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-   -   Largest 10^147-c Brilliant Number (p74*p74) (https://www.mersenneforum.org/showthread.php?t=26008)

 swishzzz 2021-01-04 05:45

base 2 brilliant numbers

3 Attachment(s)
All found before November 2018.

[CODE]
2^305 + 47261 =
7316490771476709190807652965574102572379302277 *
8909346472058358236842543861359565227710116409

2^307 - 19027 =
11775430370240476555096243348888791129599911451 *
22142766486885472775913011741866569768555016151

2^307 + 371 =
14049124283454209175234576558264433714634147209 *
18559206944869223986131361958393223284004342811
[/CODE]

 swishzzz 2021-01-11 00:34

2 Attachment(s)

[CODE]
2^309-31899 =
24781986941524378779451719636879394253653915667 *
42085504376393744737222716439904864143412540839

2^309+19499 =
23517014357815368443003507125370993433302283221 *
44349270022733603968886915824049811627149524991
[/CODE]

 Alfred 2021-01-22 09:28

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
[/CODE]

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

 Alfred 2021-02-13 09:34

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
[/CODE]

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.

 swishzzz 2021-02-26 19:55

base 2 brilliant numbers

1 Attachment(s)
[QUOTE]
2^317 - 3369 =
436065321852177727665353843557839743263823284547 *
612289870600221313399896732319435654464341654749
[/QUOTE]

A couple more found by Branger on 2020/12/30 which I don't have proof files for that are not listed on [url]https://www.alpertron.com.ar/BRILLIANT2.HTM#twobr:[/url]

[QUOTE]
2^313 - 24133 =
100788170265999753017323085706257528483989089343 *
165569021385057306060482886322484491911556750213

2^313 + 8505 =
118458567629160086527486150975362030803169102833 *
140871184348377129067049239080578375237738238409

2^315 - 19015 =
216834485254286594903496585433315946327767764161 *
307836619227101788652208469732562326355490574073

2^315 + 42701 =
228669422455046776001485409864826671274859838381 *
291904331396343474258089280492317954768687954849
[/QUOTE]

 Branger 2021-02-26 20:08

5 Attachment(s)
[QUOTE=swishzzz;572611]A couple more found by Branger on 2020/12/30 which I don't have proof files for that are not listed on [url]https://www.alpertron.com.ar/BRILLIANT2.HTM#twobr:[/url][/QUOTE]

It seems I forgot to post the proof files I had, thank you for the reminder.

 Alfred 2021-03-24 09:13

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
[/CODE]

PS: 10^201-c is ongoing (with low priority).

 Branger 2021-03-24 21:00

2 Attachment(s)
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

[/CODE]

Proof files are attached.

 bur 2021-04-03 10:05

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

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

 Alfred 2021-04-15 18:00

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
[/CODE]

I'm in doubt about any extension of this table.

PS: I've downgraded 10^201-c to very low priority.

 swishzzz 2021-04-24 23:21

smallest 340 bit brilliant number

1 Attachment(s)
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
[/CODE]

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