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schickel 2009-04-01 09:38

Odds and ends....and class records
 
Here's one from frmky's work on 107310:[code] 2252 . 18581703700371797377652321850825180028525355869621190321756974606044266713490974614892846792090744753936 = 2^4 * 1161356481273237336103270115676573751782834741851324395109810912877766669593185913430802924505671547121
2253 . 17420347219098560041549051735148606276742521127769865926647163693166500043897788701462043867585073206846 = 2 * 17 * 149 * 1897100269 * 1884269524289 * 5425131994288234817 * 75174790826303863401398476223 * 2358716659745567955700443040801
2254 . 10432951744413565590019846813840614875510125251540906326296494942183177382064134381271886700866349513154 = 2 * 3529 * 169236756613 * 31736872533046464497816899 * 275211592572291925083265020281729907377684428069651252727802199
2255 . 5220910394151538145799072012901656482715802468271035024241639668538966600836425978710428144909677286846 = 2 * 33193471 * 7192699523 * 10933813393285077738958462467788729933831222442086241209115755049590566376323382702731
2256 . 2610455434095465894427005822362005867252891540589048781794110450759076971335266579628925103569902373442 = 2 * 747357419621 * 1222588712504620068992710308769 * 1428491153867337254665860638781079547617534609608564285013229
2257 . 1305227717052972318695395632117220401909357329889153810375673067332724990195346414785234126717422895158 = 2 * 19 * 15923 * 2157137337008320170252556930420445105738070599445941835834415405938323230208778454842274047004867
2258 . 755787580218257104770707361483689669917024843645476857253960788116986556875328872109268188752908186762 = 2 * 377893790109128552385353680741844834958512421822738428626980394058493278437664436054634094376454093381
2259 . 377893790109128552385353680741844834958512421822738428626980394058493278437664436054634094376454093384 = 2^3 * 37 * 2039 * 3011 * 455953 * 136082500257722143 * 3351411112485085600331091903891415398431341132738377959889841800750719[/code]That's two lines longer than my shortest downdriver run.....

schickel 2009-04-09 10:12

Very high downdriver capture
 
Here's a 128-digit capture by KriZp:[code] 1195 . 10266795638504310153366052072949189423898628478681852217099800647077404391348760648124591000211167976820485517782454441169150528 = 2^6 * 160418681851629846146344563639831084748416069979403940892184385110584443614824385126946734378299499637820086215350850643267977
1196 . 10106376956652680307219707509309358339150212408702448276207616261966819947733936262997644265832868477182665431567103590525882678 = 2 * 49908941 * 6547758143 * 24298326971 * 693448787987 * 993189769000280189449 * 923999020028519876669775331353117572879545168715632128589735537361[/code]Let's hope this one lives long and prospers!

schickel 2009-04-09 10:16

Highest downdriver capture by a forum member
 
'course the last one is eclipsed by this one by Syd:[code] 2056 . 21698481042403489944908436512272346022682021640623793990634921005583433910885160341613927745511041531095922992195575476423580265107408 = 2^4 * 1356155065150218121556777282017021626417626352538987124414682562848964619430322521350870484094440095693495187012223467276473766569213
2057 . 20342325977253271823351659230255324396264395288084806866220238442734469291454837820263057261416601435402427805183352009147106498538226 = 2 * 7 * 17 * 59 * 487 * 919 * 3980897791891331 * 244555074583226349879513043 * 3324830131884680161477882512115625912734604062426059861896386067775869968904223397[/code]This one, at 134-digits, even beats the 133-digit capture by Benoit Chevallier-Mames on January 12, 2007. :george:

10metreh 2009-04-09 10:25

A record escape from the 2^6*127 driver at 105 digits from mdettweiler: (Directly to the downdriver too.)

[code]3139 . 368661232821388439892752361815356635406006062108223857808358172277790639490637984231985691989806461522752 = 2^6 * 127^2 * 357141283578287207720519291547209834969238311143964150180147339688789059584674716574169287453699917
3140 . 368706589764402882368132867765383131055047155373739141255431050989931115701205237920990611489313083476850 = 2 * 5^2 * 7 * 127 * 727 * 179407 * 207343 * 375043 * 4333949743 * 16873317042146023 * 11183572559341645884295000462732180293131069659712721677[/code]

schickel 2009-04-09 10:28

[QUOTE=10metreh;168618]What about Max's record escape from 2^6*127 in 102264?[/QUOTE]I didn't see anything stopping you from posting it. Remember, I'm only one person.....

Andi47 2009-04-09 10:38

Highest escape from [TEX]2^2*7[/TEX] directly to the downdriver in sequence 10212, line 1614 at size 116 digits:

[code]1612. 38785370474647525391727329181443916934390849185581660897114550925284502383340252615211048986388530210764815685448636 = 2^2 * 7^3 * 43 * 2477 * 595166205444770363 * 730870394843509331 * 610155790201223813418973543349228234288027257651351916637494956114398311
1613. 42241931938531778334536759834756907526458417633128375418926617753803678335932963697758806186731702538054761761360964 = 2^2 * 7^2 * 215520060910876420074167142014065854726828661393512119484319478335733052734351855600810235646590319071707968170209
1614. 43750572364907913275055929828855368509546218262882960255316854102153809705073426686964477836257834771556717538552826 = 2 * 7 * 79 * 5936209 * 7391286623087 * 185270191912990598559679 * 4866243467849297246608630324183117774422146880312497220371314278668053
1615. 32199801135331560549688595686955409716520062871327183423494260976019004935368210883120882715270425788504331342599174 = 2 * 7^3 * 2417 * 13327 * 82299361929619 * 942304162489457 * 12503052685758174283 * 2263558443917277927209 * 663933640967403694022797329518432051
1616. 24153914000207088183280338138755942763257364998992514867476223766985493671096092293717251285398213860235438779640826 = 2 * 7^3 * 1621 * 930719 * 149403059685104809 * 50060231171188562340080678619524484209093 * 3120394206029073593976562041259097368195791557[/code]

*very* short downdriver run in sequence 100436 (shortest possible as one line doesn't count as downdriver run):
[code] 1203 . 1834681319396002910997320469475987377605859284586016 = 2^5 * 397 * 84048608927281 * 158857877993821 * 10816353365532749129
1204 . 1786445837604643650311728698099456764226081421272464 = 2^4 * 111652864850290228144483043631216047764130088829529
1205 . 1674792972754353422167245654468240716461951332442966 = 2 * 7 * 34607 * 58153 * 3447022708022371063 * 17244589985651779526653
1206 . 1196413029507377800174247196896589096132519069084842 = 2 * 7^2 * 12208296219463038777288236703026419348291010909029
1207 . 891205624020801830742041279320928612425243796359288 = 2^3 * 29 * 277 * 7559 * 2353399016963 * 65186843059999 * 11958874338277549
1208 . 843896032383624359452100568554385892088308203640712 = 2^3 * 277 * 16670843873 * 24129386382439997 * 946706430192449358097[/code]

10metreh 2009-04-09 10:45

Shortest possible period of instability trapped between periods of stability, sequence 130396:

[code] 1879 . 28116816113339690303988014622330170683703057977402649299472740383234225520340773727555280014805801868 = 2^2 * 103 * 13520822671 * 30888267879504915313957111 * 163407600399423280028815329888275915553466823517592666159837069
1880 . 21565324983808816563811984654667078025564581223666594594163503935282011638751318233618519130031635572 = 2^2 * 3 * 35203012220653 * 51049904594899060959312313674573733053334485011911350886121619958677792338351017804027
1881 . 28753766645079851482411303379929631445535663029414286157798338764867493590360600623011151686216205164 = 2^2 * 47 * 6596958106846515056777977291049 * 23184256256278432367374111069885062192818419904693165642579699856397[/code]

schickel 2009-04-09 10:56

Very high powers of "3" from 171018:[code] 657 . 9733273362368101690506170932124491964396727918772672927812318844771080 = 2^3 * 3^6 * 5 * 19 * 271 * 654005789 * 6486798343 * 15280463215435934267822213852908299588222731
658 . 24957188436629120479618862475684430646542940166419414638123331796124920 = 2^3 * 3^7 * 5 * 11 * 487 * 3472657 * 35657693 * 31668732727301 * 13580614504575146472146061690718397
659 . 67105318270746370819655849445462881658217796399624263621897306370505480 = 2^3 * 3^8 * 5 * 11 * 137129849 * 169512694960541962278458926658942037901019875526177795903
660 . 179951712001669532634246184168160920913268819504651792633292990950326520 = 2^3 * 3^6 * 5 * 11 * 83 * 241 * 189296739433877 * 283384017539968494521 * 522831994879017762749439127
661 . 493054716312865044614781945555177872589295322220024081153475159510488840 = 2^3 * 3^6 * 5 * 11 * 53 * 509 * 761 * 2417881811 * 30967171242852931723511308349104738711430320322477
662 . 1361755284044616845378453809650426570290557502397991799138030392955034360 = 2^3 * 3^6 * 5 * 41 * 2903 * 12289 * 240491 * 14314457471 * 9274497573571969096721825047840563284052113
663 . 3346135456735622546423167765778954747242490020844892952346678327244236040 = 2^3 * 3^6 * 5 * 37 * 17884627 * 173410099410935428379741232459438420572782901932427835590731[/code]

schickel 2009-04-09 11:01

4 primes with powers >1
 
Here's one from 199272:[code] 2095 . 2147785522605617415661440711907256925999066718859981278417040166273887305703138475537897306932055568178379687763148870119800 = 2^3 * 3^2 * 5^2 * 11^2 * 17 * 857 * 5019031 * 22779667 * 217660441 * 9124624542949 * 2980859693341733136462976890706924039328597916183558908199934985818466811719023[/code]Although this actually isn't quite that rare....

schickel 2009-04-09 11:04

How about a 4-digit prime squared?
 
