playing with frmky's last upload (only half thru it)
poly is
23000623460100 -4200026754030636886542 325872963021220734540680389841 71104560237504929295111562904399389 -2515044822412759992774011178811387566386570 -214938857506910312002364866202388589245612515363 2518563929690957541751459455188308671386866572717152336 53041291506298756714237 -5115212953529178920472571451294711821103119 -2.09 5.249183e+033
[code]

Wed Jan 02 07:30:03 2013 Msieve v. 1.51 (SVN 766)
Wed Jan 02 07:30:03 2013 random seeds: 6d21a47c 93a68ff0
Wed Jan 02 07:30:03 2013 factoring 412023436986659543855531365332575948179811699844327982845455626433876445565248426198098870423161841879261420247188869492560931776375033421130982397485150944909106910269861031862704114880866970564902903653658867433731720813104105190864254793282601391257624033946373269391 (270 digits)
Wed Jan 02 07:30:05 2013 no P-1/P+1/ECM available, skipping
Wed Jan 02 07:30:05 2013 commencing number field sieve (270-digit input)
Wed Jan 02 07:30:05 2013 commencing number field sieve polynomial selection
Wed Jan 02 07:30:05 2013 polynomial degree: 6
Wed Jan 02 07:30:05 2013 max stage 1 norm: 1.08e+035
Wed Jan 02 07:30:05 2013 max stage 2 norm: 2.46e+035
Wed Jan 02 07:30:05 2013 min E-value: 0.00e+000
Wed Jan 02 07:30:05 2013 poly select deadline: 1079999
Wed Jan 02 07:41:41 2013 polynomial selection complete
Wed Jan 02 07:41:41 2013 R0: -5115212953529306844186435346484985056758031
Wed Jan 02 07:41:41 2013 R1: 53041291506298756714237
Wed Jan 02 07:41:41 2013 A0: -379896940535659287453260136796270948676592389901631962720
Wed Jan 02 07:41:41 2013 A1: -356485807960054857061300970481298628845280475487976
Wed Jan 02 07:41:41 2013 A2: -88244722381684984039807462984918078359735096
Wed Jan 02 07:41:41 2013 A3: -3323380506955608894448655022916446492
Wed Jan 02 07:41:41 2013 A4: 378527384940320290220809646801
Wed Jan 02 07:41:41 2013 A5: -4532860863907273712142
Wed Jan 02 07:41:41 2013 A6: 23000623460100
Wed Jan 02 07:41:41 2013 skew 18516337.01, size 4.775e-020, alpha -10.361, combined = 2.509e-019 rroots = 4
[/code]

11752 new stage 1 hits with norm 2e33, produced by MPI-patched CPU msieve.

poly was
[code]
23000623460100 53041291506298756714237 5115212953527564653744592445975459711681095
[/code]

40197 new stage 1 hits, most of them generated by GPU msieve on my GT540M, and the rest by MPI-patched CPU msieve.

I've run size optimization on my latest 40197 hits (a number of "line optimization failed" messages), and I'm now running root optimization in ascending order of stage 1 norm (e+33 and e+34 values, less than 1% of all size-optimized hits).
The norms, alphas and e values tend to be decreasing on average, and I haven't seen a 3e-20 norm for a while, so chances are that the best potential hits have already been found...
The best polynomial so far is better than my previous best, but still much worse than the best ones posted here:
[code]# norm 3.928016e-20 alpha -11.376284 e 2.143e-19 rroots 4
skew: 47860990.01
c0: 102243377053834035977456615540543318152506688915339403180155
c1: -6607905899690278300548521267259375978782553228004647
c2: -990115457387976288997208498176855800512746728
c3: 2374578563317318524203706157960245520
c4: 115319739334363910337347697197
c5: -3817121901056644507273
c6: 45678923690400
Y0: -4562480378270649518664783149805881289770388
Y1: 35998309767524359673137[/code]


