Odds and ends....and class records

schickel · 2009-04-01, 09:38

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

That's two lines longer than my shortest downdriver run.....

schickel · 2009-04-09, 10:12

Here's a 128-digit capture by KriZp:

Code:

 1195 .  10266795638504310153366052072949189423898628478681852217099800647077404391348760648124591000211167976820485517782454441169150528 = 2^6 * 160418681851629846146344563639831084748416069979403940892184385110584443614824385126946734378299499637820086215350850643267977
 1196 .  10106376956652680307219707509309358339150212408702448276207616261966819947733936262997644265832868477182665431567103590525882678 = 2 * 49908941 * 6547758143 * 24298326971 * 693448787987 * 993189769000280189449 * 923999020028519876669775331353117572879545168715632128589735537361

Let's hope this one lives long and prospers!

schickel · 2009-04-09, 10:16

'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

This one, at 134-digits, even beats the 133-digit capture by Benoit Chevallier-Mames on January 12, 2007.

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

schickel · 2009-04-09, 10:28

Quote:

Originally Posted by 10metreh

What about Max's record escape from 2^6*127 in 102264?

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 $2^2*7$ 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

*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

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

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

schickel · 2009-04-09, 11:01

Here's one from 199272:

Code:

 2095 .  2147785522605617415661440711907256925999066718859981278417040166273887305703138475537897306932055568178379687763148870119800 = 2^3 * 3^2 * 5^2 * 11^2 * 17 * 857 * 5019031 * 22779667 * 217660441 * 9124624542949 * 2980859693341733136462976890706924039328597916183558908199934985818466811719023

Although this actually isn't quite that rare....

schickel · 2009-04-09, 11:04

Here's one from 110432:

Code:

 1613 .  883866359463668463521525972362866107318450543014047075048557464839182863055364072700728788483776 = 2^6 * 17 * 439 * 1607^2 * 1733309 * 413414251171984964928943833274782930952904102537554377365457011053267334799073

10metreh · 2009-04-09, 14:04

Quote:

Originally Posted by schickel

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

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

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