Here's one from 110432:[code] 1613 . 883866359463668463521525972362866107318450543014047075048557464839182863055364072700728788483776 = 2^6 * 17 * 439 * 1607^2 * 1733309 * 413414251171984964928943833274782930952904102537554377365457011053267334799073[/code]

10metreh 2009-04-09 14:04

[quote=schickel;168625]Very high powers of "3" from 171018:[code] 657 . 9733273362368101690506170932124491964396727918772672927812318844771080 = 2^3 * 3^6 * 5 * 19 * 271 * 654005789 * 6486798343 * 15280463215435934267822213852908299588222731
658 . 24957188436629120479618862475684430646542940166419414638123331796124920 = 2^3 * 3^7 * 5 * 11 * 487 * 3472657 * 35657693 * 31668732727301 * 13580614504575146472146061690718397
659 . 67105318270746370819655849445462881658217796399624263621897306370505480 = 2^3 * 3^8 * 5 * 11 * 137129849 * 169512694960541962278458926658942037901019875526177795903
660 . 179951712001669532634246184168160920913268819504651792633292990950326520 = 2^3 * 3^6 * 5 * 11 * 83 * 241 * 189296739433877 * 283384017539968494521 * 522831994879017762749439127
661 . 493054716312865044614781945555177872589295322220024081153475159510488840 = 2^3 * 3^6 * 5 * 11 * 53 * 509 * 761 * 2417881811 * 30967171242852931723511308349104738711430320322477
662 . 1361755284044616845378453809650426570290557502397991799138030392955034360 = 2^3 * 3^6 * 5 * 41 * 2903 * 12289 * 240491 * 14314457471 * 9274497573571969096721825047840563284052113
663 . 3346135456735622546423167765778954747242490020844892952346678327244236040 = 2^3 * 3^6 * 5 * 37 * 17884627 * 173410099410935428379741232459438420572782901932427835590731[/code][/quote]

In one of my sequences, I remember 3^12 popping up. I don't remember where, though.

kar_bon 2009-04-09 14:51

3^12 from AQ 2514
 
[code]
2626 : 5166157449680272999393201080 = 2^3 * 3^4 * 5 * 11 * 229 * 632986518469541729693
2627 : 13859138544047661044981540520 = 2^3 * 3^8 * 5 * 11 * 103 * 167 * 521 * 3659 * 146406275777
2628 : 38082648828170336283684469080 = 2^3 * 3^12 * 5 * 1055437 * 6816361 * 249015971
2629 : 90446351500239637504377630600 = 2^3 * 3^3 * 5^2 * 19 * 1063 * 473741 * 1750529584480507
2630 : 237796980036311526340658657400 = 2^3 * 3^3 * 5^2 * 19 * 2317709357079059710922599
[/code]

kar_bon 2009-04-09 14:57

Highest power of 2: 2^19 from 8040
 
[code]
0088 : 908454368395514 = 2 * 454227184197757
0089 : 454227184197760 = 2^7 * 5 * 17 * 43 * 970902839
0090 : 722274041200640 = 2^19 * 5 * 17 * 16207393
0091 : 1113150120462760 = 2^3 * 5 * 1891007 * 14716367
0092 : 1391439145242200 = 2^3 * 5^2 * 239 * 1061 * 1907 * 14387
[/code]

10metreh 2009-04-09 15:16

[quote=kar_bon;168651][code]
0088 : 908454368395514 = 2 * 454227184197757
0089 : 454227184197760 = 2^7 * 5 * 17 * 43 * 970902839
0090 : 722274041200640 = 2^19 * 5 * 17 * 16207393
0091 : 1113150120462760 = 2^3 * 5 * 1891007 * 14716367
0092 : 1391439145242200 = 2^3 * 5^2 * 239 * 1061 * 1907 * 14387
[/code][/quote]

Thinking of high powers of 2:

Run "aliqueit 100651008". You will get a shock.

Andi47 2009-04-09 16:31

[QUOTE=10metreh;168653]Thinking of high powers of 2:

Run "aliqueit 100651008". You will get a shock.[/QUOTE]

Do you mean that [TEX]2^{12}*8191[/TEX] driver?

10metreh 2009-04-09 16:45

[quote=Andi47;168663]Do you mean that [tex]2^{12}*8191[/tex] driver?[/quote]

Yep, well spotted. :smile: The problem is you need it to change to 2^12*8191^2 - how rare is that? I wonder whether 100651008 ever escapes it! I was thinking that a more inexperienced person in aliquot sequences would not notice the 8191 immediately and not realise why the 2^12 kept hanging on.

henryzz 2009-04-09 18:02

[quote=10metreh;168665]Yep, well spotted. :smile: The problem is you need it to change to 2^12*8191^2 - how rare is that? I wonder whether 100651008 ever escapes it! I was thinking that a more inexperienced person in aliquot sequences would not notice the 8191 immediately and not realise why the 2^12 kept hanging on.[/quote]
Is 100651008 a side sequence of something that has been taken to 80 or 100 digits?

10metreh 2009-04-09 18:28

[quote=henryzz;168670]Is 100651008 a side sequence of something that has been taken to 80 or 100 digits?[/quote]

No, but it may well be a side-sequence of an unworked sequence.

mklasson 2009-04-10 16:28

[QUOTE=10metreh;168618]A record escape from the 2^6*127 driver at 105 digits from mdettweiler: (Directly to the downdriver too.)
[/QUOTE]

In this vain vein, how about this cute escape from 2^6*127 prefixed by a cubing of the 127 on the line before (from 103920):
[code]
2808 . 10444192963334529439960528322757274961873592360165927541421722296983352666960715045696 = 2^6 * 61 * 127^3 * 2797 * 130827401 * 7473474193069 * 29329571073476293 * 16283002295513626058193249706431347
2809 . 10795533033779996426764741785132961926125500619485866725877386593082726886863141184704 = 2^6 * 127^2 * 19571 * 369196501 * 1447391711847477256767185041805745248565035243484876448644241985629
2810 . 10797964568027775645118234540310689970133904303557663849788349508173570197641727715376 = 2^4 * 127 * 1787 * 70365756707 * 744646521619927660861061410418507 * 56752123260273726536765271414707111
[/code]

and 128370 just went from 2^8 to a downdriver at a height of 124 :party:
[code]
3645 . 1511634284911255639343311823523603995319243151784026839866525757409584613957260824093267942025556783702092330124999795963136 = 2^8 * 5904821425434592341184811810639078106715793561656354843228616239881189898270550094114327898537331186336298164550780452981
3646 . 1505729463485821047002127011712964917212527358222370485023297141169703424058990273999153614127019452515756031960449015510666 = 2 * 19 * 136399 * 49239977 * 282107716702711 * 20913145467582219848272735343244054951179210813996214334933644982844731511477982744127871625319
[/code]

Speaking of 128370, I notice it's one of the missing files on your 100k-200k page, Frank. Is the previous work for that seq coming or should I let an idle computer redo it a couple of nights?

Andi47 2009-04-10 18:42

[QUOTE=10metreh;168665]Yep, well spotted. :smile: The problem is you need it to change to 2^12*8191^2 - how rare is that? I wonder whether 100651008 ever escapes it! [/quote]

I have run it for a few hours (and [URL="http://factorization.ath.cx/search.php?aq=100651008&action=last&fr=&to="]uploaded[/URL] the .elf file to the database) - at least it doesn't escape 'till line 616.

[quote]I was thinking that a more inexperienced person in aliquot sequences would not notice the 8191 immediately and not realise why the 2^12 kept hanging on.[/QUOTE]

I also had to take a second look when I was seeing the persistent 2^12, but I did know what to look for.

And there are yet [URL="http://factorization.ath.cx/search.php?aq=16191903170560&action=last&fr=&to="]more drivers like this[/URL]... :grin:

10metreh 2009-04-10 18:56

[quote=Andi47;168801]I have run it for a few hours (and [URL="http://factorization.ath.cx/search.php?aq=100651008&action=last&fr=&to="]uploaded[/URL] the .elf file to the database) - at least it doesn't escape 'till line 616.



I also had to take a second look when I was seeing the persistent 2^12, but I did know what to look for.

And there are yet [URL="http://factorization.ath.cx/search.php?aq=16191903170560&action=last&fr=&to="]more drivers like this[/URL]... :grin:[/quote]

I wonder how the aliquot sequence of M43112609*2^43112608*3 progresses... :smile:

Andi47 2009-04-10 19:39

[QUOTE=10metreh;168805]I wonder how the aliquot sequence of M43112609*2^43112608*3 progresses... :smile:[/QUOTE]

I guess that no driver escape will be found before the universe ends. :wink:

schickel 2009-04-11 02:45

[QUOTE=mklasson;168788]Speaking of 128370, I notice it's one of the missing files on your 100k-200k page, Frank. Is the previous work for that seq coming or should I let an idle computer redo it a couple of nights?[/QUOTE]It depends on your preference. I'm feeding them up as I get them. (In fact I'm uploading the next batch now). But I can't guarantee how long it will be before I have them all....128370 is [b]not[/b] is this batch.

10metreh 2009-04-12 11:56

Thinking of the high powers of 3 again, I have found a 3^11 amongst the depths of 130396, shortly after the downdriver run ended. At 94 digits, is it a record?

[code] 2142 . 1448676455182071467410102997843349507617598295270624214150363226474276607289911492608743660868 = 2^2 * 3 * 313 * 1911276046395927389 * 3754409935385309419 * 53750277498721455683283628322727892784966351570749933
2143 . 1942368111900136293912079288358869017500768153960332394834493321799720170453625719855632585532 = 2^2 * 3^3 * 29 * 43 * 2179 * 57397 * 1616346698117201 * 71344481576033967234037557630052427494992518540402200337511802189
2144 . 3390736748816518491063418355192247026250610394922398709802348450809885615586380369713518134468 = 2^2 * 3^11 * 13 * 56489 * 1820743 * 4365793 * 329902199423081 * 14602081455994051 * 170169324183335472028758289731249355267
2145 . 6194774322822153065996361069576174159946335302354906188193834638759159964433470734959857302332 = 2^2 * 3^3 * 13 * 1335391 * 3304075303534696717109889111052538127770608234459108047848018928740763532721648008463
2146 . 11101189729910045350346490366387576142491469137653897291595063198933663961880379016129673618628 = 2^2 * 3 * 148784281661 * 484036399261 * 17105118762364063915743107105337221 * 750977821424967032333964851089497959[/code]

10metreh 2009-04-25 14:15

Faster, lower, longer...
 
1 Attachment(s)
Congratulations to Markus Tervooren aka Syd: the highest downdriver run became the longest at 100 digits and 535 lines!

:party::party::wblipp::bow wave::bow wave::wblipp::party::party:

A second downdriver run plunged it down to 26 digits. Side-sequence check passed. Now with 2^3*3, size 93, line 3923.

Hope I haven't missed anything!

And here's the graph:

Andi47 2009-04-25 21:50

[QUOTE=10metreh;170943]Congratulations to Markus Tervooren aka Syd: the highest downdriver run became the longest at 100 digits and 535 lines!

A second downdriver run plunged it down to 26 digits. Side-sequence check passed. Now with 2^3*3, size 93, line 3923.

Hope I haven't missed anything!

And here's the graph:[/QUOTE]

Congratulations!!

