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Old 2021-01-04, 05:45   #23
swishzzz
 
Jan 2012
Toronto, Canada

5×19 Posts
Default base 2 brilliant numbers

All found before November 2018.

Code:
2^305 + 47261 =
7316490771476709190807652965574102572379302277 *
8909346472058358236842543861359565227710116409

2^307 - 19027 =
11775430370240476555096243348888791129599911451 *
22142766486885472775913011741866569768555016151

2^307 + 371 =
14049124283454209175234576558264433714634147209 *
18559206944869223986131361958393223284004342811
Attached Files
File Type: txt 306b_brilliant.txt (35.9 KB, 102 views)
File Type: txt 307b_brilliant.txt (14.8 KB, 111 views)
File Type: txt 308b_brilliant.txt (458 Bytes, 110 views)
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Old 2021-01-11, 00:34   #24
swishzzz
 
Jan 2012
Toronto, Canada

5×19 Posts
Default

Adding 2^309±c to the above:

Code:
2^309-31899 =
24781986941524378779451719636879394253653915667 *
42085504376393744737222716439904864143412540839

2^309+19499 =
23517014357815368443003507125370993433302283221 *
44349270022733603968886915824049811627149524991
Attached Files
File Type: txt 309b_brilliant.txt (25.2 KB, 105 views)
File Type: txt 310b_brilliant.txt (14.9 KB, 112 views)
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Old 2021-01-22, 09:28   #25
Alfred
 
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May 2013
Germany

10101112 Posts
Default Largest 10^n - c with exactly five equally sized prime factors

The solutions for some smaller n are as follows.

Code:
 n       c          p          q          r          s          t
======================================================================
 41  423906303  103948841  114710363  149953891  203482813  274847773
 39  170690097   47957491   57090881   62357359   72085207   81253661
 38   17945273   14859149   26589149   49138601   69387613   74232979
 37    3737967   12265069   12316999   26021071   28269503   89987411
 36  117140009   11983739   11997917   13976143   19075949   26087251
 34    8846847    3448663    4321529    7868789    9038629    9434119
 33     992687    1743487    3112091    5050681    5613833    6500093
 32    6088257    1679213    1796947    2128781    2156351    7219523
 31    5846847    1022701    1176899    1384829    2319659    2586377
 29   13773393     303871     689957     709909     747157     899237
 28     575559     231269     236563     445649     486821     842507
 27    2939079     107837     133669     157349     468113     941861
 26   13996773     104471     105361     150889     219017     274909
 24    2962853      21961      65563      79309      92623      94547
 23    3227433      10253      45673      46573      61729      74279
 22    1218891      11807      15391      22189      35809      69257
 21    3964821      10007      13537      16811      16921      25951
 19    6735117       3041       4129       8581       9433       9839
 18     343229       1583       2707       3691       6577       9613
 17     416447       1327       1483       3001       3371       5023
 16    1176773       1033       1229       1319       1447       4127
 14     495633        181        751        859        859        997
 13      50327        281        293        347        571        613
 12      59901        131        131        211        277        997
 11     423887        101        103        113        257        331
  9     797979         41         61         67         67         89
  8       4317         17         29         43         53         89
  7       5411         11         17         19         29         97
Lines for the smallest n are written for the sake of completeness only.

I was not able to compute the results for the larger n by an algorithm -
firstly caused by the very low level of my programming knowledge but
secondly maybe by the running time of a well written program?

I'd like to get a rough estimation.

PS: Continuing with 10^201-c

Last fiddled with by Alfred on 2021-01-22 at 09:32
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Old 2021-02-13, 09:34   #26
Alfred
 
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May 2013
Germany

3·29 Posts
Default The Big Four

I've found the largest four 67-digit numbers with exactly four equally sized prime factors.

In 10^67 - c representation:

Code:
     c               p                   q                   r                   s         
===========================================================================================
 139852557   31431974044879763   46128143017681421   70125424881114271   98352831098894971 
 171158457   33992983359529783   34882916747820623   90179687845567937   93516705612649471 
 183261399   38966262167041379   40234767205193857   71686576788802147   88975803112152161 
 188505137   28896480880207309   43989844864448881   88028052195229997   89367893515033351
The size of my proving file exceeds the 4.00 MB limit for .7z attachments by far.

