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 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!

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