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Old 2009-05-15, 17:46   #34
10metreh
 
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Just had this line on 130396:

Code:
 2557 .  163578642999558897088906278322349716599304624344566325723055390699749040946044926484 = 2^2 * 211 * 10520648737 * 28132601993 * 479625488021 * 16757310841163 * 2032239779294017 * 40091306001026532281
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.

Last fiddled with by 10metreh on 2009-05-15 at 17:48
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Old 2009-05-17, 17:26   #35
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Default 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
2*17^2*p ends a downdriver run:

Code:
 2460 .  1076137657345800977469076260397107776458443388373537225658678638233839818618389284938 = 2 * 17^2 * 1861829856999655670361723633905030755118414166736223573803942280681383769235967621
 2461 .  638607640950881894934071206429425549005616059190524685814752202273714632847936894924 = 2^2 * 1471 * 8111 * 244507 * 54726257307773669403264381948767969874032413723951484902441390683263993
(Those two were computed by me, but they came up before the recent line-fest.)

Isn't it called the downdriver?

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
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
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
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
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
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
That 2*3 driver has now controlled the sequence for 336 lines, pushing it up 34 digits, and shows no signs of disappearing.
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Old 2009-05-21, 16:22   #36
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Also just spotted a high power of 7 from 130396 early on:

Code:
 134 .   1496179015544699150407849596 = 2^2 * 3 * 7^7 * 1031 * 35837 * 4097563770073
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Old 2009-05-21, 22:01   #37
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Default 4-digit prime squared: 2347^2

from n=3556 index 565:

Code:
396495022821789424734925007122343803121687465535009958098753728242418890 =  2 · 5 · 223 · 2347^2 · 115236367295669 · 186741022326241 · 1499952155963476622428538885793563
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Old 2009-05-24, 19:12   #38
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This one isn't related to the sequences, but the numbers that popped up in them. On 130396.4783, I QSed this C92:

Code:
16665913756850552081806634468279185067944988818001927397673235891862519760250370300401898953
Now, on line 4798 of the same sequence, I have a QS in progress on this C92:

Code:
16565961998929465569973995569231458754642250175304700075799691858447072215496139303052210961
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!
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Old 2009-05-26, 06:41   #39
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Default 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
Talk about a lucky escape!
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Old 2009-05-26, 06:50   #40
10metreh
 
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Quote:
Originally Posted by schickel View Post
I was just looking over the work I've done, and it turns out I didn't really notice this one <snip>
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.)
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Old 2009-05-26, 07:01   #41
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Quote:
Originally Posted by 10metreh View Post
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.)
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.....
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Old 2009-05-26, 09:29   #42
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Quote:
Originally Posted by schickel View Post
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.....
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.
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Old 2009-06-01, 00:49   #43
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Default smoothest graph

here is an example of a very smooth graph:

232680

almost straight line from 6 upto 105 digits!
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Old 2009-06-01, 00:57   #44
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Default 49-digit twin-pair factor in 2 consecutive indices

here is one remarkable from sequenz 271740:

index 250 to 252:

Code:
 250 .	 43827131606920639860265504690937848330149198375812 = 2^2 * 7 * 1565254700247165709295196596104923154648185656279
 251 .	 43827131606920639860265504690937848330149198375868 = 2^2 * 7 * 1565254700247165709295196596104923154648185656281
 252 .	 43827131606920639860265504690937848330149198375924 = 2^2 * 3 * 7^3 * 131 * 4327 * 257561021 * 72933885846923222248446787566457
two 49-digit twin-pair-factors at index 250 and 251 and

3 consecutive indices with very small differences!

Last fiddled with by kar_bon on 2009-06-01 at 00:58
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