:party::bow wave::bow wave::bow wave::bow wave::party:

schickel 2009-04-26 07:37

Also from 162126
 
Here are a couple more from after the long downdriver run:[code] 2608 . 3091193907134286513257749681522964 = 2^2 * 772798476783571628314437420380741
2609 . 2318395430350714884943312261142230 = 2 * 5 * 17 * 137 * 227 * 438522787823840540540042381
2610 . 2152053212382224395743501235206122 = 2 * 1076026606191112197871750617603061
2611 . 1076026606191112197871750617603064 = 2^3 * 2161 * 62241242838449340459957809903[/code]and[code] 2710 . 14658553592209842412770494088511137892 = 2^2 * 3664638398052460603192623522127784473
2711 . 10993915194157381809577870566383353426 = 2 * 11 * 263 * 8101 * 304656739 * 8847707567 * 87014929357
2712 . 7066760280455994391827110925769499054 = 2 * 11 * 661 * 1459 * 1571 * 22639 * 949771 * 9860265245562757
2713 . 4530362900630264561185458075346558546 = 2 * 2265181450315132280592729037673279273
2714 . 2265181450315132280592729037673279276 = 2^2 * 2439427 * 232142778848796487924493030297[/code]and even[code] 2959 . 7909206260374847588006318852930251710145056796480512 = 2^10 * 3 * 500395366582883579587513 * 5145154381552389041184367[/code]

10metreh 2009-04-26 08:44

It's now escaped 2^3*3 and is under the control of 2^5*3 at 110 digits, line 3999:

[code] 3976 . 48309901825260967076758177002731176160524728493587807411117690660530087184360241262457762133405911080856 = 2^3 * 3 * 2012912576052540294864924041780465673355197020566158642129903777522086966015010052602406755558579628369
3977 . 72464852737891450615137265504096764240787092740381711116676535990795130776540361893686643200108866621344 = 2^5 * 3 * 173 * 50535690300343 * 585923888818091 * 1086286335039248175352691651 * 135652047718770042093695798699948641389664061[/code]

Soon it'll join the 4000-line club! :party:

Just noticed my post count has reached 666 (again). :devil:

schickel 2009-04-29 08:45

Here's one from 163716
 
Here's a case of not just once, not just twice, but three times unlucky:[code] 896 . 17816302212148068146693260361020634183303630115178699088195258539053538605813380940991587683342388906962134692514568 = 2^3 * 409 * 5611151251 * 7924225319 * 122460346680256725480050067153918981379931560744661007311901870089973066353464486019005638101
897 . 15670940647896279044331700068289307182504018907048500345873656770504034679042270362903784753652750116232620006957432 = 2^3 * 1958867580987034880541462508536163397813002363381062543234207096313004334880283795362973094206593764529077500869679
898 . 13712073066909244163790237559753143784691016543667437802639449674191030344161986567540811659446156351703542506087768 = 2^3 * 1714009133363655520473779694969142973086377067958429725329931209273878793020248320942601457430769543962942813260971
899 . 11998063933545588643316457864784000811604639475709008077309518464917151551141738246598210202015386807740599692826812 = 2^2 * 2999515983386397160829114466196000202901159868927252019327379616229287887785434561649552550503846701935149923206703
900 . 8998547950159191482487343398588000608703479606781756057982138848687863663356303684948657651511540105805449769620116 = 2^2 * 41 * c113[/code]Three times with [tex]2^x * p_{115}[/tex] without getting the downdriver....'course it did manage to shed a digit.

Andi47 2009-04-29 19:03

A "high" escape from 2^4*31 (at height 123) and high powers of two in sequence 113454:

[code]2003. 248226228585690975908823929282245121387376635151150179318689690346712670239673819369791034478165119347882997056936400658768 = 2^4 * 31 * 183864442853821 * 56342260452510344069 * 926072947933587546118289 * 3138436189462562622662503 * 16621701333571345173782365028149613501
2004. 248226228585693676018044020396589220619126184756606136071878783149841690031522988304315035141384100370628966976585903238832 = 2^4 * 31^2 * 2797 * 43967059 * 131275722140482867897352399632547343527287087510501328091169293707588411074501968863388919486529779447922509
2005. 248904369546429542191539703406955013530194701861015079722473940853466847497428682168815493727921906280139104085891056941568 = 2^9 * 31 * 1583561801593 * 3606415503626917134886820350130010066218719 * 2745933954755807682303832786020696064809144107654937539905468357
2006. 264460892643405572492061442312342590220606049416595430560045391930221472598570062331351165962006812081105420775614865782272 = 2^9 * 7^2 * 19 * 31 * 617 * 29006475341691218507034949021922610538884903383202455850539230545070738018990939076675412699878400834779085882463
2007. 404520284121587966695635079846959511575325520201294856234380284031261432526860491763376740460094070098391811300850690615808 = 2^9 * 19 * 31 * 37^2 * 43 * 10313 * 5800691991114228452929 * 12227266421565005041169 * 31152216005888796902663689801253294635941281310492943986965441611
2008. 519172678938870826362370965929419971623518460317474367975271584894814511769549865848549770854394357596751426138603765192192 = 2^9 * 13 * 19 * 31 * 4139 * 15056867387 * 50414677207 * 2012221763579020250909 * 20946927877706180591383762787806365576789665854377748117071693190700257
2009. 694975743882322263727067610260120841015635917024284876933874396547214680435459837721065513320999565876207372257545847351808 = 2^9 * 31 * 59 * 743 * 4787 * 204086537 * 1022396567744510247291263852684955588726003353999378082099048840551057432907976416396227787146003632213
2010. 764973243452960959151084759421491638840058439070946385174339564677710775116606620692426260472848559710776342716902642488832 = 2^9 * 13 * 31 * 283 * 13100407422415491353207502220493830345811792640097170150931897362196545850026061658058334926093454069611395491139339
2011. 940153987570688496004791992314290417237109060141148159979825045308580937670491121353847604438158402482271061047696596049408 = 2^9 * 29 * 31 * 4457 * 9679 * 14918457864886871 * 3173746856484278734127222231050868720008871602774571871544491700405107713697093610452923573957
2012. 1066435367331785218528062400324796350265644885987072573013495909507334880210786535445578698547389360062230308748145518305792 = 2^9 * 17^2 * 31 * 411617 * 28116729006924145532171 * 20088473842747126681085674707946317180219758950189578544880817688168953279361961186746157
2013. 1270087762918478785532941115248015788617154127012406125300436716795301355568582184867530607219106760340083795964967441465344 = 2^[B]16[/B] * 31 * 163 * 23128609187 * 165826901167539080741956400467685639875522663707605269233509909592789025601155420259940826458249940309339
2014. 1368095386482290624515786659426537997586340978802118530562952834454343448452705127042424756763201339728272230919548509014016 = 2^11 * 17 * 59 * 3371 * 1410410381555697647 * 140081648686038427948546439680170315591765415740468433246150996045420116345535929821884730131247[/code]

henryzz 2009-04-29 19:27

[URL="http://factorization.ath.cx/search.php?aq=199152&action=last&fr=&to="]199152 [/URL]got the downdriver at 140 digits
[code]4584. 3678082527398653884054542844220520780523364326983319047659488761823579351022522774661266581156143991210285951864262281801742277498360179968 = 2^8 * 3^2 * 79 * 537928984032413 * 37565308386692631159977811691508555437244819360263641268065267468738803175388826661425822665984989783586890576302901671
4585. 7060974359692284571114939900771913620444545751708662248169815504643934404172979423032277607564643323670266080011953006393251825627656599552 = 2^11 * 3^2 * 13277123 * 145050946373 * 1124593100256607967 * 54315093550427477630161541429327687418370133 * 3256504487054384087656869179591341762181850951898142419
4586. 13332417477980594813535321195816979037637263559026347209135318198684680045942308111197726912360010001133931039553153980216739490548150734848 = 2^12 * 3^2 * 361664970648345128405363530702500516428962227621157422122811366066750218260153757356709171884765896298120959189267414827928046076067457
4587. 25178753591567139494453003643977383453267921324757358570768004494201083445053644433416735837445516934378883057797608152905522639769740395366 = 2 * 7 * 131 * 1399 * 36436667 * 687829669183873003 * 28632934576117589745742327 * 78831278363768120216225394957176023487 * 173473524833177929768421914423681625033983649
4588. 18345406832324023186542904014498903166858456174136115472043964167668750170755680316850125432877253483727628616724549035220487161700375444634 = 2 * 7 * 20963 * 6093179 * 1506677957634354036567085105240952834497 * 6808971335699661249205667854504142219176347247030017756050503090806629207439135235638299
4589. 13105367412213263202785292256367616634876216212539000415137937529424844101637754858051129671278521430028242420693198767887478769047620587366 = 2 * 11 * 17 * 2052075831709 * 3423982124251531951 * 4987153144267109497661949919770362580934485744235042268023392943235956253987857220230712950826304385463251
4590. 9601258478477466588734921437523567919394408983436868438096884956727400395571012722468939117203986288396015536979275541693572559535970636954 = 2 * 23 * 1866612401 * 111819149111976812735664514749483915597443993542089177806355219588018756360361340309325546840373492198077941202209417100382761899
4591. 5426798278494764199260329590350731277272725261480284478302573168903497773051401127167590785908475100730726306989028377081532086751851396646 = 2 * 7 * 103 * 167 * 5519 * 15470135077[/code]

schickel 2009-04-30 04:15

Here's a line from 125034, calculated by hhh:[code] 490 . 4603929479214701866239720288195457375726761414925531210562532549315345017399523383157304325522239673570727368750000 = 2^4 * 5^8 * 7 * 31 * 26627 * 390307 * 4065116591659443807017 * 7926869578275982438611275491 * 10136443736148485553987891530633332604017338689[/code]Look at that exponent of 5!

schickel 2009-05-01 08:59

A singleton from 199152
 
Here's one from before mataje's latest downdriver run:[code] 4382 . 423330111392695832841818088625742502913209955624808377429788326167244669172628048 = 2^4 * 26458131962043489552613630539108906432075622226550523589361770385452791823289253
4383 . 396871979430652343289204458086633596481134333398257853840426555781791877349338826 = 2 * 198435989715326171644602229043316798240567166699128926920213277890895938674669413
4384 . 198435989715326171644602229043316798240567166699128926920213277890895938674669416 = 2^3 * 13 * 45809719856587 * 1235059813286003 * 4790242222413200146589 * 7040183859626795183668712101[/code]And as an example of persistance, here's the escape from a very nasty guide. I would have bailed on this way before it got to 135 digits![code] 4571 . 333903447785943638699368525527377604253502215555678908172978199532711569759328808864243639015264786621094913664594367761414340334417312 = 2^5 * 3^2 * 7 * 165626710211281566815162959090961113220983241843094696514374106911067246904428972650914503479794040982685969079659904643558700562707
4572 . 751282757518373187073579182436599609570379985000277543389200948948601031958489819944548187784345769897463555745337327463182265752445504 = 2^6 * 3^2 * 7 * 19 * 137 * 37976231355837865997 * 480700062582837671278721421599455567037940149 * 3921233343011863571565561138411776238140437958142115230459822133[/code]I just have this to say about that....

