20060706, 08:19  #1 
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
11771_{10} Posts 
Product launch
You may find this product amusing:
196175124573517092034922493422470908957491913295260473203518969764669282857 * 509748624946200879944668835201017220741864841301635474800405920115982269129 Paul 
20060706, 10:26  #2 
Jul 2005
182_{16} Posts 
Why?

20060706, 10:30  #3 
Apr 2004
Copenhagen, Denmark
116_{10} Posts 
=10^149+21553 It's rare to find a number this well suited for SNFS with only two large prime factors.

20060706, 11:32  #4 
Jul 2005
110000010_{2} Posts 
I'd thought that the Brilliant Number search had gone beyond this range but I was mistaken. The highest they have is 10^115+12741.
http://www.alpertron.com.ar/BRILLIANT.HTM Last fiddled with by Greenbank on 20060706 at 11:33 
20060707, 10:59  #5 
"Sander"
Oct 2002
52.345322,5.52471
4A5_{16} Posts 
This makes a nice candidate for a record brilliant number.
After prp testing, traildivision and a bit of ECM, i have just over 200 numbers left. More ECM will remove quite a few of these, but still a lot of SNFS remains. I haven't checked how long a single number takes with SNFS though. 
20060707, 14:27  #6  
Bamboozled!
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May 2003
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79·149 Posts 
Quote:
You will see that it proves that 10^149+21553 is indeed the smallest 150digit brilliant number. Paul 

20060707, 17:24  #7 
Aug 2002
Buenos Aires, Argentina
2×761 Posts 
Excellent!!!
I will upload the data tonight. How long has this task ran? Would it be easy to fill the holes in the table? 
20060707, 21:15  #8  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
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79·149 Posts 
Quote:
It took so long mostly because the SNFS sieving was performed almost entirely on some of my museum pieces. At most three machines were working at once  a PPro 233, a PII300 and a Sun Ultra10. Quite often only one or two of them were sieving. The filtering, linear algebra and square root phases were run on a 1.33GHz Athlon. Each SNFS took about two weeks and I had to run dozens of them. You'll note that 21553/2 factorizations had to be completed. OK, many of them were done by trial division but a substantial ECM effort was needed too. The SNFS factorizations are easy to spot in the file I attached. They are the ones with (pxx) appended. The ECM factorizations are, essentially, those without a (pxx) and for which the factors are larger than 6 or 7 digits. I suspect that it will take a long time, possibly several years, to fill the gaps in the table, unless a number of people make a concerted effort. When I started the record stood at around 100 digits, possibly a bit more. You can see for yourself how much progress has been made in that time and how much more is required to fill the gaps. Paul 

20060708, 07:57  #9 
"Sander"
Oct 2002
52.345322,5.52471
29×41 Posts 
I count 77 SNFS tests.
For my 112 digits i did 210 SNFS tests, for 113 digits 351 and for 116 digits 53 Of course all of them were a lot easier. Do you know what is the chance the brilliant shows up within lets say the first 25K n for numbers this size? You might have been unlucky and have to run upto several hunderd K n Last fiddled with by smh on 20060708 at 07:57 
20060709, 22:12  #10  
Feb 2006
Denmark
2·5·23 Posts 
Congratulations on a great brilliant number.
Quote:
ECM will often not find the smallest factor first. My sieve to 400G found a smaller factor in 49 attached numbers below the brilliant 10^149+21553. The largest difference was for 10^149+18537 with smallest factor 1616453 and Paul's 562916230505561. 

20060710, 15:54  #11  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
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79·149 Posts 
Quote:
Nonetheless, the brill.txt file lists a prime factor of each number in the range necessary to establish that 10^149+21553 is the smallest 150digit brilliant number. Paul 

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