mersenneforum.org Smallest 10^179+c Brilliant Number (p90 * p90)
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 2019-12-15, 17:22 #23 Branger   Oct 2018 101012 Posts For the next one I had a bit more luck and found it after only 20 SNFS factorizations. 10^167+6453 = 203214913448641292965085614133875784826110271627178496334164562386280018360230767193 * 492089868321958070178727516157409397743940386446977363088474243145123507652778037821
 2020-05-01, 09:55 #24 Branger   Oct 2018 258 Posts The next one took much longer, requiring 140 SNFS factorizations, but now I am happy to report that 10^167-38903 = 203295679518280624355545616168150860499969671339902409710914658195811040122874591267 * 491894369014408217255986821288848144293491232238922901468113805403238598987818347491
 2020-08-30, 20:47 #25 Branger   Oct 2018 3×7 Posts And an additional 90 SNFS factorizations show that 10^169 + 25831 = 1578640553322706420836164892965282526510795833878698113106432074544532020287270837641 * 6334564241968890714235608069337466422072649801566867783807088391771261962286575780591
 2020-09-13, 14:26 #26 swishzzz   Jan 2012 Toronto, Canada 22·13 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.
 2020-09-13, 17:02 #27 alpertron     Aug 2002 Buenos Aires, Argentina 53D16 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.
 2020-09-19, 00:24 #28 alpertron     Aug 2002 Buenos Aires, Argentina 32·149 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
 2020-09-19, 21:21 #29 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 18E916 Posts Thank you! May I also point you at https://mersenneforum.org/showthread.php?t=22626 ?
 2020-09-25, 03:28 #30 alpertron     Aug 2002 Buenos Aires, Argentina 101001111012 Posts I've just updated the page https://www.alpertron.com.ar/BRILLIANT3.HTM with your results. Thanks a lot.
 2020-09-30, 16:03 #31 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 7·911 Posts The smallest 400-bit number with two 200-bit 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 800 400-bit 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 2020-09-30 at 16:03
2020-10-14, 08:54   #32
Alfred

May 2013
Germany

2·3·13 Posts

Quote:
 Originally Posted by Dr Sardonicus It is intuitively obvious that, if k is "sufficiently large", the smallest "2-brilliant" number n > 22k is n = p1*p2, where p1 = nextprime(2k) and p2 = nextprime(p1 + 1). Numerical evidence suggests that "sufficiently large" is k > 3. This notion "obviously" applies to any base.
Dr Sardonicus,

does this statement apply to largest 2-brilliant numbers in base 10?

If yes, please give an example.

2020-10-14, 12:52   #33
swishzzz

Jan 2012

22×13 Posts

2^293 - 33769 is the product of two 147-bit primes:

Quote:
 P45 = 126510626365064224002933822140885711272659161 P45 = 125794520368511128755464888278721782242924143
Factor file for 2^293 - c with c > 0 attached.
Attached Files
 293b_brilliant.txt (33.8 KB, 30 views)

Last fiddled with by swishzzz on 2020-10-14 at 12:55

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