:bow wave::bow wave:

:groupwave::groupwave:

10metreh 2009-05-15 17:46

Just had this line on 130396:

[code] 2557 . 163578642999558897088906278322349716599304624344566325723055390699749040946044926484 = 2^2 * 211 * 10520648737 * 28132601993 * 479625488021 * 16757310841163 * 2032239779294017 * 40091306001026532281[/code]

That's 2^2 * 211 * p11 * p11 * p12 * p14 * p16 * p20!

In fact, the first p11 was found first, then P-1 split the c71 cofactor into c36 * c35 (yes, the c36 was the one found), and msieve finished those off.

10metreh 2009-05-17 17:26

130396 - the good bits and the bad bits
 
With ~2000 new lines yesterday and some more today, I decided I'd do a nice little review of my work on this sequence:

2^3*3 for one line:

[code] 2330 . 214470669448693973928119689721972091785003597983018241463557211573430262344047993888 = 2^5 * 3^2 * 2906249516247987341 * 137917700169737410251015965689 * 1857900771945617431209217027117349
2331 . 395430296796029514639829109848160126988123967586750140512284941396766731649126213112 = 2^3 * 3^2 * 19 * 289057234500021575029114846380234010956230970458150687508980220319273926644098109
2332 . 731892917754054627973718791034752515741176817200037540772737917848401582262856415888 = 2^4 * 3^2 * 47 * 152879381 * 1323852005872169162353279939111 * 534316814435501434390623696134800713505301[/code]

2*17^2*p ends a downdriver run:

[code] 2460 . 1076137657345800977469076260397107776458443388373537225658678638233839818618389284938 = 2 * 17^2 * 1861829856999655670361723633905030755118414166736223573803942280681383769235967621
2461 . 638607640950881894934071206429425549005616059190524685814752202273714632847936894924 = 2^2 * 1471 * 8111 * 244507 * 54726257307773669403264381948767969874032413723951484902441390683263993[/code]

(Those two were computed by me, but they came up before the recent line-fest.)

Isn't it called the [B]down[/B]driver?

[code] 2869 . 1090617960007232478963479793418262141962390 = 2 * 5 * 6473 * 168109 * 100225001976161007320247959612627
2870 . 872809324473146057279321670026224226436170 = 2 * 5 * 11 * 101 * 8263729729 * 8903999865583 * 1067687280002921
2871 . 858039913971636658259221374205492622813110 = 2 * 5 * 7 * 41 * 787 * 853 * 1134682349 * 392489037709442421185227
2872 . 954542247032790100033799064896741071343690 = 2 * 5 * 7 * 29 * 97 * 1297 * 753341 * 4961303579448905969511088367
2873 . 1099325607660619302519141906493069974871990 = 2 * 5 * 7 * 19 * 73 * 251 * 6619 * 6815311977475907954410284078419
2874 . 1323758440819616276612494765223708141224010 = 2 * 5 * 7 * 19^2 * 7549 * 290471 * 73526707 * 324912320078636196271
2875 . 1550660033710886007582967793919782889406390 = 2 * 5 * 7 * 19 * 1423 * 15161 * 324329 * 166627401554863283194498909
2876 . 1809751860779086545007288523685855196225610 = 2 * 5 * 7 * 19 * 1360715684796305672937810920064552779117
2877 . 2109109311434273793053606926100056807634230 = 2 * 5 * 163 * 1293932092904462449726139218466292520021
2878 . 1710578226819699358537956046812438711470714 = 2 * 463 * 20899 * 5455543 * 6538937 * 2477771828342658390671[/code]

When I saw this line I thought I had the 2^9*3*11*31 driver for a bit:

[code] 3174 . 164359850945845496825369389512963374592 = 2^9 * 3 * 11 * 13 * 748287491558518615354427946136379[/code]

I must thank my lucky stars that this happened:

[code] 3524 . 38631876647110261884845264390616587178622026498776574916 = 2^2 * 7^2 * 3733 * 52799735190154908899726739984004476317977588877437
3525 . 40032653621705071617955014802392225935337971931696468392 = 2^3 * 7 * 1783 * 2591 * 154741782660957165961172656704467231470638813419[/code]

A short downdriver run:

[code] 4048 . 1252626134022135951271712714432237084477508839942212 = 2^2 * 313156533505533987817928178608059271119377209985553
4049 . 939469600516601963453784535824177813358131629956666 = 2 * 43 * 367 * 924239621 * 32205766062752518569559919712008131333
4050 . 506436088732207084615913578981668511203945135018182 = 2 * 2153 * 1555901 * 29952364327 * 3873065831549 * 651602395256017589
4051 . 253571368034721795324019035180936091458207378725818 = 2 * 241 * 28547 * 547639 * 975977 * 75908663 * 454221206336031775332103
4052 . 128378402049794988074533671817466825098921278211142 = 2 * 1093 * 1418809469023693169 * 41392125654411920259077214263
4053 . 64365383644361988667271145017232264806793564709018 = 2 * 32182691822180994333635572508616132403396782354509
4054 . 32182691822180994333635572508616132403396782354512 = 2^4 * 7 * 67 * 71 * 1979 * 593666321383 * 51414188569317118678035038099[/code]

One driver to another driver:

[code] 4287 . 1299626975901890432092216386564 = 2^2 * 3^2 * 7^2 * 137 * 5377737126561606965308673
4288 . 2549789525713667203317524314680 = 2^3 * 3^2 * 5 * 7 * 11 * 2819407 * 37991971 * 858739634827[/code]

And why is 4418 my unlucky number? Here ya go:

[code] 4418 . 521280515417864454016244447645088488770001218826552764116 = 2^2 * 3^2 * 14480014317162901500451234656808013576944478300737576781
4419 . 796400787443959582524817906124440746731946306540566723046 = 2 * 3 * 263 * 149411 * 20561556878347423569329 * 164280537066016128446214653[/code]

That 2*3 driver has now controlled the sequence for 336 lines, pushing it up 34 digits, and shows no signs of disappearing. :sad:

10metreh 2009-05-21 16:22

Also just spotted a high power of 7 from 130396 early on:

[code] 134 . [COLOR=black]1496179015544699150407849596[/COLOR] = 2^2 * [COLOR=#000000]3[/COLOR] * [COLOR=#000000]7^7[/COLOR] * [COLOR=#000000]1031[/COLOR] * [COLOR=#000000]35837[/COLOR] * [COLOR=#000000]4097563770073[/code][/COLOR]

kar_bon 2009-05-21 22:01

4-digit prime squared: 2347^2
 
from n=3556 index 565:

[code]
396495022821789424734925007122343803121687465535009958098753728242418890 = 2 · 5 · 223 · 2347^2 · 115236367295669 · 186741022326241 · 1499952155963476622428538885793563
[/code]

10metreh 2009-05-24 19:12

This one isn't related to the sequences, but the numbers that popped up in them. On 130396.4783, I QSed this C92:

[code][COLOR=red]166659[/COLOR]13756850552081806634468279185067944988818001927397673235891862519760250370300401898953[/code]

Now, on line 4798 of the same sequence, I have a QS in progress on this C92:

[code][COLOR=red]165659[/COLOR]61998929465569973995569231458754642250175304700075799691858447072215496139303052210961[/code]

The first six digits of the C92s are 166659 and 165659. Scary!

P.S. When I first saw the new C92, I mistook it for the old one and thought there must be a bug in aliqueit!

schickel 2009-05-26 06:41

Here's one from 88662
 
I was just looking over the work I've done, and it turns out I didn't really notice this one.......[code] 1602 . 146596415628751343110066976770654068497449280865993211308022426750187202853517452118337199283584395913644501600904 = 2^3 * 519733 * 35257626422786157293761166014726327868696350064839352924487772267247606668596532286370405401327315158370861
1603 . 128272392539553767013668011091812530830186151202995032484813490722997811210927799551529344929217366334166322259716 = 2^2 * 7 * 23 * 29 * 409 * 42538290671 * 274016269735766491916605459773709190911 * 1440687000962313032548422038538800956121705152354922644429
1604 . 149334600628163853185787426223486348405102644082128994230317816984807067212788891066116218252236188112443880364284 = 2^2 * 7 * 16879 * 315977166530185126881643771684778102132621778715159569012885447226915667001237571339949510914314888560688007
1605 . 149352295349489543552892798274700695978822070901737043166182538569851774490140960370111255424847389746203279837956 = 2^2 * 7^2 * 421189 * 1764409477 * 11863166579081 * 293858773442748181 * 8163309750001776249401480675459 * 36030796436674588940481020887718863
1606 . 154687027927915360495743052559564398717256585139065740946739235495466729700411942067911774622678406194100333422844 = 2^2 * 7^2 * 89 * 106681 * 66942525437357 * 327164034855543129331 * 3795361006303893678007703676567581238021517093752304180325478988854713
1607 . 163752736016675872075495774247047331297707613290568952723374189109231381926823283354129477371922056273001734311236 = 2^2 * 7^2 * 2836479022386832771718761 * 294545856446769041915479550623277260965121160145358180373898508144626259986822931378681
1608 . 169601048017271438935335026565381458247759180898715685436836106660761114993552369802282840167641225371377332130680 = 2^3 * 5 * 7 * 131 * 805757 * 17486832764513929802584252321 * 328158728859519096904252914670781080786006227224482153365199930421086700483[/code]Talk about a lucky escape!

10metreh 2009-05-26 06:50

[quote=schickel;174838]I was just looking over the work I've done, and it turns out I didn't really notice this one <snip>[/quote]

Nice! Have you even seen a one-line run with 2^2*7? (You can find a one-line escape from a driver further up the thread, but 2^2*7 is so much nastier than 2^3*3. (As is 2*3 - I'm getting so bored.)

schickel 2009-05-26 07:01

[QUOTE=10metreh;174840]Nice! Have you even seen a one-line run with 2^2*7? (You can find a one-line escape from a driver further up the thread, but 2^2*7 is so much nastier than 2^3*3. (As is 2*3 - I'm getting so bored.)[/QUOTE]Not that I've noticed. Discussing some of the record type stuff I've noticed with Clifford, this kind of stuff turns up all the time in the early stages of sequences. It's just that when a sequence gets into the >95-digit range and you're doing, potentially, a lot of manual work that you start to really notice these things.....

