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-   -   Smallest 10^179+c Brilliant Number (p90 * p90) (https://www.mersenneforum.org/showthread.php?t=24759)

 2147483647 2019-09-09 01:32

Smallest 10^179+c Brilliant Number (p90 * p90)

Brilliant numbers are semiprimes where both prime factors have the same number of digits.

According to [url=https://www.alpertron.com.ar/BRILLIANT.HTM]this table[/url], the smallest n such that the smallest n digit brilliant number is unknown is n=146. For the past ~2.5 weeks I've being doing a bunch of SNFS and I just found it:

10^145 + 26019 =
1712231579162695023146424005134362656947458223008859385200062175608237361 *
5840331484185181666946526399283426386742617220393273278243146252757154579

I've actually sieved all the unfactored numbers out to c = ~38k but fell behind on the postprocessing until yesterday. Took ~150 SNFS runs to find I think, although ~20 of those were with c > 26019 because c = 26019 and a few others got missed for a while because they were undersieved.

I found a few near-misses for c < 26019. There was a p72 * p74 at c = 8599 (and another at c = 32973), and a few p71 * p75s too.

 a1call 2019-09-09 01:56

Forgive my ignorance, but why would it be considered unknown?

There are plenty of known 73 dd prime numbers that are very likely to result in a 146 dd semiprime:

[url]http://factordb.com/listtype.php?t=4&mindig=73&perpage=100&start=0[/url]

What am I misunderstanding here?

 VBCurtis 2019-09-09 02:37

[QUOTE=a1call;525533]Forgive my ignorance, but why would it be considered unknown?
[/QUOTE]
Ponder the meaning of "smallest" in "smallest brilliant number of n digits."

 a1call 2019-09-09 02:56

Acknowledged,
Thank you very much.:smile:

 rudy235 2019-09-09 03:17

I would clarify further and call it "smallest possible".

 henryzz 2019-09-09 08:09

Can I suggest looking at the [URL="https://mersenneforum.org/showthread.php?t=24729"]factorization factory[/URL] if you want to do more of these. A lot of the work can be shared between numbers. I would think that a degree 2 or 3 poly with a common rational poly would make sense here.

 xilman 2019-09-09 09:04

[QUOTE=2147483647;525530]Brilliant numbers are semiprimes where both prime factors have the same number of digits.

According to [url=https://www.alpertron.com.ar/BRILLIANT.HTM]this table[/url], the smallest n such that the smallest n digit brilliant number is unknown is n=146. For the past ~2.5 weeks I've being doing a bunch of SNFS and I just found it:

10^145 + 26019 =
1712231579162695023146424005134362656947458223008859385200062175608237361 *
5840331484185181666946526399283426386742617220393273278243146252757154579[/QUOTE]Congratulations.

It's about time I set the upper limit again.

Paul

 fivemack 2019-09-11 22:19

Well, that was indecently lucky ...

10^179+1039 =

[code]
p90 factor: 140837725563903108928160798541416779343987069101706278981482452086290437833772503658895889
p90 factor: 710037027363285744751511636041030962532956891436161203659956860276022774234895368099896351
[/code]

10^179+n for n<1039 is either prime, or divisible by a prime <2^23, or divisible by a prime in the list below

[code]
19 14101387
49 14147552822097691663
57 35782408050786092825897707
103 3108967483
109 383943298877
141 706598062641397
231 1451243290927197419514136787
237 2500422969821983
253 106469781304792106087
301 974764229
333 900576964916303
369 10571453393
391 10206877
469 17093751491
481 29314808171939
487 99321412503984693433
559 70893363894244915493
627 96071164333023421
631 1677873931457
657 8969231
757 735502689743
769 11193310726676637973
811 69672262968268248649729
823 1144280823821
829 8505508806737
879 37531709701
889 794674405363
901 22545947828834902287109968139
937 420490046629
993 57163357
1033 3191058343795684819
[/code]

A few core-months of ECM, and this was the second SNFS job (about 700k thread-seconds sieving)

 lavalamp 2019-09-17 06:30

[QUOTE=rudy235;525536]I would clarify further and call it "smallest possible".[/QUOTE]Do you think that merely calling it the smallest would leave open the possibility of finding a smallester one?

 VBCurtis 2019-09-17 06:33

[QUOTE=lavalamp;525972]Do you think that merely calling it the smallest would leave open the possibility of finding a smallester one?[/QUOTE]

smallest possible versus smallest known. In other contexts, a useful distinction.

 rudy235 2019-09-17 07:20

[QUOTE=VBCurtis;525973]smallest possible versus smallest known. In other contexts, a useful distinction.[/QUOTE]

Yes.

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