What's next?

[R.D. Silverman]

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.

[xilman]

Originally Posted by R.D. Silverman

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.

The simple answer is that we haven't decided yet. We try not to reserve stuff too far in advance and the current project still has a few weeks to run.

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

[R.D. Silverman]

Originally Posted by xilman

<snip>

Perhaps a more significant benchmark would be to clear the base 2 tables to 768 bits.


Paul

I am all for that!!!!

[frmky]

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

[xilman]

Originally Posted by frmky

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

That's an idea!

I seemed to have started something with the x^y+y^x prime-finding 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

[akruppa]

Originally Posted by frmky

Based on GGNFS experience, it seems that the linear SNFS polynomial, 99^20 x - 100^20 would make things difficult.

I'm curious... what would be difficult about it? From first inspection, it looks to me like the norms on both sides will be well balanced, the algebraic poly has very nice root properties, the skewness on both sides is close to 1 and even the resultant has a couple of nice small factors. I haven't actually tried sieving, but in theory this one looks like a winner to me...

Alex

[xilman]

Originally Posted by R.D. Silverman

I am all for that!!!!

"That" being clearing the base-2 tables to 768 bits.

There are currently six unreserved numbers in this category.

I just asked Sam Wagstaff to reserve 2,751+,c221 (aka the 221-digit cofactor of 2^751+1) for our next project. It has a 221-digit 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 2-3 weeks.

Next in line is yet to be decided, but doing the 153-digit cofactor of 2^760+1 by GNFS has some attraction.


Paul

[JHansen]

Originally Posted by xilman

Next in line is yet to be decided, but doing the 153-digit cofactor of 2^760+1 by GNFS has some attraction.

OK. It would be fun to see a NFSNET GNFS again, I think.

Here's the polynomials a quick run with Kleinjungs tools turned up:

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 3.22e-012
M: 6467723141847565045770368595275819653284432337188636474118541913625083684674764941908019832620889202048853768204112271553122703814378535845220148970745

I used parameters I have extrapolated from the values TK gives in his examples: p=7, n=4.3e21, N=1.07e19 and e=2.25e-12

--
Cheers,
Jes

[dleclair]

One, two, three, four,
I declare a polynomial war:

BEGIN POLY #skewness 338426.24 norm 2.48e+021 alpha -6.56 Murphy_E 3.24e-012
X5 98172960
X4 -82316491050132
X3 -7016882552064350507
X2 6195174028086183212875569
X1 -1253129843099006975317373181033
X0 -21601946848639065371631884401124337
Y1 14056738126231207
Y0 -70491898205291098614634360840
M 168917999881140384023064067094596474191250689613877026744649091136283195101878644780477580371903270124175189817678537257352051829549020009739469904899683
END POLY

I'm searching with:

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 2.8e-12 -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

[JHansen]

Originally Posted by dleclair

One, two, three, four,
I declare a polynomial war:

Originally Posted by dleclair

I'm searching with:

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 2.8e-12 -v -v

I used

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 2.28E-012

Originally Posted by dleclair

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.

Ahh, that's cheating! I just let my home PC (AMD64 3400) loose before I went to bed, and those polynomials were found when I got up 7 hours later.

Also notice, that your polynomials only score 0.62% higher than mine.

--
Cheers,
Jes

[dleclair]

I just let my home PC (AMD64 3400) loose before

AMD64 3400?! Now who is cheating? My machines are practically steam-powered by comparison. No, just kidding, but they are mere Athlon 2500's.

I will gladly do a "real" poly search if you want me to?

It's by no means certain that NFSNET will do 2^760+1 but even if we don't then we've done a small favour to whoever eventually takes it on.

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