10metreh 2009-05-26 09:29

[quote=schickel;174841]Not that I've noticed. Discussing some of the record type stuff I've noticed with Clifford, this kind of stuff turns up all the time in the early stages of sequences. It's just that when a sequence gets into the >95-digit range and you're doing, potentially, a lot of manual work that you start to really notice these things.....[/quote]

Even though I'm not doing much manual work, I still always look back at the factors to see if anything odd turned up. I spotted the one-line 2^3*3 run as soon as it started because I was busy watching the computer, knowing that the guide could change quickly.

kar_bon 2009-06-01 00:49

smoothest graph
 
here is an example of a very smooth graph:

[url=http://factorization.ath.cx/aliquot.php?type=1&aq=232680]232680[/url]

almost straight line from 6 upto 105 digits!

kar_bon 2009-06-01 00:57

49-digit twin-pair factor in 2 consecutive indices
 
here is one remarkable from sequenz [url=http://factorization.ath.cx/search.php?query=&se=1&aq=271740]271740[/url]:

index 250 to 252:

[code]
250 . 43827131606920639860265504690937848330149198375812 = 2^2 * 7 * [b]1565254700247165709295196596104923154648185656279[/b]
251 . 43827131606920639860265504690937848330149198375868 = 2^2 * 7 * [b]1565254700247165709295196596104923154648185656281[/b]
252 . 43827131606920639860265504690937848330149198375924 = 2^2 * 3 * 7^3 * 131 * 4327 * 257561021 * 72933885846923222248446787566457
[/code]

two 49-digit twin-pair-factors at index 250 and 251 [b]and[/b]

3 consecutive indices with very small differences!

Greebley 2009-06-10 14:51

I have some statistics about the numbers that reach certain values before merging or termination.

To get the limit from 300k to 5 million, at least* 2672 numbers of the 67390 terminated or merged before 2^64, so less than 65k numbers to check. :devil:

A count of the numbers that reach 10^15 (1 Quadrillion):

For numbers <=300000, the count is 3740 or about 1.2%
For numbers <= 1 million, the count is 12916 or about 1.3%
For numbers <= 5 million, the count is 67390 or about 1.35%

A count of the numbers that reach 10^12(1 trillion) but don't reach 10^15 before merging or termination:
For numbers <=300000, the count is 340 or about .113%
For numbers <= 1 million, the count is 1271 or about .127%
For numbers <= 5 million, the count is 7070 or about .141%

A count of the numbers that reach 10^9(1 billion) but don't reach 10^12 before merging or termination:
For numbers <=300000, the count is 662 or about .22%
For numbers <= 1 million, the count is 2493 or about .25%
For numbers <= 5 million, the count is 16274 or about .34%

* - A sequence stopped if it went over 2^64 or if it had a (possibly prime) cofactor > 2^52 with no primes under 2^26 dividing it. The second condition means I didn't test every number up to 2^64 so some might merge or terminate before 2^64 would be reached.

Batalov 2009-06-15 10:30

a five-digit number squared
 
[quote=schickel;168627]Here's one from 110432:[code][FONT=Arial Narrow] 1613 . 883866359463668463521525972362866107318450543014047075048557464839182863055364072700728788483776 = 2^6 * 17 * 439 * 1607^2 * 1733309 * 413414251171984964928943833274782930952904102537554377365457011053267334799073[/FONT][/code][/quote]
From 134856:
[FONT=Arial Narrow] 3379 . 84959577112658511249647834283135668 = 2^2 * 383 * 25357^2 * 86249748121303912397851[/FONT]

R. Gerbicz 2009-06-15 11:42

[QUOTE=Greebley;176920]I have some statistics about the numbers that reach certain values before merging or termination.

To get the limit from 300k to 5 million, at least* 2672 numbers of the 67390 terminated or merged before 2^64, so less than 65k numbers to check. :devil:

A count of the numbers that reach 10^15 (1 Quadrillion):

For numbers <=300000, the count is 3740 or about 1.2%
For numbers <= 1 million, the count is 12916 or about 1.3%
For numbers <= 5 million, the count is 67390 or about 1.35%

A count of the numbers that reach 10^12(1 trillion) but don't reach 10^15 before merging or termination:
For numbers <=300000, the count is 340 or about .113%
For numbers <= 1 million, the count is 1271 or about .127%
For numbers <= 5 million, the count is 7070 or about .141%

A count of the numbers that reach 10^9(1 billion) but don't reach 10^12 before merging or termination:
For numbers <=300000, the count is 662 or about .22%
For numbers <= 1 million, the count is 2493 or about .25%
For numbers <= 5 million, the count is 16274 or about .34%

* - A sequence stopped if it went over 2^64 or if it had a (possibly prime) cofactor > 2^52 with no primes under 2^26 dividing it. The second condition means I didn't test every number up to 2^64 so some might merge or terminate before 2^64 would be reached.[/QUOTE]

On [URL="http://www.aliquot.de/aliquote.htm"]http://www.aliquot.de/aliquote.htm[/URL] there is also some stat, for example: "The extension of calculation limit from C60 up to C80 reduces the number of OE-sequences about 2 - 2.5%. " or see the work: [URL="http://christophe.clavier.free.fr/Aliquot/site/Aliquot.html"]http://christophe.clavier.free.fr/Aliquot/site/Aliquot.html[/URL] raising the mean size from 103 digits to 135 digits on 74 sequences resulted none of them is eliminated. That's why it is called these type of problems law of small numbers and very probable that Catalan's conjecture is false.

Greebley 2009-06-15 14:26

Ya I have seen those - I was mostly contributing the 5 million case which I think is new with the 1 million and 300k for comparison (since I didn't go to 30 or 80 digits). I was hoping to make it up to 10 million, but ran out of memory around 6 million.

Since his values total a bit over 10,440 for the first 1 million, then 2476 terminated between 1 quadrillion and 80-100 digits.

Ya, I am also thinking it is false.

kar_bon 2009-07-09 20:58

71-digit twin
 
as in post #44 now i got 2 factors (twins) in consecutive indices:

seq 247840:

[code]
698. 1947292834179145293256748179082560222447097478093195308505991094604768308 =
2^2 * 7 * [b]69546172649255189044883863538662865087396338503328403875213967664456011[/b]
699. 1947292834179145293256748179082560222447097478093195308505991094604768364 =
2^2 * 7 * [b]69546172649255189044883863538662865087396338503328403875213967664456013[/b]
[/code]

Greebley 2009-07-12 16:55

2^2 - the weak downguide
 
I was noticing with 2^2 that it works sort of as a 'downguide' if you don't have a 3 or 5. I was wondering why it didn't pick up a 7 along the line until I realized it can't - if you have 2^2 - it will never pick up a 7 unless it changes 2 exponent first - this follows from the fact that 2^2 makes the siqma always be divisible by 7 so sigma - n is never divsible by 7 - fairly obvious if you think about it (which I hadn't)

So that means 2^2 is only lost when you get a prime not equal to 7 mod 8, or two primes equal to 1 mod 4. It is somewhat difficult to pick up a power of 3 because there are usually 4 odd terms so the chances are one of them will be divisible by 3 meaning sigma - n isn't. 5 is more likely to appear (and disappear)

Therefore 2^2 will generally lead to small a reduction in size if 3 or 5 isn't present. With higher values, the chances of two or less primes is reduced and you can keep your 2^2 longer. Picking up a 3 or 5 will send it up again, but value can also be lost again for another downrun.

For 2^3 (and larger), I think it less likely to have no primes less than 15 and primes like 3 and 5 send the sequence up faster, so I don't think this will work as a 'down guide' except for a few steps.

10metreh 2009-07-12 16:58

[quote=Greebley;180714]For 2^3 (and larger), I think it less likely to have no primes less than 15 and primes like 3 and 5 send the sequence up faster, so I don't think this will work as a 'down guide' except for a few steps.[/quote]

In addition, 11 and 13 will also cause an increase.

Greebley 2009-07-12 17:08

Actually it just occurred to me that with 2^3 you can never pick up 3 or 5 for similar reasone (sigma 2^3 = 15) so you only have to worry about 7, 11, or 13. Maybe it can have a chance at a down run with it and my statement above about it only being a few steps isn't quite correct.

I think it also twice as likely that you will lose a 3 than gain it with 2^2. The reason is that you lose it if all the sigma terms aren't divisible by 3, but to gain it you need all the sigma terms not divisible by 3 AND the remainder (mod 3) is correct (so one out of two). I bet this is the other reason 2^2 seems to work as a down driver (not have a 3 or 5). For 5 you have 4 times the chance of losing it compared to gaining it.

Greebley 2009-07-19 14:23

As you probably know, you have to manually fix any term that is a square over 2000. I have fixed a lot of these - they are usually between 2000-7000.

Well I just found a potential record breaker: Sequence 495246 at index 256 contains 444793^2. That is very high compared to the rest.

I have not yet found a third power over 2000.

kar_bon 2009-07-21 16:30

highest squares and driver
 
the highest squares for all open seqs upto k=1M:

495246:i256 444793
570690:i996 193771
352440:i778 150517
224250:i37 112297
85176:i740 94543
364924:i608 79367
814890:i1334 71263
180768:i344 61253
864666:i320 56489
679932:i349 53591
559176:i1086 52433
424020:i282 50833
685146:i727 48497
417336:i168 46511
717696:i95 44417


the only seqs <1M with the current driver 2^9*1023 (= 2^9*3*11*31) are:
363270 and 604560

there's no seq <1M with the driver 2^12*8191.

Greebley 2009-07-21 16:40

Interesting to know.

