[QUOTE=RobertS;299365]Just in case:
The log file of my script, which runs ECM on the last composites of 4788.
Factors of terms 3373-3408, so only 3372 is missing

Line 3387 was a nice shot.

A lurker[/QUOTE]
Some factors are missing, but your factors are defintely of help to close the gap. (A c99 or a c78 here and there. Not too much trouble.)

Almost there... 3404... ...It was [URL="http://factordb.com/aliquot.php?type=1&aq=4788"]all the same sequence[/URL] after all. That's a relief. My job is done here.

Gap is filled now.

jumped to i4807

trivia : i4788: C122= 6241907618...68<122> = 2^4 · 11 · 31 · 6496661 · 25322483587171<14> · 164303024281086101<18> · 17904179958078803880992339<26> ·23639945956200306806712736616774832458124891819074685667<56>

[QUOTE=firejuggler;299385]jumped to i4807[/QUOTE]
[QUOTE=Batalov;299366]I am bowing out at +1398, c112..[/QUOTE]
Well, the last I checked my abacus 3409+1398 was 4807 :ouch1:
Not a really big surprise here.

[QUOTE=firejuggler;299385]trivia : i4788: C122= 6241907618...68<122> = 2^4 · 11 · 31 · 6496661 · 25322483587171<14> · 164303024281086101<18> · 17904179958078803880992339<26> ·23639945956200306806712736616774832458124891819074685667<56>[/QUOTE]

the thing that I find interesting is that 2^4 has persisted since 4318 according to the find function in my browser ( and yes I checked for gaps beforehand in the range I looked at.

[QUOTE=Batalov;299389]That's is [B]very[/B] interesting! This is called a 2^4*31 driver, ...man.[/QUOTE]

doh didn't look for other commonalities. not all 490 have 31^1 though some are raised higher.still seems interestingly long for one thing to persist since that's over 10% of the length of the sequences for 2^4 in a row. doh 496 a perfect number.

I put an .elf file with the last 2307 iterations in the first posting of the thread. I'll try to update it every once in a while.

C112?
 

Seems no one's doing it. I'll do it, shouldn't take more than an hour or two.

Close Lines
 

[URL="http://factordb.com/index.php?id=1100000000508881663"]Line 4824[/URL]
[URL="http://factordb.com/index.php?id=1100000000508882727"]Line 4825[/URL]

Unfortunately, "bc - An arbitrary precision calculator language" returned 0 for (large-small)/small, and I have not the slightest clue to pari/gp. (Anybody who cares can surely figure it out on their own.)

Edit: 4826 is pretty close as well, though not quite as close as the first two.

C122
 

I'll have NFS on the C122 (line 4826) done in 12-13 hours.

[QUOTE=Dubslow;299298]So much happened while I was gone! So close! 33 digits... dang. How easy is it to escape 2^4*31?[/QUOTE]I think it's probably the easiest of the perfect number drivers. 2*3 is the worst, since the line has to essentially factor as 2 * 3^2 * p, 2^2 * 7 is a little easier, since you can have, essentially, 2 other factors for the eascape, and 2^6 * 127 is very hard, since the 127 doesn't get raised above 1 very often.

[URL="http://web.archive.org/web/20110717085734/http://www.lafn.org/~ax810/aliquot.htm"]Clifford[/URL] records the highest escape from 2^4 * 31 as 129 digits in 5778. I escaped it at 113 digits in 48462 via this factorization:[code] 1236 . c113 = 2^4 * 31^2 * 6188785238747719 * 230402350198068564832070130054678954206970878230960200048690011877198238894335419716602085901
1237 . c113 = 2^5 * 31 * 71 * 746231 * 144030777132837510217987539096343417010500889513 * 2902096090182134830390738125010054022390760487434126181[/code]I guess we can keep plugging away on 4788 while there's still hope. If we want another community project, we can pick up [URL="http://factordb.com/sequences.php?se=1&aq=3366&action=last20&fr=0&to=100"]3366[/URL] when Dubslow runs out of steam. (Interesting because it is >165 digits with no driver presently....)

PS. For those of you that haven't seen it yet, here's the graph (2 troughs at 33 and 35 digits):

[QUOTE=schickel;299423]
[URL="http://web.archive.org/web/20110717085734/http://www.lafn.org/%7Eax810/aliquot.htm"]Clifford[/URL] records the highest escape from 2^4 * 31 as 129 digits in 5778. I escaped it at 113 digits in 48462
[/QUOTE]
Wow! that means I can make history with 95280 (a merge from my initial reservation of 6^7=279936) which is now a C132=D4*3*7*C128, and maybe with 189140 too, but this is still small C122=D4*...*C112.