PS: I do not forget about 10^201 - c.
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Old 2021-02-26, 19:55   #27
swishzzz
 
Jan 2012
Toronto, Canada

5F16 Posts
Default base 2 brilliant numbers

Quote:
2^317 - 3369 =
436065321852177727665353843557839743263823284547 *
612289870600221313399896732319435654464341654749
A couple more found by Branger on 2020/12/30 which I don't have proof files for that are not listed on https://www.alpertron.com.ar/BRILLIANT2.HTM#twobr:

Quote:
2^313 - 24133 =
100788170265999753017323085706257528483989089343 *
165569021385057306060482886322484491911556750213

2^313 + 8505 =
118458567629160086527486150975362030803169102833 *
140871184348377129067049239080578375237738238409

2^315 - 19015 =
216834485254286594903496585433315946327767764161 *
307836619227101788652208469732562326355490574073

2^315 + 42701 =
228669422455046776001485409864826671274859838381 *
291904331396343474258089280492317954768687954849
Attached Files
File Type: txt 317b_brilliant.txt (2.9 KB, 83 views)
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Old 2021-02-26, 20:08   #28
Branger
 
Oct 2018

2·3·5 Posts
Default

Quote:
Originally Posted by swishzzz View Post
A couple more found by Branger on 2020/12/30 which I don't have proof files for that are not listed on https://www.alpertron.com.ar/BRILLIANT2.HTM#twobr:
It seems I forgot to post the proof files I had, thank you for the reminder.
Attached Files
File Type: txt 2_311_minus_factored.txt (20.4 KB, 89 views)
File Type: txt 2_311_plus_factored.txt (166.2 KB, 87 views)
File Type: txt 2_313_minus_factored.txt (54.0 KB, 92 views)
File Type: txt 2_313_plus_factored.txt (19.1 KB, 95 views)
File Type: txt 2_315_plus_and_minus_factored.txt (138.4 KB, 87 views)
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Old 2021-03-24, 09:13   #29
Alfred
 
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May 2013
Germany

3·29 Posts
Default Largest 10^n - c with exactly five equally sized prime factors, part 2

The solutions for n = 42, 43, 44 are as follows.

Code:
 n       c          p          q          r          s          t
======================================================================
 44 1561244849  182407289  762137381  766498163  960663391  976882183
 43   15301041  104012933  175136021  748629481  781365433  938460631
 42   46553637  108481379  192785767  207688121  301662217  763198063
PS: 10^201-c is ongoing (with low priority).
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Old 2021-03-24, 21:00   #30
Branger
 
Oct 2018

2·3·5 Posts
Default

I tried to look for brilliant numbers of the form 2^351+-c, and at least these ones were not in the factordb previously.

Code:
2^351-37629
=
54108213336623751930603114360343420697261006546122961
*
84774509249511338538855788282246318289861325315685779


2^351+74939
=
64719303637275716983586303735926609113831544522059491
*
70875256286568216854922693686888410014999992674845257
Proof files are attached.
Attached Files
File Type: txt 2_351_minus_factored.txt (85.3 KB, 74 views)
File Type: txt 2_351_plus_factored.txt (169.6 KB, 77 views)
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Old 2021-04-03, 10:05   #31
bur
 
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Aug 2020
79*6581e-4;3*2539e-3

22·3·5·7 Posts
Default

While doing aliquot factoring I came across this humble C114 = P57 * P57:

Code:
140257568274260684468077810723210454538642881063207195453406733448965467421304070266933449577747915090059669116521
=
455667808354640170880989459219806232327469502542982654137
* 
307806620750132280327670158666075502855210576269751690033
Yes, I know I could just have created this on the fly, but I didn't... ;)

Last fiddled with by bur on 2021-04-03 at 10:05
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Old 2021-04-15, 18:00   #32
Alfred
 
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May 2013
Germany

3·29 Posts
Default Largest 10^n - c with exactly five equally sized prime factors, part 3

The solutions for n = 46, 47, 48, 49 are as follows.
Code:
 n       c          p          q          r          s          t
======================================================================
 49  292349261  4199063917 6046596823 6692964461 7518662791 7826676379
 48   19443339  1039529507 4173506713 4220264131 6326926399 8632362059
 47   84075503  1186228591 2527734631 2889263309 3333025919 3463174067
 46  360258269  1055755553 1528954747 1668451013 1794793691 2068778527
I'm in doubt about any extension of this table.

PS: I've downgraded 10^201-c to very low priority.
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Old 2021-04-24, 23:21   #33
swishzzz
 
Jan 2012
Toronto, Canada

9510 Posts
Default smallest 340 bit brilliant number

Test run of Amazon EC2 free tier. A 103 digit snfs job with factmsieve.py takes around 2.5 hours on a single t2 micro Windows instance running at 10% CPU capacity, perhaps this will be faster on a Linux instance with CADO.

Code:
2^339 + 15885

Sat Apr 24 15:56:40 2021  p51 factor: 887592350957138861091733941658539740396245192826267
Sat Apr 24 15:56:40 2021  p52 factor: 1261696734859514200896533536322632897894845904544119
Attached Files
File Type: txt 340b_brilliant.txt (12.3 KB, 63 views)
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