Did you search for 3rd powers? I am curious if there is one over 2000 somewhere in the db for the < 1M seqs. My guess is 'no' but I find it hard to guess how big the biggest third power (or greater?) would be.

kar_bon 2009-07-21 17:26

there're 181 seqs <1M with factor-cubes with 3 or more(yes!!!) digits:

the highest:
853332:i246 2161
729000:i1173 953
758322:i1774 853
710430:i97 727
129792:i796 691
101820:i1029, 599
179082:i1244 467
759150:i254 349
104904:i1215 311
170196:i941 277
900648:i292 277
438360:i568 263
990504:i2441 227

addendum to squares: 84 seqs with 5 and more digits squared
seq 366600 is the only with two squared factors with 5 digits:
index 521 with 12583^2 and index 698 with 11677^2

10metreh 2009-07-21 17:49

130396 kept a factor of 463 on two consecutive lines:

[code] 4957 . 207961754206463616793765484277213110316700348230083722919599534410914792242769427053913835672610213079911826 = 2 * 3 * 7 * 11 * [COLOR=red]463[/COLOR] * 2663 * 4019 * 5216329541 * 3013631473500903889 * 58589184986816593541 * 98627656344820166776497833078801051794543235077
4958 . 312036716334136823340977893106923114227632032874921556898327624777563236085802615865976096686699753441227374 = 2 * 3 * 11 * 13 * [COLOR=red]463[/COLOR] * 3617 * 5557 * 39079456455361764369665589516847777866075252947065734155131730765968715049059907798872958315049[/code]

kar_bon 2009-07-21 18:20

here's another (choosen by random factor 797):

seq 11040:
[code]
3089 . 12563635146189922567676918255521152501614657939034576489878225480274222972082687585340536504 = 2^3 * 797 * 7561 * 20029 * 31334389 * 152340173 * 7112643748185163 * 383232004715380729172605955304225485941024022981
3090 . 11027035763528304587318683831357921028676237819707309270841087002896163582995304973630439496 = 2^3 * 797 * 835069183494260895441058999 * 2071037761339551333276963104943700514825471559385096671130379
[/code]

same in seq 021318: index 556 and 557.

those 2 only for seqs <30000!

another choice: factor 9973 (the last <10000):
found only a near miss in seq 34908: index 3998 and 4007!

interesting but hard to find, needs some programming to search for highest factor!

gd_barnes 2009-07-26 21:58

Sequence 280686 has now eclipsed sequence 5352 as the longest known sequence that I am personally aware of that is ever-increasing. With small factors of only 2*3 that have never gone away, it has increased every time up to i=943 and is still only at 109 digits.

3^2 thru 3^6 have popped in from time to time but have quickly gone away. There was also a fairly long run of 2^2 thru 2^7 from i=406 to 495 but that also went away. It's been mostly 2*3.

I thought that 5352 was a slow increaser but it is currently at i=935 and 126 digits.

I'm guessing that others can quickly come up with an ever-increasing sequence that is at i>1000 but 280686 should be a good starting point for discussion about such a record. I'm not done with it yet but am getting close. Aliqueit.exe is currently working on a hard C99. I'll release it if I get a hard C>=100.


Gary

gd_barnes 2009-07-27 23:11

I have now released 280686 at i=946; sz 109; C102; 2*3

To make it official: Sequence 280686 at i=946 is the longest-running ever-increasing sequence that I am aware of.

I'd like to challenge others to find a longer ever-increasing sequence or extend 280686 higher to perhaps >= 120 digits to see if it could be "cracked" or reach 1000 indexes. Maybe someone could come up with a list of sequences longer than 500 indexes that are ever-increasing.


Gary

gd_barnes 2009-07-29 02:36

19278 will top 280686 as for the longest ever-increasing sequence sometime on Wednesday unless it acquires the downdriver in the next 2 indexes. :smile:

gd_barnes 2009-07-30 08:19

19278 is pushing towards 1000 ever-increasing indexes and is maintaining its very slow creep upwards with the 2*3 small factors that occassionally morph into 2*3^2 or 2*3^3 before going back to 2*3 fairly quickly.

I'm currently at i=982 with a size of only 102 and am processing a tough C100.

gd_barnes 2009-08-02 09:57

19278 finally ended it's ever-increasing run. After 1048 ever-increasing indexes, it lost it's factor of 3 at 1048 for a single index and went down before regaining the 3 right back at 1049 and starting its treck upward again. It's currently working at i=1049 at size 108 on a tough C100 (again).

Bummer!

Therefore, the unofficial records at the moment are:

Longest ever-increasing sequence: 280686 at 946.

Longest ever-increasing run anywhere within a sequence: 19278 at 1048.

That's something else people could check for anywhere in their sequences: Any run that is ever-increasing for longer than 1048 indexes even if there are some down runs elsewhere in the sequence.


Gary

10metreh 2009-08-02 10:32

In fact, you escaped the 2 * 3 driver at line 1045. Good luck, it's now got a "blue" guide (as found in the reservations list).

gd_barnes 2009-08-04 08:46

Even better: While maintaining the 2^2 guide, it has now dropped its factor of 3 again so has only been guided by 2^2 up until the current i=1065, when it went to 2^3 but still no factor of 3. Now it's on its way slowly down. Just gotta drop those one or two powers of 2 and I'll be rolling.

This one is really interesting so I've kept it going longer than usual. I've already solved two hard C100's (I usually stop there) and am currently working on a hard C102.

10metreh 2009-08-04 09:37

[QUOTE=gd_barnes;183967]This one is really interesting so I've kept it going longer than usual. I've already solved two hard C100's (I usually stop there) and am currently working on a hard C102.[/QUOTE]

Out of interest, what is the largest GNFS you've done?

Andi47 2009-08-04 10:23

[QUOTE=10metreh;183974]Out of interest, what is the largest GNFS you've done?[/QUOTE]

I guess, with "hard Cxyz" he means a composite which won't split by ECM. (But I'm curious about his largest GNFS too.)

gd_barnes 2009-08-04 12:31

[quote=10metreh;183974]Out of interest, what is the largest GNFS you've done?[/quote]

Correct, "hard" means it won't split by ECM alone and would be inefficient to run msieve (or yafu) on. Namely the amount of ECM curves that either Aliquiet.exe -or- Syd's DB runs by default...whichever happens to be greater for the length of cofactor in question. In other words, I let Aliquiet.exe run until it encounters GNFS and then I'll let Syd's DB hack away at it and if it finds a factor, I'll stop and restart Aliquiet.exe on the next index after putting the correct factorization in the ELF file.

Don't ask about GNFS. lol I haven't done any GNFS because I've had nothing but problems with it and as an admin for two prime seach projects, just don't have the personal time to dedicate to figuring out such issues (or even to continue posing questions for them) after already spending 2-3 hours at it after posing a couple of questions in this forum, which were answered reasonably. It's just that I kept getting different errors everytime I'd correct something.

Alas, I got a PM from Karsten a little while ago. He's going to send me a Windows care package of what he uses. It should include all necessary folders, everything modified as needed or instructions on exactly what to change, etc. I have the CYG or CWG thingie on my machine so that's not the issue. It gets through all of the relations but just won't find factors.

Believe it or not, I set the msieve to limit to 105 digits and I've done no GNFS on 19278 yet! That way it almost never goes to GNFS. The longest msieve has run on a very slow 1.6 Ghz machine so far has been 11 hours (one core) on one of the C100's that I encountered for 19278. It looks like the C102 that it is currently running on will run 16-20 hours. Crazy as it sounds, that's what I'm doing at the moment, which is why this is the first time I've tried to crack a "hard" C>100.

I will say one thing: If you don't know much about factoring to begin with, installing the GNFS stuff is extremely user unfriendly.



Gary

Greebley 2009-08-04 13:41

Oddly my experience was the opposite. With aliqueit, I didn't have to learn anything about ggnfs. A few questions on which lines to change in one file and it was up and running. Aliqueit has been good enough to solve c124's for me (I haven't tried higher due mostly to time issues and unhopeful sequences).

Without aliqueit though, I would agree with you. It is a slow learning process.

kar_bon 2009-08-09 22:20

just an eye-catcher
 
seq 514362:

[code]
797. 54774007141558011978068252997076650753477483251993617134897929348854871916939908 = 2^2 * 7^2 * 19 * 47 * [color=red]809[/color] * 4492799284639 * 182624065052414174365741 * 471458466985844972666218524873323471
798. 65244331251233353677332675714371474327771637340806111972762959309446601195124092 = 2^2 * 7 * 19 * [color=red]809^2[/color] * 4820597909 * 38871670116409488185353775390712595475476773499321140165887639
[/code]

Andi47 2009-08-28 18:54

2-digit cubed:

[code] 1029 . 231495364150475836544553534586087621550385708329062091066961390970945743804067744125728860552 = 2^3 * 23^3 * 283 * 44449 * 78059 * 165095641614636849667 * 14671069732418718140864010666279846895553901374490181157[/code]

from sequence 522348

kar_bon 2009-08-28 22:47

[QUOTE=Andi47;187829]2-digit cubed:

from sequence 522348[/QUOTE]

see post #56 for the highest cubes so far!

here's another sort of remarkables from seq 276:i1234

[code]
2406164941137993885146722410688929757159749303856305199137999910618479232219773684619394509425175460058349351330170
= 2 * 3 * 5 *
[b]566[/b]1545200582541702864324356927 *
[b]566[/b]5048649574629338619029305493 *
2500722589298704536579935613492765852985685104885849
[/code]

both 566... are P31!!!

Mini-Geek 2009-08-31 11:33

[code]Mon Aug 31 02:17:41 2009 factoring 195676107863988180517848073492543644940604662461972464243353598981074052753143825201209897621800399 (99 digits)
...
Mon Aug 31 02:17:43 2009 commencing square root phase
Mon Aug 31 02:17:43 2009 reading relations for dependency 1
...
Mon Aug 31 02:20:56 2009 reading relations for dependency 2
...
Mon Aug 31 02:24:09 2009 reading relations for dependency 3
...
Mon Aug 31 02:27:22 2009 reading relations for dependency 4
...
Mon Aug 31 02:30:33 2009 reading relations for dependency 5
...
Mon Aug 31 02:33:52 2009 reading relations for dependency 6
...
Mon Aug 31 02:37:12 2009 reading relations for dependency 7
...
Mon Aug 31 02:40:33 2009 reading relations for dependency 8
...
Mon Aug 31 02:43:51 2009 sqrtTime: 1568
Mon Aug 31 02:43:51 2009 prp47 factor: 50327499727490646814499045113166645927535479917
Mon Aug 31 02:43:51 2009 prp52 factor: 3888055415498875305644642541143657281099569913707947
Mon Aug 31 02:43:51 2009 elapsed time 00:26:10
[/code]AFAIK, this is the most dependencies I've had to go through for any of my GNFS runs before it found the factors. What are the odds that the factors wouldn't be found until the 8th (or, for that matter, nth) dependency? I think I remember hearing the odds for finding factors in any one dependency is about 1/2, so the probability of finding none in 7 would be 1/(2^7)=1/128, followed by another 1/2 chance for the 8th.

