Polynomial Request Thread

[firejuggler]

R0: -697013904459768580991097397641011
R1: 5606793472754501
A0: -1847971520796502134306506190386798968500
A1: 40821386607537415162180472039027730
A2: 65031139921790296595480109002
A3: 11389536971489005146365
A4: -2922818243778546
A5: 105066936
skew 4418742.30, size 5.992e-017, alpha -7.710, combined = 2.022e-013 rroots = 5

exact same score

[wombatman]

Hahahaha, nice!

[frmky]

Originally Posted by frmky

They aren't directly comparable. I will test this degree 5 poly and the best degree 6 I find to see which sieves better. Thanks!

For the C216, Gimeral's e 3.612e-16 degree 5 poly sieves about 15% better than a degree 6 poly with e 4.662e-16.

[VBCurtis]

Originally Posted by frmky

For the C216, Gimeral's e 3.612e-16 degree 5 poly sieves about 15% better than a degree 6 poly with e 4.662e-16.

Does this suggest that perhaps msieve's root-opt for deg 6 is rough enough that the theoretical "line" for deg 5 vs deg 6 is lower than real-world work?

Are the CADO root-opt tools better for deg 6? Perhaps someone could collect the best few hundred hits for a CADO root-opt run?

[firejuggler]

after running for the night, I got

R0: -696455968474482254849269323572607
R1: 348684257076673921
A0: 214663815990857477983089978209004516580928
A1: 177424600277632306484616564575041074
A2: -34342254092265056219064954433
A3: -8565004414637263688679
A4: 546856311911345
A5: 105488460
skew 6382404.47, size 6.264e-017, alpha -7.953, combined = 2.130e-013 rroots = 3

for the latest composite

[jasonp]

Originally Posted by VBCurtis

Does this suggest that perhaps msieve's root-opt for deg 6 is rough enough that the theoretical "line" for deg 5 vs deg 6 is lower than real-world work?

Are the CADO root-opt tools better for deg 6? Perhaps someone could collect the best few hundred hits for a CADO root-opt run?

I suspect it's less the crossover point between degree 5 and 6 than the scaling factor between degree-5 E-values and degree-6 E-values. Hopefully everyone knows but it's worth repeating: the E-value algorithm was invented to compare polynomials of like degree only.

My anecdotal experience is that the best output from the CADO root-opt tools is noticeably better than what you get with Msieve, but on average they work equivalently well. Even among same-degree polynomials, the definition of E-value would make one think that a polynomial with X percent better E-value would sieve X percent more efficiently, but experience with RSA768 shows the difference is much smaller than that. i.e. we found lots of degree-6 polynomials with half the E-value score of the one actually used for RSA768, that sieved maybe 15-20% slower.

[bdodson]

Originally Posted by bdodson

OK; 11,323+ is at 3t60 =.c 60% of a t65. That's
the same amount of ecm pretesting as 10,770M; while
gnfs 221 is a lot harder, four times at least. Probably
enough to have found a p62; but there's still lots of
space in [p63,p79] for factors in ecm-range. I'm
taking a break; pending 10,770M. -Bruce

OK, never mind the polyn search for 11,323+ C221:

Input number is 47684588221623639056961705608173079138153779302378955848869404
42648307317037627130989942393222503668627639186419734789253370
97393792502082005378750936019951281361678639264962841236093010
58482691872665246622667910987254487 (221 digits)
Using B1=400000000, B2=15892277350966, polynomial Dickson(30), sigma=4180268258
Step 1 took 3510272ms
Step 2 took 1859204ms
********** Factor found in step 2: 482632031053134403896770035981249734273506307638396123269389497006923
Found probable prime factor of 69 digits: 482632031053134403896770035981249734273506307638396123269389497006923
Probable prime cofactor 98801126227724201982197175315480431013249163755336329531650444
70656245838965370494907444192757868193236504714266221744759846
9879406843807465214724901669 has 152 digits

on one of the pc's running 8 curves on an i7. This near the end
of a new 7t55. Ah, there was another 1.8t55 of left-overs from
last weekend's count. Looks like my total curve count is c. 23.3t55*,
out of 25t55 for t65. Wow! a new highest count for me; not so
much luck, as sustained effort.

Please apply this to the account with the two p62's "not found"
for not having run enough on the NFS@Home 3+ gnfs's! -Bruce

*PS - OK, that's 127,215 curves with B1=400M, default B2, to
be precise. This p69 is just short of my previous, the current
10th-of-the-top10, 482... -vs- 563...

[frmky]

Originally Posted by bdodson

OK, never mind the polyn search for 11,323+ C221:

Damn! Here's the difference between ECM factoring and ECM pretesting.

How about 3,697+?

[wombatman]

If I might ask a slightly stupid question, does "t55" refer to running the number of curves suggested by GMP-ECM to find a factor of a given digit length? If so, does "7t55" refer to doing this 7 times? Thanks!

[xilman]

Originally Posted by wombatman

If I might ask a slightly stupid question, does "t55" refer to running the number of curves suggested by GMP-ECM to find a factor of a given digit length? If so, does "7t55" refer to doing this 7 times? Thanks!

That's how I use the term.

[lorgix]

Originally Posted by fivemack

From trial sieving it looks like firejuggler's http://www.mersenneforum.org/showpos...&postcount=169 (c5=107173200) is the best of the C178 so far, with wombatman's http://www.mersenneforum.org/showpos...&postcount=176 in second place.

I think we're ready to think about sieving that one; may I propose

4788.5154

17285154910805941577069464828335617544658066950627644021728302169526833018711670895092479561808160256160945139573800969912234390238908363042669550995167201537635764747005337

as a next polynomial-selection target? It's received an enormous amount of ECM from yoyo@home - I suspect twice as many cycles as will be required for the sieving.

Probably a little late, but I found another decent poly for the C178. I will move on to the C175 now.

R0: -11708475821133910619711215298497638
R1: 4937254133390405269
A0: -802914511260679636038420993144191107255975
A1: 374850392085650921707293481711138160
A2: 191485557559647650556457788274
A3: -14221948389865248927299
A4: -1608862500793698
A5: 20456280
skew 11155110.94, size 1.875e-017, alpha -7.644, combined = 1.030e-013 rroots = 5