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

 Alfred 2020-09-26 07:55

Largest 10^147-c Brilliant Number (p74*p74)

1 Attachment(s)
[QUOTE]10^147-28239 = p74 * p74,
10749227813857812842560638866039571941385856753480714536650423387382761653
93029938272478375299202950793413839971743799143685170784039618216410820237
[/QUOTE]

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 [url]https://www.alpertron.com.ar/BRILLIANT.HTM[/url] is missing this number,
I hope it is new.

 Alfred 2020-09-29 07:01

Largest 10^151-c Brilliant Number (p76*p76)

1 Attachment(s)
[QUOTE]10^151 - 13731 = p76 * p76
2957232918876522618810099296027476287595656664821641247443138343849506540789
3381539525063545948219909981524129301893159430786891936664579050739840837321
[/QUOTE]

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.

[url]https://www.alpertron.com.ar/BRILLIANT.HTM[/url] does not show this number yet.

 swishzzz 2020-09-30 01:16

Could I reserve 152 digits? I've already begun sieving and am about 10 SNFS factorizations in.

 Alfred 2020-09-30 06:18

Yes, of course.

I'd like to take the numbers 10^153-c.

 Alfred 2020-10-06 20:32

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

1 Attachment(s)
[QUOTE]
10^153 - 24783 = p77 * p77
19616824731935528323413429323217946126629367330558378295828024144442130486423
50976649568165522929056351388822365973469595971165560920473974037361186978679
[/QUOTE]

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.

[url]https://www.alpertron.com.ar/BRILLIANT.HTM[/url] does not show this number yet.

 swishzzz 2020-10-11 17:56

1 Attachment(s)
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 [url]https://www.alpertron.com.ar/BRILLIANT.HTM[/url], 10^35-783 = 290795768932439557 * 343883958033904381 is a larger 35 digit brilliant number.

Reserving 10^155+c (156 digits).

 Alfred 2020-10-15 14:46

Largest 10^86 - c 3-Brilliant Number (p29 * p29 * p29)

1 Attachment(s)
[QUOTE]
10^86 - 2007389 splits as p29 * p29 * p29
33967693446721619162411558729
46163945373677107485245801167
63772144891696172285401983877
[/QUOTE]

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.

 swishzzz 2020-10-19 13:53

1 Attachment(s)
10^155+7213 is the smallest 156-digit number that factors into two 78-digit primes:

[QUOTE]
p78 factor: 211747224607852036333730181480768862317143398243227651081775505848031153848949
p78 factor: 472261207603529495511913284148545388735587409943720544148422568230650370558937
[/QUOTE]

Factor file for 10^155+c attached.

 swishzzz 2020-10-25 03:27

1 Attachment(s)
2^303 - 39727 is the largest 303-bit number that splits into two 152-bit primes:

[CODE]
p46 factor: 3755140210209107891033403488267039571419053517
p46 factor: 4339728185480567523635423762618623528383356693
[/CODE]

 swishzzz 2020-10-31 18:20

3 Attachment(s)
A few more 2-bit brilliant numbers:

[CODE]
2^297 - 7405 =
465449598594965125759568006862384515773478687 *
547061374229242156241055675491722178284755341

2^297 + 4301 =
447742596479348597082150804288878401042937171 *
568696163920948572072084351914463588415143263

2^299 - 31527 =
1006551460876452757803140363636308794862182167 *
1011888639335310739700404874667161763668291983
[/CODE]

 swishzzz 2020-11-02 14:02

2 Attachment(s)
Remaining base 2 brilliant numbers below 2^300:

[CODE]
2^295 - 13429 =
198510202319234021827282742860868097914815709 *
320675579978917834648228904658346016622753671

2^295 + 175343 =
199744320796412845995530912316777151860992621 *
318694288812019609071170106942006301252918091
[/CODE]

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)
[/CODE]

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