Andi47 2009-08-31 19:30

not record-breaking, but still a high power of 2 in sequence 522348:

[code]1106 . 117957006795443564706559806559733988151107700632356683434170620357205905182866206355340843956931920 = 2^4 * 5 * 394369 * 417577 * 971053321582270613 * 40497986982346005651289 * 227676340876500352213694894339949654644013389
1107 . 156294386185629296480055232759108742516550650821606278719469995837353299917159741475789081533732080 = 2^4 * 5 * 1325766445328643518013758521 * 1473622925217472662488070745113229239676692930636164143369513453757531
1108 . 207090061695958817836073183679912947924879527561409477894358383064358254081122019249844385990180864 = [B][COLOR="Red"]2^17[/COLOR][/B] * 19 * 37 * 53 * 16517386358098740629 * 2567301113077624954647850482736715304027540430973473053897368120281417
1109 . 249118838756610415034737610086481080945358879807690516464159461029754565636957302654912492413743936 = 2^6 * 19 * 37 * 43 * 761 * 15860963 * 10668137569456528577295052240525204527346449218621619384134621051924562139483381867
1110 . 298455576296218633160874067628449578723699678675330779642547194748889494094935979535436254046421184 = 2^6 * 19 * 41 * 167 * 7913701 * 82989433442147 * 2188740466464341 * 129486543576567074639562631 * 192585884214910798185892031291[/code]

schickel 2009-09-08 07:44

Check this out:[code]2423. 277629778585911849643287493387641122012726696503327039613225502287356249389590278653069430257049775938414576932228882069336576 = 2^9 * 3 * 11^2 * 31 * 48186764533956196688398283615279175902524378308723062671694753324001837251314628365260484401564057907199499739692485141
2424. 561569324866958059505740611625001360434833545199911511944933402353970595356216700002799529383577955875429485158372056930391808 = 2^8 * 3 * 11 * 31 * c121[/code]Turns out the 2^9 driver is pretty darn persistent.....

10metreh 2009-09-08 16:38

[QUOTE=schickel;188990]Check this out:[code]2423. 277629778585911849643287493387641122012726696503327039613225502287356249389590278653069430257049775938414576932228882069336576 = 2^9 * 3 * 11^2 * 31 * 48186764533956196688398283615279175902524378308723062671694753324001837251314628365260484401564057907199499739692485141
2424. 561569324866958059505740611625001360434833545199911511944933402353970595356216700002799529383577955875429485158372056930391808 = 2^8 * 3 * 11 * 31 * c121[/code]Turns out the 2^9 driver is pretty darn persistent.....[/QUOTE]

Clifford will be pleased :razz:

schickel 2009-09-13 03:29

Two in a row!
 
This one took two tries (479632):[code] 1248 . 117817016878785319006492302352690532758653456115423793341334544008108127079781481780624820223619471936102581760 = 2^9 * 3 * 5 * 11^2 * 31 * 1427 * 12044273 * 2984329241 * 106022145943107893 * 752058890281945109169558629348973124879433668213147687907006832509
1249 . 309836948446180204109058953115321603892913695932097324027900347710818395846990550767815026104030474468551784960 = 2^9 * 3 * 5 * 11^2 * 31 * 10755359280795267238078837071063049988507012572067494641286641191196875133540450003881431135864827520597
1250 . 814026164554055263522891249548435850227745982948873878582392731712968330907093356108168568582407337467481455616 = 2^10 * 3 * 11 * 31 * 6781 * 1747891 * 6352924861 * 8734847831977 * 1181477950582045778002740994994095486701945453792815702851118984443758859[/code]'course, if I had managed this one first, I could have broken the record twice....

rodac 2009-09-20 00:15

Hello :smile:

I have seen that the sequences 102072 and 84822 merge on the high number 8001424452.

Is it the highest merge or do higher merges exist for the sequences beginning under 10^6 ? :mellow:

10metreh 2009-09-26 09:17

I think this (from 561528) deserves a mention:

[code] 1036 . 71094710687983183844919102767194019196508346229508893331072158254253024 = 2^5 * 3 * 1650319073869 * 448743467082178452665495095520409784795027434211306683401
1037 . 115528904868085757101698250966761985958397205888720298576829386853993456 = 2^4 * 3 * 31 * 9578651569 * 140393827859333 * 57734490065613001922702391819708499345226431
1038 . 192548174812308009005850008281205656482758736773962038786778936849937424 = 2^4 * 3 * 11 * 31 * 36473 * 4580369 * 38362720102611887 * 1835534041930821535794648296871101360297
1039 . 367607450056871344163226559143246541078296820121953003541746713485888496 = 2^4 * 3 * 11^2 * 17 * 31 * 842362576273624117 * 142576522306516388341908183152293740611449587143
1040 . 773280231597512060758513426291947499984934839199800796393662040325604368 = 2^4 * 3 * 31 * 191 * 182014885871571913 * 14948365277722592526241143135667985643529318345267
1041 . 1299596619595818710359615964667111134892726708030099977487706986844994544 = 2^4 * 3^2 * 31 * 1039 * 15131 * 33806660782490118793381 * 547770869057047907455856785713158783249
1042 . 2458655444417498478002917878888202447361634579165352522409213121755325456 = 2^4 * 3^3 * 31 * 79 * 8965390009038543814169 * 259212506923388580098398032219732848789958043
1043 . 4918463563680012192048854062754860794062670360340844438308714628683586544 = 2^4 * 3 * 31 * 3305419061612911419387670741098696770203407500229062122519297465513163
1044 . 8197439272800020320081423437924767990104450600568074063847857714472648208 = 2^4 * 3 * 19 * 31^2 * 73 * 218572384991437 * 586194623429865512819516645359676097249515156813669
1045 . 15151640610443533457428395582174705392323922919144158357946775424339137392 = 2^4 * 3 * 31^2 * 328469489473715172073976664545931004863074985239857751429647403406589
1046 . 25293464567433963110384499076694871098476226163410006291088568651921102488 = 2^3 * 3 * 19 * 31 * 16886251 * 1581495610435661 * 164911053796141581211 * 406284997838064176028497473[/code]

This is my first ever (!) escape from 2^4 * 31, and it came just nine lines after I acquired it. Even though it went straight into 2^3 * 3, that one is very easy to escape from in my experience - it is actually less persistent than the downdriver.

10metreh 2009-10-11 08:51

Lines 667 and 670 of sequence 701184 are oddly similar:

[code] 667 . 177286387848755915467003171896178179159030958854732054743450091945986257513367907171821928041364 = 2^2 * 3^3 * 7 * 11 * 199 * 293 * 2081 * 250693 * 65331192259 * 2262270909179549267 * 4741991067576476261927654017720344624117895413853
...
670 . 2021438949074275057896853040743137850595987718393484123165484498834552307908486254143820808598636 = 2^2 * 3^2 * 7 * 11 * 47 * 163 * 2063 * 257893 * 176013952099 * 533779889413141967 * 1904293377948420261416322664999293292768947564238789[/code]

Both of them are divisible by 2^2, 3^2 (although it is 3^3 in line 667), 7 and 11. They both have prime factors between 150 and 200 (667 has an extra factor of 293 and 670 has an extra factor of 47), between 2050 and 2100, and even between 250000 and 258000 (and those two both end in 93). Above this, they have factors of 11 and 12 digits (both ending with 9), and 18 and 19 digits (both ending in 67) respectively. The large cofactors are p49 and p52.

Maybe if we looked at sequences in other bases, we'd find loads more of these...

rodac 2009-10-11 13:01

Hello

another recreational class records

I am looking for the longest sequences who are reaching n digits
My list is uncomplete, there are certainly longer sequences fort a part of them.

an important part of them are side-sequences, and the most little are ending sequences.

If you know "better" sequences, please let me know ! :smile: I'll edit my reply, up to rectify

Reaching:
3 digits: 30 (i6)
4 digits: 138+520 (i7)
5 digits: 180 (i13)
6 digits: 138 (i23)
7 digits: 922252 (i66)
8 digits: 8844 (i119)
9 digits: 8844 (i147)
10 digits: 8844 (i209)
11 digits: 8844 (i214)
12 digits: 8844 (i216)
13 digits: 22734 (i252)
14 digits: 22734 (i258)
15 digits: 22734 (i264)
16 digits: 33552 (i616)
17 digits: 33552 (i620)
18 digits: 33552 (i623)
19 digits: 31482 (i688)
20 digits: 33552 (i807)
21 digits: 33552 (i811)
22 digits: 579480 (i936)
23 digits: 579480 (i942)
24 digits: 579480 (i947)
25 digits: 579480 (i955)
26 digits: 189948+579480 (i970)
27 digits: 579480 (987)
28 digits: 358488 (i1169)
29 digits: 358488 (i1172)
30 digits: 233280 (i1216)
31 digits: 297444 (i1438)
32 digits: 297444 (i1442)
33 digits: 297444 (i1445)
34 digits: 297444 (i1451)
35 digits: 297444 (i1463)
36 digits: 765264 (i1923)
37 digits: 765264 (i1945)
38 digits: 765264 (i1949)
39 digits: 765264 (i1952)
40 digits: 765264 (i1955)
41 digits: 765264 (i1958)
42 digits: 765264 (i1963)
43 digits: 765264 (i1967)
44 digits: 765264 (i1970)
45 digits: 765264 (i1974)
46 digits: 765264 (i1977)
47 digits: 765264 (i1980)
48 digits: 765264 (i1983)
49 digits: 765264 (i1987)
50 digits: 765264 (i1990)
51 digits: 765264 (i1993)
52 digits: 765264 (i1996)
53 digits: 763476 (i2253)
54 digits: 763476 (i3424)
55 digits: 763476 (i3428)
56 digits: 763476 (i3432)
57 digits: 731520 (i3819)
58 digits: 731520 (i3823)
59 digits: 731520 (i3826)
60 digits: 227646 (i4147)
61 digits: 227646 (i4159)
62 digits: 227646 (i4168)
63 digits: 227646 (i4178)
64 digits: 227646 (i4184)
65 digits: 227646 (i4190)
66 digits: 227646 (i4196)
67 digits: 227646 (i4205)
68 digits: 227646 (i4223)
69 digits: 227646 (i4243)
70 digits: 227646 (i4252)
71 digits: 227646 (i4262)
72 digits: 227646 (i4270)
73 digits: 227646 (i4290)
74 digits: 389508 (i4849)
75 digits: 389508 (i4862)
76 digits: 389508 (i6927)
77 digits: 389508 (i6930)
78 digits: 389508 (i6934)
79 digits: 389508 (i6938)
80 digits: 389508 (i6974)
81 digits: 389508 (i6978)
82 digits: 389508 (i6982)
83 digits: 389508 (i6985)
84 digits: 389508 (i7046)
85 digits: 389508 (i7049)
86 digits: 389508 (i7053)
87 digits: 389508 (i7067)
88 digits: 389508 (i7074)
89 digits: 314718 (i8572)
90 digits: 314718 (i8574)
91 digits: 314718 (i8577)
92 digits: 314718 (i8579)
93 digits: 314718 (i8581)
94 digits: 314718 (i8584)
95 digits: 314718 (i8586)
96 digits: 314718 (i8589)
97 digits: 314718 (i8591)
98 digits: 314718 (i8594)
99 digits: 314718 (i8596)
100 digits: 314718 (i8598)

schickel 2009-10-17 04:46

:cool::cool::cool:

And here's the third one, at 133 digits:[code]1617. 2134390794384631128138103307530851968113625211386755303950857993760988778141536341335611817814108590056259067825205204879184058837504 = 2^9 * 3 * 11 * 23 * 31^2 * 8363 * 26725961669999161825177411960621757699 * 25570744721776150163466156594603011284449885586297345250081499429913577034186689459
1618. 4554715592545393510883800490221878991371679408645789636606399298425473469081361444258606401965259036529868527847942849313204918826496 = 2^9 * 3 * 11 * 31^2 * 15855317 * 3431934844399367027129931389745167305493 * 5155134629985305597589873038635034727381118905063583204318430511351841819211411
1619. 9123206389271434528062314811099301096595326324145346171671712648071542240085965287560573341681028925785537542968720231237632827675392 = 2^8 * 3 * 11 * 31 * 37 * 12157 * c109[/code]Turns out the 2^9 (etc.) driver is pretty darn persistent.....and very harsh, adding a digit every 3 lines or so.