Or should I pray for 618480 (1856: C140=2^4*3^3*...*C134) to get a 31?? :razz:
(and then pray harder to lose it in few terms? hehe)

[QUOTE=schickel;299423]I think it's probably the easiest of the perfect number drivers. 2*3 is the worst, since the line has to essentially factor as 2 * 3^2 * p, 2^2 * 7 is a little easier, since you can have, essentially, 2 other factors for the eascape, and 2^6 * 127 is very hard, since the 127 doesn't get raised above 1 very often.

[URL="http://web.archive.org/web/20110717085734/http://www.lafn.org/~ax810/aliquot.htm"]Clifford[/URL] records the highest escape from 2^4 * 31 as 129 digits in 5778. I escaped it at 113 digits in 48462 via this factorization:[code] 1236 . c113 = 2^4 * 31^2 * 6188785238747719 * 230402350198068564832070130054678954206970878230960200048690011877198238894335419716602085901
1237 . c113 = 2^5 * 31 * 71 * 746231 * 144030777132837510217987539096343417010500889513 * 2902096090182134830390738125010054022390760487434126181[/code][/quote]So you're saying we basically need 31^2 and hope the rest isn't smooth?[QUOTE=schickel;299423]I guess we can keep plugging away on 4788 while there's still hope. If we want another community project, we can pick up [URL="http://factordb.com/sequences.php?se=1&aq=3366&action=last20&fr=0&to=100"]3366[/URL] when Dubslow runs out of steam. (Interesting because it is >165 digits with no driver presently....)[/QUOTE]I still see the C145 that was being finished off by CC... (though if he emailed me in the last few days I missed it. I suppose I'll check.) Edit: Wow... it really got piled in. Somehow I missed his email from two weeks ago. :doh!::ouch1::blush: I'll get right on it (after the C122 finishes, for which I'm using all four cores).

[QUOTE=Dubslow;299431]So you're saying we basically need 31^2 and hope the rest isn't smooth?[/QUOTE]

Escaping from 2^4*31 isn't very hard, see the elf file for 5778. Between line 390-973 we have 2^4*31^e, for e>0. And for 21 times e=2, for one time e=3 and for the rest e=1. So escaping it is easy but on the next line we see again 2^4*31. I would say it is hard to kill the 31 as a factor in 2^4*31.

Double Post
 

[QUOTE=R. Gerbicz;299445]Escaping from 2^4*31 isn't very hard, see the elf file for 5778. Between line 390-973 we have 2^4*31^e, for e>0. And for 21 times e=2, for one time e=3 and for the rest e=1. So escaping it is easy but on the next line we see again 2^4*31. I would say it is hard to kill the 31 as a factor in 2^4*31.[/QUOTE]

Looks like 972 and 804 were potential escapes, but the rest of them were definitely pretty darn smooth. (If my understanding of schickel is accurate.)



Edit: I have the last post, so I'll use it. That C122 split as a P59*P63, a pretty nice split. In the meantime, the C124 is almost ready for NFS; [code]sum: have completed work to t38.16[/code]That means 1224@3M. I'm bowing out here to tackle 3366, as previously noted.

From the tail of sequence 4788, it appears that 31 gets raised to the square only in 1/(2*31) iterations. (Not 1/31 that one would expect from a random process.)

From the same tail, the average gain in every 62 iterations is 10.7 digits (1.49x per iteration).

I advanced the sequence by a couple of iterations. I will not run NFS on the current c124 @ i4841, if it comes to that (so far I have run ECM 800@1M + 300@3M).

What happened to the aliquot.de page? It has not been updated since the April 1 day at all?

Does not contain information regarding the advance for the 4788 (aka 314718) sequence more than 2000 lines; nor the merge of the 345324 sequence (maybe this was being the last one as of now? 9230 open end sequences being remaining below 1000000?)

Mr. Creyaufmüller been on over a long vacation, or otherwise being suffering from a major illness, sorry?

I see that Mr. Clavier's page as well as has got no information relative to the advance for this 4788 sequence, nor since the 92[B]8[/B]2 sequence downdriver capture event at all, but this is not being worth mentioning at all; since this is being relatively a new incident.

Can the condition be given to escape (to break away) off from the 2[sup]4[/sup]*31 driver, to be needed as such?
(31 being raised to the higher even powers is being very rarer enough, though)

