20190909, 01:32  #1 
Dec 2016
12_{16} Posts 
Smallest 10^179+c Brilliant Number (p90 * p90)
Brilliant numbers are semiprimes where both prime factors have the same number of digits.
According to this table, 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 nearmisses for c < 26019. There was a p72 * p74 at c = 8599 (and another at c = 32973), and a few p71 * p75s too. 
20190909, 01:56  #2 
"Rashid Naimi"
Oct 2015
Remote to Here/There
11110111101_{2} Posts 
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: http://factordb.com/listtype.php?t=4...ge=100&start=0 What am I misunderstanding here? Thanks in advance. 
20190909, 02:37  #3 
"Curtis"
Feb 2005
Riverside, CA
2·3·769 Posts 

20190909, 02:56  #4 
"Rashid Naimi"
Oct 2015
Remote to Here/There
7·283 Posts 
Acknowledged,
Thank you very much. 
20190909, 03:17  #5 
Jun 2015
Vallejo, CA/.
970_{10} Posts 
I would clarify further and call it "smallest possible".

20190909, 08:09  #6 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
2·2,897 Posts 
Can I suggest looking at the factorization factory 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.

20190909, 09:04  #7  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
3^{3}·389 Posts 
Quote:
It's about time I set the upper limit again. Paul 

20190911, 22:19  #8 
(loop (#_fork))
Feb 2006
Cambridge, England
14351_{8} Posts 
Well, that was indecently lucky ...
10^179+1039 =
Code:
p90 factor: 140837725563903108928160798541416779343987069101706278981482452086290437833772503658895889 p90 factor: 710037027363285744751511636041030962532956891436161203659956860276022774234895368099896351 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 Last fiddled with by fivemack on 20190911 at 22:24 
20190917, 06:30  #9 
Oct 2007
Manchester, UK
2472_{8} Posts 

20190917, 06:33  #10 
"Curtis"
Feb 2005
Riverside, CA
2·3·769 Posts 

20190917, 07:20  #11 
Jun 2015
Vallejo, CA/.
2·5·97 Posts 

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