e6 unique relations if that's any indication. 
20210612, 05:50  #231  
"Max"
Jun 2016
Toronto
37D_{16} Posts 
Quote:
If it fails at the last stages, please post the error message in the thread. Some of us have experience resolving at least some of the common problems. 

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