[COLOR=Blue]Iteration line factoring into[/COLOR] [COLOR=Red]The next subsequent line mutates into[/COLOR]
[COLOR=Blue]2[sup]4[/sup]*31[sup]2[/sup]*(1 mod 4 prime)[/COLOR] [COLOR=Red]2*31[/COLOR]
[COLOR=Blue]2[sup]4[/sup]*31[sup]2[/sup]*(3 mod 8 prime)[/COLOR] [COLOR=Red] 2[sup]2[/sup]*31[/COLOR]
[COLOR=Blue]2[sup]4[/sup]*31[sup]2[/sup]*(7 mod 16 prime)[/COLOR] [COLOR=Red]2[sup]3[/sup]*31[/COLOR]
[COLOR=Blue]2[sup]4[/sup]*31[sup]2[/sup]*(15 mod 32 prime)[/COLOR] [COLOR=Red]2[sup]>4[/sup]*31[/COLOR]
[COLOR=Blue]2[sup]4[/sup]*31[sup]2[/sup]*(1 mod 4 prime)*(1 mod 4 prime)[/COLOR] [COLOR=Red]2[sup]2[/sup]*31[/COLOR]
[COLOR=Blue]2[sup]4[/sup]*31[sup]2[/sup]*(1 mod 4 prime)*(3 mod 8 prime)[/COLOR] [COLOR=Red]2[sup]3[/sup]*31[/COLOR]
[COLOR=Blue]2[sup]4[/sup]*31[sup]2[/sup]*(1 mod 4 prime)*(7 mod 16 prime)[/COLOR] [COLOR=Red]2[sup]>4[/sup]*31[/COLOR]
[COLOR=Blue]2[sup]4[/sup]*31[sup]2[/sup]*(3 mod 8 prime)*(3 mod 8 prime)[/COLOR] [COLOR=Red]2[sup]>4[/sup]*31[/COLOR]
[COLOR=Blue]2[sup]4[/sup]*31[sup]2[/sup]*(1 mod 4 prime)*(1 mod 4 prime)*(1 mod 4 prime)[/COLOR] [COLOR=Red]2[sup]3[/sup]*31[/COLOR]
[COLOR=Blue]2[sup]4[/sup]*31[sup]2[/sup]*(1 mod 4 prime)*(1 mod 4 prime)*(3 mod 8 prime)[/COLOR] [COLOR=Red]2[sup]>4[/sup]*31[/COLOR]
[COLOR=Blue]2[sup]4[/sup]*31[sup]2[/sup]*(1 mod 4 prime)*(1 mod 4 prime)*(1 mod 4 prime)*(1 mod 4 prime)[/COLOR] [COLOR=Red] 2[sup]>4[/sup]*31[/COLOR]


Even the perfect square factoring or otherwise twice perfect square line is being very highly rare enough that they mutate into an odd number, leading furthermore into very rapid terminating finishes off, away

Does somebody continue with i5042?
Do we need some ecm on the C140?
yoyo

I am about 2/3 through sieving line 5042.

Now, a c154 in i5053...

I'll run some ECM on it.
yoyo

[QUOTE=yoyo;304827]I'll run some ECM on it.
yoyo[/QUOTE]
I have ran 4500 curves on line 5053 @ B1=8e7, B2=970297861270

And in case anyone wants to sieve, here is the best poly I've found:

[code]# sieve with ggnfs lasieve4 I14e on alg side from Q=10M to 44.25M
# est ~55M raw relations (avg. 0.075 sec/rel C2D @ 3.4GHz)
# aq4788:5053
n: 4971642585436245304199897805331756055600565137800595796541924807311330928440209616093596113532104862769676040335033925797736632789395821441130573387502777
# norm 7.319935e-15 alpha -7.656319 e 3.609e-12 rroots 5
skew: 5010876.48
c0: 38901470682692277686014924063065162624
c1: 177561617447121028456763126761848
c2: 35348168490786629838457703
c3: -14260968711721830002
c4: -1118618692636
c5: 229320
Y0: -464741779151076619911716995751
Y1: 134905220251425821
rlim: 20000000
alim: 20000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
[/code]

C154_4788_5053 was factored by someone and sequence is advanced to 5056 c143.

[QUOTE=Batalov;308168]C154_4788_5053 was factored by someone and sequence is advanced to 5056 c143.[/QUOTE]
p61 factor of line 5053 was found by yoyo@home:
[url]http://www.rechenkraft.net/yoyo/y_factors_ecm.php[/url]

[QUOTE=jrk;308177]p61 factor of line 5053 was found by yoyo@home:
[url]http://www.rechenkraft.net/yoyo/y_factors_ecm.php[/url][/QUOTE]

Dang, nice hit. Too bad it's almost done sieving in RSALS :razz:

During last night a threw 1500@11e6 at the c143 on i5056.

[QUOTE=Batalov;308168]sequence is advanced to 5056 c143.[/QUOTE]
I found a p50 via ecm:
[code]Using B1=80000000, B2=970297861270, polynomial Dickson(30), sigma=7396671262133668370
Step 1 took 257397ms
Step 2 took 132159ms
********** Factor found in step 2: 27726112512152614091012437650886401627564888513659
Found probable prime factor of 50 digits: 27726112512152614091012437650886401627564888513659
Probable prime cofactor 774400542816425749794501457746540727271775646086386521943702162057522353477124577938249738833 has 93 digits
[/code]

[QUOTE=jrk;308561]I found a p50 via ecm:[/QUOTE]Wow! I never seem to have luck like that....

