mersenneforum.org Smallest prime with a digit sum of 911
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 2014-09-24, 22:54 #1 Stargate38     "Daniel Jackson" May 2011 14285714285714285714 25916 Posts Smallest prime with a digit sum of 911 Given that the smallest number with a digit sum of 911 is 3*10^101-1=7*17*461*42703*128060437587372995319339355138356780636701102819820530493717889157422282840645351747588735187, find the smallest prime with a digit sum of 911.
 2014-09-24, 23:45 #2 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2×33×132 Posts 4*10^101-10^76-1
2014-09-25, 00:05   #3
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

2·33·132 Posts

Quote:
 Originally Posted by Stargate38 Given that the smallest number with a digit sum of 911 is 3*10^101-1=7*17*461*42703*128060437587372995319339355138356780636701102819820530493717889157422282840645351747588735187, ...
This is completely immaterial ;-) How could you possibly use this?

Quote:
 Originally Posted by Stargate38 find the smallest prime with a digit sum of 911.
That's how the problem should be phrased.

2014-09-25, 02:56   #4
ewmayer
2ω=0

Sep 2002
República de California

2·13·443 Posts

Quote:
 Originally Posted by Batalov 4*10^101-10^76-1
If that is the same as

399999999999999999999999989999999999999999999999999999999999999999999999999999999999999999999999999999,

then we agree. :)

 2014-09-25, 13:51 #5 Stargate38     "Daniel Jackson" May 2011 14285714285714285714 601 Posts I didn't know it was that simple! Thanks. That other, non-prime number that I gave you was just a lower bound, because it's the smallest mathematically possible case of a number whose digits sum to 911. Last fiddled with by Stargate38 on 2014-09-25 at 13:52 Reason: fix emoticon
 2014-09-28, 05:26 #6 MatWur-S530113     Apr 2007 Spessart/Germany 2428 Posts hmmm, if you write 911 to a base 912 or larger then 911 itself is the smallest prime with digit sum 911
 2014-09-29, 14:18 #7 Stargate38     "Daniel Jackson" May 2011 14285714285714285714 601 Posts Of course, that makes sense because in base>911, 911 itself has a size of only one significant figure. I don't know how to do bases >94 though. I do know that 91110=10911, though. This works for any number: n10=10n

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