20050414, 15:15  #1 
Nov 2003
2^{2}×5×373 Posts 
What's next?
Hi,
What's next after 11,212+? May I suggest 7,253 and 11,217? (both easy) 7,253 has been among the first 5 holes in any table for the longest period of time. It first appeared as a 5th hole back in July '98. For a more ambitious project 2,719+ and 2,736+ would be nice. Along with my doing 2,737+ and 2,749+ it would finish all base 2 numbers to 750 bits. 
20050414, 16:36  #2  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2·7^{2}·109 Posts 
Quote:
I thought Jens Franke was going to do 7,253 but perhaps I misremembered. Sam is well overdue his normal schedule for reminding us who is doing what, so perhaps we should ask him for an update. We don't want to do anything too easy or sieving takes too little time and administrative costs outweigh computational cost. Perhaps a more significant benchmark would be to clear the base 2 tables to 768 bits. Paul 

20050414, 17:49  #3  
Nov 2003
2^{2}×5×373 Posts 
Quote:


20050414, 21:36  #4 
Jul 2003
So Cal
2·3·349 Posts 
If you're ever up for a change of pace, the 151 digit cofactor of the 200 digit number 100^99+99^100 is still up for grabs. ECM is complete at the 50 digit level, plus 400 curves at B1=100M. Plus, it'd be interesting to see whether SNFS or GNFS would be better here. Based on GGNFS experience, it seems that the linear SNFS polynomial, 99^20 x  100^20 would make things difficult.
Greg 
20050415, 09:07  #5  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2×7^{2}×109 Posts 
Quote:
I seemed to have started something with the x^y+y^x primefinding project. Andrey Kulsha found lots of primes and strong pseudoprimes and began the XYYXF project to factor numbers of this type. (100,99).c151 has been one of his most wanted numbers for a long time now. I'll give it some thought. Paul 

20050424, 16:22  #6  
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
Quote:
Alex 

20050508, 20:08  #7  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2×7^{2}×109 Posts 
Quote:
There are currently six unreserved numbers in this category. I just asked Sam Wagstaff to reserve 2,751+,c221 (aka the 221digit cofactor of 2^751+1) for our next project. It has a 221digit cofactor and so there is a fair chance that we may find a record penultimate factor of well over a hundred digits. We won't start this one until the current number has finished sieving, in perhaps 23 weeks. Next in line is yet to be decided, but doing the 153digit cofactor of 2^760+1 by GNFS has some attraction. Paul 

20050509, 06:18  #8  
Apr 2004
Copenhagen, Denmark
2^{2}×29 Posts 
Quote:
Here's the polynomials a quick run with Kleinjungs tools turned up: Code:
skew: 1496831.27 norm: 4.08e+021 c5: 1860300 c4: 22190654371344 c3: 8418423029876628259 c2: 41938613797493867472132508 c1: 9910997260157184158283808947544 c0: 10607495285858568709187938891462034824 alpha: 6.86 Y1: 508011226531636067 Y0: 155820412163502072585879250581 Murphy_E 3.22e012 M: 6467723141847565045770368595275819653284432337188636474118541913625083684674764941908019832620889202048853768204112271553122703814378535845220148970745  Cheers, Jes Last fiddled with by JHansen on 20050509 at 06:19 

20050511, 18:45  #9 
Mar 2003
7×11 Posts 
One, two, three, four,
I declare a polynomial war: Code:
BEGIN POLY #skewness 338426.24 norm 2.48e+021 alpha 6.56 Murphy_E 3.24e012 X5 98172960 X4 82316491050132 X3 7016882552064350507 X2 6195174028086183212875569 X1 1253129843099006975317373181033 X0 21601946848639065371631884401124337 Y1 14056738126231207 Y0 70491898205291098614634360840 M 168917999881140384023064067094596474191250689613877026744649091136283195101878644780477580371903270124175189817678537257352051829549020009739469904899683 END POLY pol51m0b v v b 2_760P p 7 n 5e22 a 0 A 400000 and pol51opt b 2_760P n 4.3e21 N 1.07e19 e 2.8e12 v v I've actually distributed the search over a three machines and am not quite finished the entire range. I'm about three quarters done and the polynomials above are the best I've found so far. Jes, what norm bound (n) did you use for pol51m0b? Don 
20050511, 19:26  #10  
Apr 2004
Copenhagen, Denmark
2^{2}×29 Posts 
Quote:
Quote:
pol51m0b.exe b 2760P v v p 7 n 3.32E+023 a 0 A 3000 and pol51opt.exe b 2760P v v n 4.30E+021 N 1.07E+019 e 2.28E012 Quote:
Also notice, that your polynomials only score 0.62% higher than mine.  Cheers, Jes Last fiddled with by JHansen on 20050511 at 19:35 

20050511, 19:42  #11  
Mar 2003
7·11 Posts 
Quote:
Quote:
I'm willing to coordinate a search so we're not searching the same ranges. If there are others who are interested in participating, let me know. Jes, perhaps you and I can settle on some parameters to use and start dividing up the search space. I have no experience selecting parameters for a number this large so advice from you or anyone else is heartily welcome. Don 