Is anybody working on this one? A big, juicy C152 is waiting...

i5061
 

FWIW, I've done
500 @ 43e6
100 @ 11e7

... and counting.

i5061
 

[QUOTE=RichD;310296]FWIW, I've done
500 @ 43e6
100 @ 11e7

... and counting.[/QUOTE]

I have performed a total of
1000 @ 43e6
and 200 @ 11e7.

I'll leave the rest of the fun to others.....

Maybe yoyo can include this one in his yoyo@home ECM queue?

I queued the full number of curves for B1=43M and B1=110M.
Status can be seen here [url]http://www.rechenkraft.net/yoyo/y_status_ecm.php[/url]
yoyo

I would say the composite is ready for nfs?
yoyo

You could say that :)

Going to fire up polyselect for 24 hours or so.

edit: btw are you sure you ran ECM on the correct composite? You list it as C154_4788_i5061 but the composite is a C152 instead.

Yes it is the right one. I just named it wrong.

[code]# aq4788:5061
# sieve with gnfs-lasieve4I14e on -a side from Q=10M to 36M
n: 25305824600081944729165370824049670634810398220504258587536675413626397626006286945769087706247551951278859792156551171312969226107154263675841986864617
# norm 1.306682e-14 alpha -6.991306 e 5.153e-12 rroots 3
skew: 1816182.29
c0: 1219388919304911923615174545236121303
c1: 88391453767400538321717977839
c2: -1072262380586207133513545
c3: -2530532609701828765
c4: -124263630908
c5: 357396
Y0: -147915712018571895603313627080
Y1: 720982958857859479
rlim: 20000000
alim: 20000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5
[/code]

I started sieving, will do the postprocessing as well.

Done. Now there's a c150 waiting. I did 4000 curves @ 11e6.

I'll run 7600 @ 43e6.

So far no success: [url]http://www.rechenkraft.net/yoyo/y_status_ecm.php[/url]

Seems to be ready for sieving now ;)

Ok, I will run polynomial selection.

Where will the integer be sieved, manually here or by NFS@Home?

[QUOTE=pinhodecarlos;314322]Where will the integer be sieved, manually here or by NFS@Home?[/QUOTE]

I could do it again, will take 9-10 days.

[QUOTE=BigBrother;314399]I could do it again, will take 9-10 days.[/QUOTE]
Here's a poly:
[code]# aq4788:5067
# sieve with gnfs-lasieve4I14e on -a side from Q=8M to 29M
n: 164780106049386825191602252622167821318074147967651834674322788053096834969635651742686936605345665300498016198337069511419145901633532457378386637411
# norm 2.207132e-14 alpha -6.566319 e 7.073e-12 rroots 1
skew: 952865.00
c0: 18418205538186781961181546270270999
c1: -18216654101158808136908178822
c2: 541561846886688351812920
c3: -108828458454673618
c4: -367065283359
c5: 299880
Y0: -55974668421033828459255373120
Y1: 39193224719697509
rlim: 16000000
alim: 16000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.55
alambda: 2.55
[/code]

Started sieving...

Done. Now at line 5073 with a c149, 4000 11e6 curves done.

I'll do some curves: [url]http://www.rechenkraft.net/yoyo/y_status_ecm.php[/url]

No factor so far: [url]http://www.rechenkraft.net/yoyo/y_status_ecm.php[/url]

I've started polynomial selection.

[QUOTE=jrk;316014]I've started polynomial selection.[/QUOTE]

I can do the sieving and postprocessing again, I love this teamwork! :smile:

jfk, what do you use for poly selection?

For polynomial selection, jrk uses (and contributes to) msieve.

[QUOTE=debrouxl;316025]For polynomial selection, jrk uses (and contributes to) msieve.[/QUOTE]

I meant the hardware he uses.

[QUOTE=BigBrother;316030]I meant the hardware he uses.[/QUOTE]

Nvidia card.

[QUOTE=BigBrother;316016]I can do the sieving and postprocessing again, I love this teamwork! :smile:[/QUOTE]
Here's a poly:
[code]# aq4788:5073
# sieve with gnfs-lasieve4I14e on -a side from Q=7M to 29M
n: 29712030350422056407764987099112246876809290443496977616436205075052415484201116636430793917656509571664421538011459411836589836444181684355772841911
# norm 2.618315e-14 alpha -6.295424 e 7.663e-12 rroots 5
skew: 1166080.80
c0: 23750490127131804180671875097430105
c1: 665524504274009633437655504074
c2: 502177263538284124971913
c3: -940909512238674179
c4: -306611097123
c5: 296100
Y0: -39838125003638225433615547286
Y1: 46716866412058447
rlim: 14000000
alim: 14000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.55
alambda: 2.55
[/code]

[QUOTE=BigBrother;316016]jfk, what do you use for poly selection?[/QUOTE]
msieve on a GTX 570

[QUOTE=jrk;316139]Here's a poly:[/QUOTE]
Thanks, I have started sieving.
[QUOTE=jrk]msieve on a GTX 570[/QUOTE]
That's a bigger gun than mine :)

Now at line 5078, I'm already sieving the c133.

