[QUOTE=jyb;395120]Okay, thanks. For future reference for everyone listening, all Homogeneous Cunninghams in the current range have received a full t50's worth of ECM, in addition to several hundred curves at B1=110M.[/QUOTE]

Good to know :smile:

A Factoring Challenge
 

I would be curious to know whether we (writ large) can reduce the number of composites to less than 100 by the end of this year. So far there have been 17 factorizations in the first 41 days of this year. At that rate, we would just make it. Of course, the numbers will become more difficult, but that could possibly be made up for by having more people involved (versus just the two who have contributed so far this year).

So consider this a challenge/request to all with available sievers: come try your hand at factoring some Homogeneous Cunningham numbers and we'll see how far we can get.

Note: I make no claims about the real-world merits of attempting to achieve this goal. The value of these factorizations is highly subjective, and has been much discussed earlier in this thread and elsewhere.

I removed four and will remove four more.

(I've removed all last canidates with "tricky" polynomials. For the rest, we can write a simple auto-snfs-poly-generation CGI script, except for the few GNFS numbers.)

Here is a little script "snfspolyHC.pl" for the remaining homogeneous Cunningham numbers (takes care of 4s, 8s and 9s; all snfs difficulties are in 220..250, so we will use sextics):
give it something like "9^244+8^244" or "5^326+4^326" on input:
[CODE]#!/usr/bin/perl -w

use Math::BigInt;

while(<>) {
next unless /^\s*(\d+)\^(\d+)([+-])(\d+)\^(\d+)/ && $1 && $2 && $4 && $2==$5;
$a = $1;
$n = $2;
$s = $3;
$b = $4;
print "#============================\n";
print "# $a^$n $s $b^$n snfs poly\n";
print "#============================\n";
die "This is a difference of cubes! take care of algebraic factors" if($n % 3 == 0);
$s = '' if $s eq '+';
$nb = $n;
if($a==4) {$a=2; $n*=2;}
if($a==8) {$a=2; $n*=3;}
if($a==9) {$a=3; $n*=2;}
if($b==4) {$b=2; $nb*=2;}
if($b==8) {$b=2; $nb*=3;}
if($b==9) {$b=3; $nb*=2;}
$N = int(($n+2.5)/6);
$NB = int(($nb+2.5)/6);
$c0 = $c6 = 1;
$c6 *= $a ** ($n - 6*$N) if($n > 6*$N);
$c0 *= $a ** (6*$N - $n) if($n < 6*$N);
$c0 *= $b ** ($nb - 6*$NB) if($nb > 6*$NB);
$c6 *= $b ** (6*$NB - $nb) if($nb < 6*$NB);
print "n: \n";
print "type: snfs\n";
printf "skew: %.4f\n", exp((log($c0)-log($c6))/6);
print "lss: 1\n";
print "#lss: 0 # change to lss to 0 if -a, based on trial sieving\n";
print "c6: $c6\n";
print "c0: $s$c0\n";
print "Y1: ",Math::BigInt->new($b)->bpow($NB), "\n";
print "Y0: -", Math::BigInt->new($a)->bpow($N), "\n";
}
[/CODE]

When I tested it I got: [code]
echo &quot;9^244+8^244&quot; | snfspolyHC.pl
#============================
# 9^244 + 8^244 snfs poly
#============================
n:
type: snfs
skew: 0.6934
lss: 1
#lss: 0 # change to lss to 0 if -a, based on trial sieving
c6: 9
c0: 1
Y1: 5316911983139663491615228241121378304
Y0: -443426488243037769948249630619149892803
[/code]Should it have something after n:

Chris

No, you put n there yourself when you will reserve the number.
__________________________

If Tom would add the script right to the reservation CGI ("doreserve.pl"), then the user will have the complete poly.
It would be helpful to include "#res: <1234>" field into the poly file.

A couple of small factors for 12^227+7^227 ;-)
[CODE](12^227+7^227)/(12+7) =
p115 factor: 1376647037617242752227905564172736610842733025297380117354019799793620877182644535546373325832157740316054764882807
p130 factor: 3602190257582089888345851440271921198438294838778023735623207574893294545711578194180214570962803784134867904079057743216801146747
[/CODE]

Okay, well apparently the answer to my question is "Yes, we can get the number of composites down below 100 by the end of the year...if Serge contributes." Indeed, 9 factorizations in 4 days is quite a contribution! Thanks, Serge.

Anyone else want to get in on the action?

[QUOTE=jyb;396272]Okay, well apparently the answer to my question is "Yes, we can get the number of composites down below 100 by the end of the year...if Serge contributes." Indeed, 9 factorizations in 4 days is quite a contribution! Thanks, Serge.

Anyone else want to get in on the action?[/QUOTE]

I do what I can with the hardware I have available. One 5-yr old I7 home PC,
an I7 laptop, and 9 i5 based PC's available nights and weekends. --> i.e. not much.

Our server has been down for almost a week, so my current sieve job has been mostly stalled.

Of course help would be nice......

[QUOTE=jyb;396272]Okay, well apparently the answer to my question is "Yes, we can get the number of composites down below 100 by the end of the year...if Serge contributes." Indeed, 9 factorizations in 4 days is quite a contribution! Thanks, Serge.

Anyone else want to get in on the action?[/QUOTE]
My resources are as limited as the next guy's. :rolleyes: ...logarithmically speaking. That is to say, we factor a few more, and all we will get as a result will be an extension from Paul. The number will never be under 100!

I did try to squeeze it into the "Need For Speed" competition. These are easily automated, conveyor belt-style. There are no tricky polynomials and/or GNFS' left. Only plain sextics.

Interesting!
[QUOTE]"Homogeneous Cunninghman numbers" is [URL="http://www.leyland.vispa.com/numth/factorization/anbn/main.htm"]the term I use for those numbers[/URL]...[/QUOTE]
:orly owl: