mersenneforum.org Largest 10^147-c Brilliant Number (p74*p74)
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2020-09-26, 07:55   #1
Alfred

May 2013
Germany

2×43 Posts
Largest 10^147-c Brilliant Number (p74*p74)

Quote:
 10^147-28239 = p74 * p74, 10749227813857812842560638866039571941385856753480714536650423387382761653 93029938272478375299202950793413839971743799143685170784039618216410820237
No 10^147-c with c>0 smaller than 28239 splits as p74*p74.

The attached file shows one factor (prime or composite but with less digits)
for any of these c's - or it indicates that 10^147-c is prime.

Since https://www.alpertron.com.ar/BRILLIANT.HTM is missing this number,
I hope it is new.
Attached Files
 147odd.ok.txt (173.5 KB, 152 views)

2020-09-29, 07:01   #2
Alfred

May 2013
Germany

2×43 Posts
Largest 10^151-c Brilliant Number (p76*p76)

Quote:
 10^151 - 13731 = p76 * p76 2957232918876522618810099296027476287595656664821641247443138343849506540789 3381539525063545948219909981524129301893159430786891936664579050739840837321
No 10^151-c with c>0 smaller than 13731 splits as p76*p76.

The attached file shows one factor (prime or composite but with less digits)
for any of these c's - or it indicates that 10^151-c is prime.

https://www.alpertron.com.ar/BRILLIANT.HTM does not show this number yet.
Attached Files
 151odd.ok.txt (79.0 KB, 190 views)

 2020-09-30, 01:16 #3 swishzzz   Jan 2012 Toronto, Canada 5·19 Posts Could I reserve 152 digits? I've already begun sieving and am about 10 SNFS factorizations in.
 2020-09-30, 06:18 #4 Alfred     May 2013 Germany 2·43 Posts Yes, of course. Thank you for your information. I'd like to take the numbers 10^153-c.
2020-10-06, 20:32   #5
Alfred

May 2013
Germany

8610 Posts
Largest 10^153-c Brilliant Number (p77*p77)

Quote:
 10^153 - 24783 = p77 * p77 19616824731935528323413429323217946126629367330558378295828024144442130486423 50976649568165522929056351388822365973469595971165560920473974037361186978679
No 10^153-c with c>0 smaller than 24783 splits as p77*p77.

The attached file shows the smallest prime factor
for any of these c's - or it indicates that 10^153-c is prime.

https://www.alpertron.com.ar/BRILLIANT.HTM does not show this number yet.
Attached Files
 153odd.ok.txt (127.6 KB, 139 views)

2020-10-11, 17:56   #6
swishzzz

Jan 2012

5·19 Posts

10^151+14541 =
1892066823280306942402672399836621036921105169101702440417171708556479073929 *
5285225594021482704171643427873368811118569345423620874203438445689349531429

Factors of all n=10^151+c with c < 14541 and n either prime or with no prime factors < 20M attached in the file.

Also the entry for 35 on here is incorrectly listed on https://www.alpertron.com.ar/BRILLIANT.HTM, 10^35-783 = 290795768932439557 * 343883958033904381 is a larger 35 digit brilliant number.

Reserving 10^155+c (156 digits).
Attached Files
 152_brilliant.txt (15.2 KB, 133 views)

2020-10-15, 14:46   #7
Alfred

May 2013
Germany

2×43 Posts
Largest 10^86 - c 3-Brilliant Number (p29 * p29 * p29)

Quote:
 10^86 - 2007389 splits as p29 * p29 * p29 33967693446721619162411558729 46163945373677107485245801167 63772144891696172285401983877
10^86 - 2007389 is the largest 86-digit number with three 29-digit prime factors.

The appended file proves this.

Any line (except the last one) has exactly two entries.

The first shows c.

The second is either the letter 'p' (indicating that 10^86-c is prime) or
a prime factor of 10^86 - c with length different from 29.

The file contains a line for any odd 1 <= c <= 2007389, of course.
Attached Files
 86odd.ok.txt.7z (2.54 MB, 138 views)

2020-10-19, 13:53   #8
swishzzz

Jan 2012

5×19 Posts

10^155+7213 is the smallest 156-digit number that factors into two 78-digit primes:

Quote:
 p78 factor: 211747224607852036333730181480768862317143398243227651081775505848031153848949 p78 factor: 472261207603529495511913284148545388735587409943720544148422568230650370558937
Factor file for 10^155+c attached.
Attached Files
 156_brilliant.txt (8.2 KB, 123 views)

2020-10-25, 03:27   #9
swishzzz

Jan 2012

5F16 Posts

2^303 - 39727 is the largest 303-bit number that splits into two 152-bit primes:

Code:
p46 factor: 3755140210209107891033403488267039571419053517
p46 factor: 4339728185480567523635423762618623528383356693
Attached Files
 303b_brilliant.txt (35.6 KB, 121 views)

2020-10-31, 18:20   #10
swishzzz

Jan 2012

5×19 Posts

A few more 2-bit brilliant numbers:

Code:
2^297 - 7405 =
465449598594965125759568006862384515773478687 *
547061374229242156241055675491722178284755341

2^297 + 4301 =
447742596479348597082150804288878401042937171 *
568696163920948572072084351914463588415143263

2^299 - 31527 =
1006551460876452757803140363636308794862182167 *
1011888639335310739700404874667161763668291983
Attached Files
 297b_brilliant.txt (6.7 KB, 105 views) 298b_brilliant.txt (3.8 KB, 110 views) 299b_brilliant.txt (28.7 KB, 109 views)

2020-11-02, 14:02   #11
swishzzz

Jan 2012

5×19 Posts

Remaining base 2 brilliant numbers below 2^300:

Code:
2^295 - 13429 =
198510202319234021827282742860868097914815709 *
320675579978917834648228904658346016622753671

2^295 + 175343 =
199744320796412845995530912316777151860992621 *
318694288812019609071170106942006301252918091
2^295 + c took an unusually long time with nearly 700 SNFS factorizations and 8 p45*p45 (147-bit * 149-bit) near misses before one was finally found:

Code:
17679 135424819131071650335816726305171046618468269 (45 digits)
28295 125056028398373651690810269127016407925857333 (45 digits)
68783 137665243947612845545922338816114028907278423 (45 digits)
90429 129289940650813391118621997356910828821798721 (45 digits)
112521 131584492955893608563695147526439257589143029 (45 digits)
124865 119468736668192803702619666384916214225482473 (45 digits)
148539 123275618234627848456962842180515532135679871 (45 digits)
165689 177963429546572797306584739591706914778068901 (45 digits)
Attached Files
 295b_brilliant.txt (9.9 KB, 114 views) 296b_brilliant.txt (141.8 KB, 125 views)

Last fiddled with by swishzzz on 2020-11-02 at 14:03

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