How does a 2^4 * 31 driver break?

[QUOTE=richs;317694]How does a 2^4 * 31 driver break?[/QUOTE]
the easiest way is when you succeed to raise 31 at ^2 :smile:

[QUOTE=LaurV;317706]the easiest way is when you succeed to raise 31 at ^2 :smile:[/QUOTE]

Or any even power. Then the sequence is effectively class 4, which means it needs to the rest (besides 2^4*31^(2n)) needs to be a product of 4 primes or less, but that's not sufficient. (There are some restrictions on what each prime has to be mod 4 or mod 8 etc. Also, and other prime raised to an even power doesn't count against that 4.)

what are you talking there? Almost any multiple of 31 would do it (look to the 3rd column after zero)

[CODE](02:56:07) gp > forstep(i=1,1000,2, a=2^4*31*i;s=sigma(a)-a;v=factorint(s); if(v[1,2]!=4, print(i", "i%31", "i\31",\t"a"
, "s", "v)))
31, 0, 1, 15376, 15407, [7, 1; 31, 1; 71, 1]
93, 0, 3, 46128, 77004, [2, 2; 3, 3; 23, 1; 31, 1]
155, 0, 5, 76880, 107818, [2, 1; 31, 1; 37, 1; 47, 1]
217, 0, 7, 107632, 138632, [2, 3; 13, 1; 31, 1; 43, 1]
279, 0, 9, 138384, 261795, [3, 1; 5, 1; 31, 1; 563, 1]
341, 0, 11, 169136, 200260, [2, 2; 5, 1; 17, 1; 19, 1; 31, 1]
403, 0, 13, 199888, 231074, [2, 1; 31, 1; 3727, 1]
465, 0, 15, 230640, 508152, [2, 3; 3, 1; 31, 1; 683, 1]
527, 0, 17, 261392, 292702, [2, 1; 31, 1; 4721, 1]
589, 0, 19, 292144, 323516, [2, 2; 31, 1; 2609, 1]
713, 0, 23, 353648, 385144, [2, 3; 31, 1; 1553, 1]
775, 0, 25, 384400, 569873, [31, 2; 593, 1]
837, 0, 27, 415152, 816168, [2, 3; 3, 1; 31, 1; 1097, 1]
899, 0, 29, 445904, 477586, [2, 1; 31, 1; 7703, 1][/CODE](in fact i said "the easiest way" as a joke, there is no other way, and I was expected the question "what is the harder way?" from some nitpicker and I could reply "raising 31 at 4th power", hehe)

[QUOTE=BigBrother;317691]Now at line 5078, I'm already sieving the c133.[/QUOTE]
found by ECM:
prp44 = 23684003947956653714782183866686101195981013 (curve 1 stg2 B1=46000000 sigma=3481469303)

[QUOTE=RobertS;317749]found by ECM:
prp44 = 23684003947956653714782183866686101195981013 (curve 1 stg2 B1=46000000 sigma=3481469303)[/QUOTE]

Meh, I did 1000 curves @ 11M...:cry:

[QUOTE=Dubslow;317734]Or any even power. Then the sequence is effectively class 4, which means it needs to the rest (besides 2^4*31^(2n)) needs to be a product of 4 primes or less, but that's not sufficient. (There are some restrictions on what each prime has to be mod 4 or mod 8 etc. Also, [STRIKE]and[/STRIKE] an other prime raised to an even power doesn't count against that 4.)[/QUOTE]

[QUOTE=LaurV;317741]what are you talking there? Almost any multiple of 31 would do it (look to the 3rd column after zero)