But the above polynomial is, in fact, not the main reason why I'm writing this post. I'm writing it because, in the output, I noticed several outliers with shorter c0, very low skew, and terrible indicated e values, despite norms comparable to those of the "normal" polynomials.
Here are several examples:
[code]# norm 2.372578e-20 alpha -10.426309 e 1.964e-20 rroots 2
skew: 1197.46
c0: 18481412854226641032415109537792402344324145678149569243
c1: -412818324451811043545670157890441895685514959354757096
c2: 2456685007867823022280006789699102572790645669
c3: -66233377310249932462663890531016567923
c4: 496905266675509984230728250988
c5: -1336373776546492878581
c6: 1500024500100
Y0: -8062516096127221174983998069912229229885966
Y1: 34136309016942249143093

# norm 2.368751e-20 alpha -10.846135 e 2.245e-20 rroots 4
skew: 1377.05
c0: -2642388665373048624150808121402634764591949455367447825
c1: 438501348563241987768009661055349213982843345699856290
c2: -4693749974898874734068961081565468612650025973
c3: -186189783670734795089307249827424690087
c4: 2924675753151214297925870173078
c5: -12806778906904494395723
c6: 23456710532640
Y0: -5098500528781644024246804152176670963216164
Y1: 22196851711482804191917

# norm 3.036890e-20 alpha -11.223265 e 2.666e-20 rroots 4
skew: 1334.97
c0: -28576717055994791421425058746265638291236302755674259745
c1: 222801134536579704276697225767050208595951749040306072
c2: 1398221794954370584472235616298871514610192843
c3: -124644134602986531319500832562710506959
c4: 690941799193854044069220331794
c5: 1776275142072176247887
c6: 1900035882108
Y0: -7751040741275170619614657060899972044441224
Y1: 109564369221121497194087

# norm 2.288852e-20 alpha -10.619501 e 2.490e-20 rroots 2
skew: 1766.88
c0: 1393418822768280472160344800352078143099930198234976875
c1: 85215789369701604171965788635140830817277453757134150
c2: -368799273673517383122693984287542029297070690
c3: -73498701786682246657794324606801605568
c4: 1583577793726330690346273176767
c5: 2617296398705592280666
c6: 1800000012120
Y0: -7821227202316007911700848546218259081952266
Y1: 240333343470261878614787

# norm 2.319390e-20 alpha -10.667771 e 1.962e-20 rroots 4
skew: 1197.42
c0: -60297133975171382084881582505263853794821480445420380429
c1: 735812972956460443707231473680530061138485617982676392
c2: 5483937239726035047381552949647510651082363571
c3: -183781698612356696913135396595290025285
c4: 443631729780461087297695693254
c5: 1570418878625124677333
c6: 2300058204444
Y0: -7508108080138893173363569991159709738912898
Y1: 42471148941794878087325
[/code]
Where do these come from ?

[URL="http://dubslow.tk/random/rsa.dat.gz"]~221K[/URL] hits (~5.7MB) with a 2e33 norm. I think I'll call it quits for now and go play with mfaktc 0.20 :smile:

The 'norm' value is a numerically-computed integral that does not depend on translation and skew, so it is a more approximate measure of polynomial quality than the Murphy E score.

Usually when the low-order coefficients are extremely small it is an indication that the size optimization cannot do very much with the hit from stage 1; my experience is that you can force the skew to be small and can find a weak local optimum in the neighborhood of the original hit, but better optima are almost always very far away.

Dubslow, thanks for the contributions!

After collecting a few stage 1 hit, and meddling with the second stage, i'm left wondering why, in the first part of the second stage, we allow such a high norm.From what I seen, unless your norm is below 5e34 you won't have a final murphy score above 1e-19.
It make no sense to allow a "stage2_norm=1e100". Now, if there is a good explanation, I'm all ears.

The stage 2 norm is set deliberately too large so that all the outputs from the size optimization make it into the output file. That's really just so we can get a statistical idea of how rare it is to get a polynomial with good size. Of course, if you then ran the root optimization on everything it's a disastrously bad idea.

[quote]Of course, if you then ran the root optimization on everything it's a disastrously bad idea.[/quote]
Indeed, firejuggler, unless it's for testing purposes (e.g. the MPI patch), as ~99% of the size-optimized hits have no chance of producing a good full polynomial (whatever the size of the number to be factored, it seems - we get similar ~1% ratios for C15x-C16x and the RSA-896 C270).

Here's another 6 million hits: [url]https://www.dropbox.com/s/9j8oml7r5hthx6g/rsa896_3.dat.m.gz[/url]