20191215, 17:22  #23 
Oct 2018
2^{3}·3 Posts 
For the next one I had a bit more luck and found it after only 20 SNFS factorizations.
10^167+6453 = 203214913448641292965085614133875784826110271627178496334164562386280018360230767193 * 492089868321958070178727516157409397743940386446977363088474243145123507652778037821 
20200501, 09:55  #24 
Oct 2018
11000_{2} Posts 
The next one took much longer, requiring 140 SNFS factorizations, but now I am happy to report that
10^16738903 = 203295679518280624355545616168150860499969671339902409710914658195811040122874591267 * 491894369014408217255986821288848144293491232238922901468113805403238598987818347491 
20200830, 20:47  #25 
Oct 2018
2^{3}·3 Posts 
And an additional 90 SNFS factorizations show that
10^169 + 25831 = 1578640553322706420836164892965282526510795833878698113106432074544532020287270837641 * 6334564241968890714235608069337466422072649801566867783807088391771261962286575780591 
20200913, 14:26  #26 
Jan 2012
Toronto, Canada
1001011_{2} Posts 
Are these recently found brilliant numbers tracked anywhere? https://www.alpertron.com.ar/BRILLIANT.HTM doesn't seem to have anything above 155 digits.
Reserving 10^147  n for n < 10000. 
20200913, 17:02  #27 
Aug 2002
Buenos Aires, Argentina
2^{4}·5·17 Posts 
At this moment I'm making changes to my calculator that factors and finds the roots of polynomials (you can see it at https://www.alpertron.com.ar/POLFACT.HTM). After that, I will update the page of brilliant numbers.
You can select whether you want to appear with your real name or with the username at this forum. Thanks a lot for your efforts. 
20200919, 00:24  #28 
Aug 2002
Buenos Aires, Argentina
2^{4}·5·17 Posts 
I've just added the discoveries posted to this thread to https://www.alpertron.com.ar/BRILLIANT.HTM and also fixed the errors detected at https://www.alpertron.com.ar/BRILLIANT2.HTM

20200919, 21:21  #29 
(loop (#_fork))
Feb 2006
Cambridge, England
1901_{16} Posts 
Thank you! May I also point you at https://mersenneforum.org/showthread.php?t=22626 ?

20200925, 03:28  #30 
Aug 2002
Buenos Aires, Argentina
2^{4}·5·17 Posts 
I've just updated the page https://www.alpertron.com.ar/BRILLIANT3.HTM with your results. Thanks a lot.

20200930, 16:03  #31 
(loop (#_fork))
Feb 2006
Cambridge, England
37·173 Posts 
The smallest 400bit number with two 200bit prime factors is
0x98B1A3CA31877A7140FEFFA30608FBAB17232646BEC3BAA167 * 0xD699697AC5B27CD0A75D35F9E19320D82A4F4101B550C65E97 = 2^399+198081 (about 15 curves at b1=1e6 for 2^399+{1..10^6} and then SNFS on about 800 400bit numbers taking a median of 15740 seconds on one thread of i9/7940X) I've got an evidence file with a prime factor of less than 200 bits for every 2^399+N which is composite and coprime to (2^23)! but am not quite sure where's best to put it Last fiddled with by fivemack on 20200930 at 16:03 
20201014, 08:54  #32  
May 2013
Germany
5×17 Posts 
Quote:
does this statement apply to largest 2brilliant numbers in base 10? If yes, please give an example. 

20201014, 12:52  #33  
Jan 2012
Toronto, Canada
3·5^{2} Posts 
2^293  33769 is the product of two 147bit primes:
Quote:
Last fiddled with by swishzzz on 20201014 at 12:55 

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