[CODE](02:56:07) gp > forstep(i=1,1000,2, a=2^4*31*i;s=sigma(a)-a;v=factorint(s); if(v[1,2]!=4, print(i", "i%31", "i\31",\t"a"
, "s", "v)))
31, 0, 1, 15376, 15407, [7, 1; 31, 1; 71, 1]
93, 0, 3, 46128, 77004, [2, 2; 3, 3; 23, 1; 31, 1]
155, 0, 5, 76880, 107818, [2, 1; 31, 1; 37, 1; 47, 1]
217, 0, 7, 107632, 138632, [2, 3; 13, 1; 31, 1; 43, 1]
279, 0, 9, 138384, 261795, [3, 1; 5, 1; 31, 1; 563, 1]
341, 0, 11, 169136, 200260, [2, 2; 5, 1; 17, 1; 19, 1; 31, 1]
403, 0, 13, 199888, 231074, [2, 1; 31, 1; 3727, 1]
465, 0, 15, 230640, 508152, [2, 3; 3, 1; 31, 1; 683, 1]
527, 0, 17, 261392, 292702, [2, 1; 31, 1; 4721, 1]
589, 0, 19, 292144, 323516, [2, 2; 31, 1; 2609, 1]
713, 0, 23, 353648, 385144, [2, 3; 31, 1; 1553, 1]
775, 0, 25, 384400, 569873, [31, 2; 593, 1]
837, 0, 27, 415152, 816168, [2, 3; 3, 1; 31, 1; 1097, 1]
899, 0, 29, 445904, 477586, [2, 1; 31, 1; 7703, 1][/CODE](in fact i said "the easiest way" as a joke, there is no other way, and I was expected the question "what is the harder way?" from some nitpicker and I could reply "raising 31 at 4th power", hehe)[/QUOTE]

As far as I can tell, every example there has 31^2, which does not contradict what I said. (None of these small multipliers has more than four odd-powered prime factors.)
[code]>>> for i in range(1,1000,2):
... n = 2**4*31*i
... s = a.aliquot(n)
... v = a.factor(s)
... if v[2] != 4:
... print("{}, {}, {}, \t{}={}, \t{}, {}".format(i, i%31, i//31, n, a.factor(n), s, v))
...
31, 0, 1, 15376=2^4 * 31^2, 15407, 7 * 31 * 71
93, 0, 3, 46128=2^4 * 3 * 31^2, 77004, 2^2 * 3^3 * 23 * 31
155, 0, 5, 76880=2^4 * 5 * 31^2, 107818, 2 * 31 * 37 * 47
217, 0, 7, 107632=2^4 * 7 * 31^2, 138632, 2^3 * 13 * 31 * 43
279, 0, 9, 138384=2^4 * 3^2 * 31^2, 261795, 3 * 5 * 31 * 563
341, 0, 11, 169136=2^4 * 11 * 31^2, 200260, 2^2 * 5 * 17 * 19 * 31
403, 0, 13, 199888=2^4 * 13 * 31^2, 231074, 2 * 31 * 3727
465, 0, 15, 230640=2^4 * 3 * 5 * 31^2, 508152, 2^3 * 3 * 31 * 683
527, 0, 17, 261392=2^4 * 17 * 31^2, 292702, 2 * 31 * 4721
589, 0, 19, 292144=2^4 * 19 * 31^2, 323516, 2^2 * 31 * 2609
713, 0, 23, 353648=2^4 * 23 * 31^2, 385144, 2^3 * 31 * 1553
775, 0, 25, 384400=2^4 * 5^2 * 31^2, 569873, 31^2 * 593
837, 0, 27, 415152=2^4 * 3^3 * 31^2, 816168, 2^3 * 3 * 31 * 1097
899, 0, 29, 445904=2^4 * 29 * 31^2, 477586, 2 * 31 * 7703[/code]

[QUOTE=richs;317694]How does a 2^4 * 31 driver break?[/QUOTE][QUOTE=Batalov;317969]Because of my avatar, I will reserve 804588.[/QUOTE]Most elegant is this way....... (from 804588):[code] 1947 . c114 = 2^4 * 31^2 * 9218757242216532814830455218507779571072152947622474831189587924445638638177013241155356122322458800614403093
1948 . c114 = 2 * 31 * 1217 * 4679[/code](2^4 * 31 ran from i1643:c64...)

It's good to see that there is still some life in a lot of these sequences!

[QUOTE=Dubslow;317764](None of these small multipliers has more than four odd-powered prime factors.)[/QUOTE]
Hmmm... That is what I missed in your first post, or at least, sounded very complicate as you said it... So, you say that having 5 or more primes different of 2 or 31 in the list, all at odd powers, will make impossible to kill a 2, or breed a new 2. Now, I did not know this, and after a couple of unsuccessful attempts to get a counterexample with pari/gp, I swore I would take the pencil (but not yet). I took gp and did "select 5 random primes, do their product, times 2^4, times an even random power of 31, factor its sigma minus itself, and if the power of 2 is not 4, then print it; repeat forever". When I use 4 primes, it murders few drivers every second (i.e. printing lines), but with 5 or more primes, it prints nothing after 15 minutes. Now I must take the pencil to understand why... And thanks for teaching me something new.

