20060729, 14:39  #1 
Einyen
Dec 2003
Denmark
2·5^{2}·67 Posts 
10^147+19
10^147+19 =
11210754325987903848222358333498946062147584250342963305961590952868977237 * 89200063699717094086741570686240243731188867201010229921060666406453209287 (both primes according to primo) and since 10^147+1 to 10^147+17 have these factors: 10^147+1: 7 10^147+3: 17 10^147+5: 3 10^147+7: 19 10^147+9: 27779 10^147+11: 3 10^147+13: 421 10^147+15: 5 10^147+17: 3 it should be the smallest 148digit brilliant number? Here is all the smallest factors of the numbers up to 10^147+1229: 10^147+x.txt Last fiddled with by ATH on 20060729 at 14:41 
20060729, 15:22  #2 
Nov 2003
2×1,811 Posts 
Amazing! With such a small addition. Congratulations.
A previous interesting case is 10^77+3. BTW, since you factored all between 10^147+19 and 10^147+1231 I guess you did that by ecm and you basically found the brilliant number on your first snfs attempt? 
20060729, 16:00  #3 
Einyen
Dec 2003
Denmark
2·5^{2}·67 Posts 
Yes, only a few ecm factors most of which turned out to be unnecessary and then snfs on 19. I never tried any gnfs or snfs before, so I had to figure out how to use ggnfs, it took awhile.

20060806, 07:46  #4  
Oct 2004
Austria
2×17×73 Posts 
Quote:
Prime cofactor: P39=538925768921415130739706333069119686561 Edit: Ooops, sorry, seems I have misinterpreted Cosmaj's Line. It has already been factored here. Last fiddled with by Andi47 on 20060806 at 07:53 

20060807, 05:58  #5 
Nov 2003
2·1,811 Posts 
Sorry, what I wanted to say is that 10^77+3 is another known and already factored case. Fortunately it's a small one so it didn't cost you a lot of your cpu time (less than 10 minutes by msieve?).
BTW, my name is Kosmaj, pronounced "Cossmai". Thanks. 