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 2006-07-29, 14:39 #1 ATH Einyen     Dec 2003 Denmark 2·52·67 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 148-digit 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 2006-07-29 at 14:41
 2006-07-29, 15:22 #2 Kosmaj     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?
 2006-07-29, 16:00 #3 ATH Einyen     Dec 2003 Denmark 2·52·67 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.
2006-08-06, 07:46   #4
Andi47

Oct 2004
Austria

2×17×73 Posts

Quote:
 Originally Posted by Kosmaj A previous interesting case is 10^77+3.
it has a factor: P39=185554311496620532371770351611143673123
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 2006-08-06 at 07:53

 2006-08-07, 05:58 #5 Kosmaj     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.

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