[QUOTE=LaurV;317985]Hmmm... That is what I missed in your first post, or at least, sounded very complicate as you said it... So, you say that having 5 or more primes different of 2 or 31 in the list, all at odd powers, will make impossible to kill a 2, or breed a new 2. Now, I did not know this, and after a couple of unsuccessful attempts to get a counterexample with pari/gp, I swore I would take the pencil (but not yet). I took gp and did "select 5 random primes, do their product, times 2^4, times an even random power of 31, factor its sigma minus itself, and if the power of 2 is not 4, then print it; repeat forever". When I use 4 primes, it murders few drivers every second (i.e. printing lines), but with 5 or more primes, it prints nothing after 15 minutes. Now I must take the pencil to understand why... And thanks for teaching me something new.[/QUOTE]

Don't think I'm any sort of genius. If you figure out why, please tell me. :razz:

I was guessing/extrapolating from [URL="http://dubslow.tk/aliquot/analysis.html"]what Clifford wrote[/URL].
[quote=Mr. Stern] Let a change in the exponent a be termed a mutation. This occurs only when the 2s count of t is equal to or less than the class of 2^a*v. In the former case, the exponent a increases and in the latter, a is reduced to the 2s count of t. The stability of a guide depends upon its class: the smaller the class, the more stable the guide. For example, a [B]class 2[/B] guide will mutate if t is the product of [B]two primes[/B] of the form 4n+1 or is a prime of the form 8n+3 or 4n+1. But a [B]class 1[/B] guide mutates only when t is [B]a prime[/B] of the form 4n+1.[/quote]

Simply extrapolate that a class n driver might be broken if it factors into n or less odd-powered primes.

(From another part of what he said, and some numerology on my part, I'm fairly sure that when v in a perfect-driver is raised to an odd power, the overall class is raised to the power of 2. That is, 2^[B]1[/B] * 3^2 is class [B]1[/B], 2^[B]2[/B] * 7^2 is class [B]2[/B], and 2^[B]4[/B] * 31^2 is class [B]4[/B], and class 4 means what it does as above. (Edit: This can easily be proven. For a perfect driver, v=2^p-1, v prime. Thus 2s_count(v) = pow_of_2(sigma(v)) = pow_of_2(2^p) = p. Thus p + (-1) = p-1 = power of two in the driver, as in the example below. (The only part I don't understand is how you can just add the two separate 2s counts to get the class.))
[quote=Stern, Clifford]When the class of a driver is zero or -1, a small 2s count of t is not sufficient in itself to effect a change in the exponent a because the 2s count of t is always greater than zero. Help is required from one of the components of v by having its exponent aquire an even power in order to temporarily raise the driver's class above zero. For example, when the 2^2 · 7 driver takes the form 2^2 · 7^2, its class of -1 temporarily increases by 3 (the 2s count of 7) so a mutation will occur when the 2s count of t is 2 or 1.[/quote]

[QUOTE=LaurV;317985]So, you say that having 5 or more primes different of 2 or 31 in the list, all at odd powers, will make impossible to kill a 2, or breed a new 2. Now, I did not know this, and after a couple of unsuccessful attempts to get a counterexample with pari/gp, I swore I would take the pencil (but not yet) ... I must take the pencil to understand why... And thanks for teaching me something new.[/QUOTE]

The next aliquot value is σ(N)-N.

σ(p^a*q^b*s^c)=σ(p^a)*σ(q^b)*σ(s^c)

σ(p)=p+1, so 2|σ(p)

With 5 or more distinct primes at odd powers,

2^4||N and 2^5|σ(N), so 2^4||σ(N)-N

Of course sometime 4|p+1, so you can get to 2^5 with fewer than five distinct primes

BTW: Is somebody working on the remaining C137?

not me

[QUOTE=yoyo;318307]BTW: Is somebody working on the remaining C137?[/QUOTE]

I have, there's now a c157...I've done 4500 curves @ 11M.

[QUOTE=BigBrother;318454]I have, there's now a c157...I've done 4500 curves @ 11M.[/QUOTE]
I'll run 7600 curves @ 43M.
Is this sufficient or is there more ecm work needed afterwards before sieving?
yoyo

7600 curves @ 43M and
18000 curves @ 110M are nearly finished.
--> [url]http://www.rechenkraft.net/yoyo/y_status_ecm.php[/url]

So it's ready for poly selection and sieving.

I'll do some polynomial selection on line 5090 then.

[QUOTE=jrk;318972]I'll do some polynomial selection on line 5090 then.[/QUOTE]
[code]# aq4788:5090
# sieve with gnfs-lasieve4I14e on -a side from Q=14M to 52M
n: 8374327569413539810901920945263678454893759704694555600405639071317862735095308914776912141767260025721657158537572439908820353807769081049095605313290020819
# norm 4.445289e-15 alpha -8.003400 e 2.765e-12 rroots 3
skew: 4637906.71
c0: -54793648072112317736444227992754082925
c1: -56691314237249339434200660853380
c2: 10438564799147159280451246
c3: -10825871566381031957
c4: 240685011582
c5: 251160
Y0: -2016507505028946018191325948896
Y1: 1244363122820723777
rlim: 28000000
alim: 28000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.5
alambda: 2.5[/code]

Thanks jrk, I'll start sieving + postprocessing.

