Reserved for MF - Sequence 4788 - Page 51

Andi47 · 2009-11-23, 08:29

Quote:

Originally Posted by jrk

Code:

Using B1=43000000, B2=388112953420, polynomial Dickson(30), sigma=1033163144
Step 1 took 138254ms
Step 2 took 77893ms
********** Factor found in step 2: 314401460320696602393783174941
Found probable prime factor of 30 digits: 314401460320696602393783174941
Probable prime cofactor 8008382854566027043204017961675695251441834519040939952694150641178698834997735974059700130106717640670945550858659647 has 118 digits

Me too, but with B1=1e6:

Code:

Run 55 out of 950:
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1225682356
Step 1 took 17734ms
Step 2 took 7328ms
********** Factor found in step 2: 314401460320696602393783174941
Found probable prime factor of 30 digits: 314401460320696602393783174941
Probable prime cofactor 8008382854566027043204017961675695251441834519040939952694150641178698834997735974059700130106717640670945550858659647 has 118 digits

schickel · 2009-11-23, 10:38

Quote:

Originally Posted by Andi47

...I found this factor by ECM:

Code:

Found probable prime factor of 43 digits:

Wow! Congrats on that factor!

10metreh · 2009-11-23, 16:27

Quote:

Originally Posted by henryzz

how do you find the optimal polynomial then?
look for the highest alpha or the smallest norms?

You can't really except by test sieving, but luckily degree-4 numbers don't take too long.

10metreh · 2009-11-23, 18:06

BTW: 171 digits is a new record height for stability to be achieved. The old record was 164 in 1134 (which also holds the records for highest escapes from 2^5 * 3^2 * 7 and 2^5 * 3).

jrk · 2009-11-23, 21:44

About 1/3 of t45 done on the c142 so far. In case no factor is found, here is a decent poly:

EDIT: I'm still poly-searching, so a better poly may turn up later.

Code:

n: 2348305321333187128721643453051615911877612201981824607595341595725431644675331447201502622476698707484077353247893830745261323782457787822233
# norm 1.016167e-13 alpha -7.694154 e 1.640e-11
skew: 1981323.38
c0: -290064811140012999156642070938904104
c1:  619521716085998538893959511396
c2: -301271769660356610615830
c3: -758842805286610009
c4: -135175380936
c5:  76140
Y0: -1985312530063977010532771629
Y1:  7024691883228631
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
alambda: 2.6
rlambda: 2.6
alim: 12500000
rlim: 12500000

When ECM is finished, sieve with 13e from Q=2M to 20M.

axn · 2009-11-23, 22:38

Quote:

Originally Posted by henryzz

how do you find the optimal polynomial then?
look for the highest alpha or the smallest norms?

Why bother? Degree-4 jobs are so fast that you could pick _any_ one of them (found by msieve) and you should be fine.

jrk · 2009-11-24, 05:15

About 1/2 of t45 is done on the c142.

10metreh · 2009-11-24, 07:24

Quote:

Originally Posted by jrk

When ECM is finished, sieve with 13e from Q=2M to 20M.

Have you tested against 14e?

jrk · 2009-11-24, 08:57

Quote:

Originally Posted by 10metreh

Have you tested against 14e?

Yes

Code:

$ for i in `seq 2000000 2000000 20000000`; do ~/ggnfs/bin/gnfs-lasieve4I13e -a test.poly -f $i -c 1000; done 
Warning:  lowering FB_bound to 1999999.
total yield: 1132, q=2001037 (0.02852 sec/rel)
Warning:  lowering FB_bound to 3999999.
total yield: 2029, q=4001003 (0.02795 sec/rel)
Warning:  lowering FB_bound to 5999999.
total yield: 1257, q=6001013 (0.02944 sec/rel)
Warning:  lowering FB_bound to 7999999.
total yield: 1814, q=8001029 (0.03114 sec/rel)
Warning:  lowering FB_bound to 9999999.
total yield: 1255, q=10001009 (0.03446 sec/rel)
Warning:  lowering FB_bound to 11999999.
total yield: 1352, q=12001001 (0.03404 sec/rel)
total yield: 1213, q=14001007 (0.03523 sec/rel)
total yield: 1345, q=16001081 (0.03771 sec/rel)
total yield: 1546, q=18001031 (0.03830 sec/rel)
total yield: 1268, q=20001001 (0.04148 sec/rel)

Code:

$ for i in `seq 4000000 2000000 12000000`; do ~/ggnfs/bin/gnfs-lasieve4I14e -a test.poly -f $i -c 1000; done 
Warning:  lowering FB_bound to 3999999.
total yield: 3986, q=4001003 (0.03817 sec/rel)
Warning:  lowering FB_bound to 5999999.
total yield: 2489, q=6001013 (0.03885 sec/rel)
Warning:  lowering FB_bound to 7999999.
total yield: 3824, q=8001029 (0.03783 sec/rel)
Warning:  lowering FB_bound to 9999999.
total yield: 2675, q=10001009 (0.04045 sec/rel)
Warning:  lowering FB_bound to 11999999.
total yield: 2877, q=12001001 (0.03917 sec/rel)

14e is about 85% as fast as 13e. It would lower the duplication rate, though, so maybe it would be worth the hit. I took a guess that 13e is better.

jrk · 2009-11-24, 20:56

I stopped poly searching. The best one is still the one posted earlier. I think this number is ready for sieving.

Andi47 · 2009-11-25, 08:27

Quote:

Originally Posted by jrk

14e is about 85% as fast as 13e. It would lower the duplication rate, though, so maybe it would be worth the hit. I took a guess that 13e is better.

So - do we use 13e or 14e?

2009-11-23, 18:06	#554
10metreh Nov 2008 2322₁₀ Posts	BTW: 171 digits is a new record height for stability to be achieved. The old record was 164 in 1134 (which also holds the records for highest escapes from 2^5 * 3^2 * 7 and 2^5 * 3). Last fiddled with by 10metreh on 2009-12-26 at 11:54 Reason: correcting - 2^7 3^2 * 5?*

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2009-11-24, 05:15	#557
jrk May 2008 3×5×73 Posts	About 1/2 of t45 is done on the c142.

2009-11-24, 20:56	#560
jrk May 2008 2107₈ Posts	I stopped poly searching. The best one is still the one posted earlier. I think this number is ready for sieving.