20220409, 15:52  #2179  
"Curtis"
Feb 2005
Riverside, CA
2×2,689 Posts 
Quote:
Can you post the correct poly? I'm too lazy to solve it myself. 

20220409, 15:57  #2180  
Apr 2020
3^{2}·89 Posts 
Quote:


20220409, 15:59  #2181 
Apr 2020
3^{2}·89 Posts 
Octics are 4x^8  4x^6 + 2x^4  2x^2 + 1 and 4x^8 + 4x^6 + 2x^4 + 2x^2 + 1 for L/M respectively with rational poly x2^112.
Last fiddled with by charybdis on 20220409 at 16:05 
20220409, 19:25  #2182 
May 2009
Russia, Moscow
2794_{10} Posts 
Hi guys, please help with the poly for this number, it's coming from aliquot sequence 785232:i11564 and has been extensively pretesting with ECM.
Code:
352877742600973079835183371695411433700853057958818602576415399270295381830689655616389775032026933352863953179853062837564251029973458211102638237510254736154595759284806157937293481849369639 Code:
# norm 6.924663e19 alpha 8.346006 e 1.189e14 rroots 5 skew: 674203189.34 c0: 12156751162560026744092104233803184753091159062565 c1: 72189372820466863675203441698166602254409 c2: 414382659223223227257288010313925 c3: 1294095825076902904381917 c4: 1100937170066360 c5: 244524 Y0: 17055346886074176922358825954465247094 Y1: 81657367824113953559 
20220411, 04:57  #2183 
Apr 2010
2^{2}·3·19 Posts 
785232:i11564
Here you go:
Code:
# norm 1.240318e18 alpha 7.532287 e 1.760e14 rroots 5 skew: 11166512.66 c0: 44549465986335687101170388652004286183559000 c1: 1859383291756161743996868361630553379 c2: 2480181312007428947856509788106 c3: 32775893275167804691699 c4: 27296412874693386 c5: 158760000 Y0: 5365159453367507252900879330459589554 Y1: 216465220778528055553 
20220411, 08:14  #2184 
May 2009
Russia, Moscow
101011101010_{2} Posts 
Thank you, very good poly!

20220411, 19:40  #2185  
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
2^{3}·7·107 Posts 
Quote:
Are there any slightly larger candidates with the same algebraic polynomials that would be best as snfs? I wonder whether there is any sense in attempting a nfs factory approach to factoring them. I have been wondering for a while if it would be worth creating some forum datasets for common snfs algebraic polynomials (e.g. x^6+x^5+x^4+x^3+x^2+x+1). Octics may be good candidates as the rational side would be easier to factor. Last fiddled with by henryzz on 20220411 at 19:42 

20220411, 20:57  #2186  
Apr 2020
1100100001_{2} Posts 
Quote:
Code:
221 2 2634 L 264.2 0.83 /3 254 2 2658 M 266.6 0.95 /3 204 2 2694 L 270.2 0.75 /3 204 2 2694 M 270.2 0.75 /3 241 2 2706 M 271.5 0.88 /3 241 2 2742 L 275.1 0.87 /3 261 2 2766 M 277.5 0.94 /3 224 2 2778 M 278.7 0.8 /3 276 2 2778 L 278.7 0.99 /3 281 2 2802 L 281.1 0.99 /3 Two obstacles that immediately stand out: Greg would need to get the batch smoothness step set up on NFS@Home, and the disk space requirements would be rather large. 

20220412, 10:03  #2187  
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
2^{3}·7·107 Posts 
Quote:
The most critical thing for disk space is the proportion of relations smooth on the algebraic side that are smooth on the rational side. An octic means the rational side isn't actually that big which might make this possible. Will attempt to get some numbers when I have a chance. Maybe some form of proof of concept polynomial where candidate factorisations are smaller might be better than this one. The degree halved polynomials for x^171 or x^191 might be good candidates as the OPN project has lots of candidates and alternative polynomials aren't amazing. I am unsure what the best size ratio between the common/unique polys is. I suspect that very difficult common polynomials may be the best candidates. 

20220412, 11:57  #2188  
Apr 2020
3^{2}·89 Posts 
Quote:
If there are some smaller OPN composites with the x^171 reciprocal octic then they may be more reasonable candidates for a forum effort. Quote:


20220412, 13:06  #2189  
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
2^{3}×7×107 Posts 
Quote:
The method currently available to the forum involves using the normal sieve routines with a polynomial on one side that is trivially smooth for every a/b pair and then running the code from https://mersenneforum.org/showthread.php?t=24729 on the results. As far as I am aware Kleinjung's factory code isn't available to the forum. Your numbers suggest to me that an octic polynomial may be hard enough that many(10s if not 100s) factorisations need to be enabled in order to be faster. This may not completely exclude the x^171 reciprocal octic. The sextic for x^71 would also be a good candidate(for lots of smaller snfs at least). 

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