Done. Now a c142, i did 2500 curves @ 11M.

I'm on the way to run the remaining 2000 curves @ 11M and all 7600 curves @ 43M
[url]http://www.rechenkraft.net/yoyo/y_status_ecm.php[/url]
Than it should be ready for poly selection.

yoyo

[QUOTE=yoyo;321190]I'm on the way to run the remaining 2000 curves @ 11M and all 7600 curves @ 43M
[url]http://www.rechenkraft.net/yoyo/y_status_ecm.php[/url]
Than it should be ready for poly selection.

yoyo[/QUOTE]Thanks for the curves on this!

I tested this with 13e and 14e, and 13e was faster:
[code]# aq4788:5092
# sieve with gnfs-lasieve4I13e on -a side from Q=5M to 28M
n: 3238114994632594078561692035793248345252367607175839279854296540202819610802094946260134433670226031546620607092618552912026260669563166921097
# norm 1.386546e-13 alpha -7.579466 e 1.996e-11 rroots 5
skew: 563159.26
c0: -5882998195968185728055243874372032
c1: 89466041702508339671293834568
c2: 130871500078342131868742
c3: -711520983095349071
c4: -474398782818
c5: 720720
Y0: -1350539687452470269709112005
Y1: 52254842350198729
rlim: 7500000
alim: 15000000
lpbr: 28
lpba: 28
mfbr: 56
mfba: 56
rlambda: 2.5
alambda: 2.5
[/code]

I'll start sieving again :)

c157....I did 4000 curves @ 11M.

I'll run 7800 curves @ 43M.

I've started polynomial selection.

Apparently yoyo@home found the p47 diving c157 and is running the needed curves for the c130 two iterations ahead.

[QUOTE=rajula;321961]Apparently yoyo@home found the p47 diving c157 and is running the needed curves for the c130 two iterations ahead.[/QUOTE]

factordb now has a c160.

i5106
 

Now a c134 remains at index 5106. Still with the driver.
(Not me.)

... and is somebody working on it?

If no one is in a hurry, I'll put my antique machines on it. I estimate it would take me about a week...

Hmm... a little off on my estimate. Now there's a c139. I am working on it, but this one probably will take a week for me. My feelings will not be hurt if someone beats me to the factors...

Now a c151 on line 5113.

A c139 in i5119...

The i5109 c139 broke down to a c116 (via ECM) that was relatively quick to finish a little after 1:00 AM. I didn't wait up.:smile: I told the system to go ahead and submit, in case no one else posted the factors.

I am currently running curves on the new c139 (only at 1290@3M so far). I'll plod along with this one unless someone else gets impatient...

I'm getting a really poor relations ratio. I'm seeing less than 85k relations per 100k q. Is this a sign of a poor polynomial, or does this just happen sometimes?

I had one machine working the polynomial while my main one is running the ECM and now that I have a candidate, I have several machines running with it while the main one finishes ECM. At this point, would a restart with a better poly make a big enough difference to warrant running a few more hours of selection?

Here's a bit of the log:
[code]
Sat Dec 29 10:27:50 2012 expecting poly E from 2.16e-11 to > 2.49e-11
Sat Dec 29 10:27:50 2012 searching leading coefficients from 1 to 2846669
Sat Dec 29 15:27:48 2012 polynomial selection complete
Sat Dec 29 15:27:48 2012 R0: -1728427528919286628495180538
Sat Dec 29 15:27:48 2012 R1: 30361745983217
Sat Dec 29 15:27:48 2012 A0: 27794688864805293268138545836950245
Sat Dec 29 15:27:48 2012 A1: 41756348327044212147658721274
Sat Dec 29 15:27:48 2012 A2: -54605224849948984856272
Sat Dec 29 15:27:48 2012 A3: -24857135575026902
Sat Dec 29 15:27:48 2012 A4: 5603890979
Sat Dec 29 15:27:48 2012 A5: 276
Sat Dec 29 15:27:48 2012 skew 3199130.95, size 2.219e-13, alpha -5.811, combined = 2.596e-11 rroots = 5
[/code]

I'll run some GPU stage 1. Do you know how many hits you got in those five hours?

Edit: Perhaps the ggnfs parameters are off?

Edit2: YAFU (it's probably msieve's data) suggests around 50 CPU hours of poly select, so unless you were running 8 cores or something, that's probably a woefully bad poly. How many core hours total did you run?