Andi47 2009-10-17 07:01

I had forgotten to post [URL="http://www.mersenneforum.org/showpost.php?p=191858&postcount=672"]this one[/URL] also here:

*very* persistent [COLOR="Red"]2[SUP]2[/SUP]*7[/COLOR] driver in sequence [URL="http://factorization.ath.cx/search.php?se=1&aq=565656&action=last20&fr=&to="]565656[/URL], lasting for *at least* 480 lines. (Several times when it was at 2[SUP]2[/SUP]*7[SUP]2[/SUP] or 2[SUP]2[/SUP]*7[SUP]3[/SUP], it failed to escape the driver and went back to 2[SUP]2[/SUP]*7.)

Batalov 2009-10-18 21:46

Yet another steep(-est) sequence? :smile:
[URL]http://factordb.com/aliquot.php?type=1&aq=707778[/URL]

schickel 2009-10-29 05:29

My hardest downdriver start ever (starting at line 1023 in 29772):[code]c133 = 2^2 * 167 * p65 * p66 (!)
c133 = 2^2 * p132
c133 = 2 * 5 * 47 * p60 * p70 (!)
c133 = 2 * 617 * p39 * p41 * p50[/code]Luckily, the p39 came out via ECM. Line 1032, however, is currently running NFS on a c122.... :cry:

10metreh 2009-10-29 07:59

[QUOTE=schickel;194149]My hardest downdriver start ever (starting at line 1023 in 29772):[code]c133 = 2^2 * 167 * p65 * p66 (!)
c133 = 2^2 * p132
c133 = 2 * 5 * 47 * p60 * p70 (!)
c133 = 2 * 617 * p39 * p41 * p50[/code]Luckily, the p39 came out via ECM. Line 1032, however, is currently running NFS on a c122.... :cry:[/QUOTE]

Glad to hear that all those months of work on 29772 have paid off :smile:

schickel 2009-10-30 00:04

[QUOTE=10metreh;194158]Glad to hear that all those [strike]months[/strike] [B]years[/B] of work on 29772 have paid off :smile:[/QUOTE]Actually, I started work on 29772 on or around 8/9/07 at this point:[code]29772 714. 2^3 * 3^3 C99 sz 104[/code]and have been working on it steadily, except for short time outs while resolving downdriver runs on other sequences....

That's why I started the "[strike]Released[/strike] [color=blue]Retired[/color] sequences" thread originally, I envisioned people spending more time on sequences at higher levels.

gd_barnes 2009-10-31 06:16

[quote=Batalov;193198]Yet another steep(-est) sequence? :smile:
[URL]http://factordb.com/aliquot.php?type=1&aq=707778[/URL][/quote]

Got you beat handily with 210222 [URL="http://factorization.ath.cx/search.php?se=1&aq=210222&action=last20&fr=&to"]here[/URL]. It hits 107 digits at i=292 vs. your i=296. :smile: Although, I am going to guess that 707778 may beat (or at least tie) 210222 to 110 digits. 707778 has the terrible 2^3*3*5 driver vs. 210222 that has various unstable guides of 2^2*3, 2^2*3^2, 2^2*3^3, 2^3*3, etc. so 707778 is increasing more rapidly at the moment.

One that was increasing more rapidly at the same time that 707778 was and is probably a better one is 111624 [URL="http://factorization.ath.cx/search.php?se=1&aq=111624&action=range&fr=275&to"]here[/URL]. It hits 107 digits at i=295 to still best 707778 by a single index but still had the horrific 2^5*3*7 driver combined with a consistent factor of 5 to hit 110 digits at an astounding i=303. I continued with 111624 because I never got a hard C>100 until it hit size 114. By that time, "unfortunately" it had dropped the nasty driver in favor of the slowly increasing 2*3 driver.

Therefore, I will claim the following records:
To 110 digits: 111624 at i=303
To 107 digits: 210222 at i=292

That is until someone comes along with a better record. Can anyone top these? :smile:

It is possible that 210222 may hit 110 digits faster due to the unstable guides that could become a driver at any point but it appears doubtful. I had to stop with it at size 107 with a hard C106 at i=295.

Analysis: At their respective current rates of increase, 210222 and 707778 appear that they would only hit size 109 by i=303. Therefore I think that 111624 is the standard to beat to 110 digits. If you have the resources, those two might be interesting to take to at least 110 digits.

I knew advancing some of those sequences from the "shortest sequences" list might prove useful at some point. :smile:


Gary

rodac 2009-11-09 23:33

267240 has probably a record of fastest increasing; reaching:

80 digits at i: 192
90 digits at i: 217
100 digits at i: 248
110 digits at i: 279
115 digits at i: 294

... and why not 120 digits... and more... on the same run... ?

gd_barnes 2009-11-10 00:55

You shattered every record that I have seen. 267240 is an amazingly steep sequence.

Editors note here: We should probably classify this kind of record to more "normalize" the sequences. Otherwise I could start with a 100-digit sequence and say I'm the fastest to 100 digits and likely to 110, 120, etc. Therefore I propose the following for defining the steepest increasing sequences: Subtract the # of digits in the starting sequence to come up with the "number of increased digits". In the case of 267240, it would be 104 "increased digits" at i=279 and 109 increased digits at i=294.

One thing we can likely say for sure now: 267240 is probably the steepest sequence for all sequences < 1M regardless of the above such normalization.

Greebley 2009-11-10 15:07

I think your final point is true for all records. The sequence has to start less than 1 million (maybe someday 2 million?) to be part of the records. Finding a down driver at 161 digits isn't a record if you started at 160 digits for example.

rodac 2009-11-13 14:22

I have found that in the sequence 1576865792 (a multiple of 2^12 * M13)

246 . 95615155791455932871346912618444108138195554304 = 2^12 * 3^4 * 2879 * 8191 * 62299 * 8374739 * 29587193 * 791675232007057
247 . 190153732022250349964985901560333145395254685696 = 2^12 * 3^4 * 467 * 8191^2 * 194687 * 93957661943418129687790579
248 . 379179337312086710293691976503037057120353470464 = 2^11 * 3^4 * 1571 * 8191 * 177630108496290212528975772739516973
249 . 754260160665184128947212768516987905021923014656 = 2^11 * 3^4 * 71 * 103 * 195202003 * 1128513979 * 2822405513685538750327

a 2^12 * 8191 escape ! :smile:

Andi47 2009-11-13 14:33

[QUOTE=rodac;195706]I have found that in the sequence 1576865792 (a multiple of 2^12 * M13)

246 . 95615155791455932871346912618444108138195554304 = 2^12 * 3^4 * 2879 * 8191 * 62299 * 8374739 * 29587193 * 791675232007057
247 . 190153732022250349964985901560333145395254685696 = 2^12 * 3^4 * 467 * 8191^2 * 194687 * 93957661943418129687790579
248 . 379179337312086710293691976503037057120353470464 = 2^11 * 3^4 * 1571 * 8191 * 177630108496290212528975772739516973
249 . 754260160665184128947212768516987905021923014656 = 2^11 * 3^4 * 71 * 103 * 195202003 * 1128513979 * 2822405513685538750327

a 2^12 * 8191 escape ! :smile:[/QUOTE]

WOOOW!! :w00t:

rodac 2009-11-13 14:49

[quote=Andi47;195708]WOOOW!! :w00t:[/quote]
I think it's possible to find others 2^8191 escapes...
Take odd multiples of 2^12 * 8191 (who are not already computed) and run them with aliqueit...

I have put the sequence 1576865792 into the DB.

Friday 13, my day of chance... :smile:

10metreh 2009-11-13 16:27

[QUOTE=rodac;195706]I have found that in the sequence 1576865792 (a multiple of 2^12 * M13)

246 . 95615155791455932871346912618444108138195554304 = 2^12 * 3^4 * 2879 * 8191 * 62299 * 8374739 * 29587193 * 791675232007057
247 . 190153732022250349964985901560333145395254685696 = 2^12 * 3^4 * 467 * 8191^2 * 194687 * 93957661943418129687790579
248 . 379179337312086710293691976503037057120353470464 = 2^11 * 3^4 * 1571 * 8191 * 177630108496290212528975772739516973
249 . 754260160665184128947212768516987905021923014656 = 2^11 * 3^4 * 71 * 103 * 195202003 * 1128513979 * 2822405513685538750327

a 2^12 * 8191 escape ! :smile:[/QUOTE]

I wonder whether Cilfford will count that as a proper record :razz:

henryzz 2009-11-13 18:39

[quote=10metreh;195730]I wonder whether Cilfford will count that as a proper record :razz:[/quote]
the starting number is probably a bit high
i expect it has to be <1M

10metreh 2009-12-18 17:46

A nice ECM factor from 669696:3853 just popped up:

[code][Dec 18 2009, 16:51:36] c89: running 353 ecm curves at B1=25e4...
Using B1=250000, B2=128992510, polynomial Dickson(3), sigma=3333392745
Step 1 took 3578ms
Step 2 took 2172ms
********** Factor found in step 2: 1345784422944376323441464979454015733
[Dec 18 2009, 17:28:09] *** prp37 = 1345784422944376323441464979454015733[/code]

Found at quite a low B1. :smile:

The group order was:[code][ <2, 3>, <3, 3>, <7, 1>, <11, 1>, <79, 1>, <293, 1>, <379, 1>, <9781, 1>,
<41593, 1>, <106531, 1>, <111323, 1>, <1911757, 1> ]
[/code]


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