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Old 2014-09-24, 22:54   #1
Stargate38
 
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Default 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.
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Old 2014-09-24, 23:45   #2
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4*10^101-10^76-1
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Old 2014-09-25, 00:05   #3
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Quote:
Originally Posted by Stargate38 View Post
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 View Post
find the smallest prime with a digit sum of 911.
That's how the problem should be phrased.
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Old 2014-09-25, 02:56   #4
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Quote:
Originally Posted by Batalov View Post
4*10^101-10^76-1
If that is the same as

399999999999999999999999989999999999999999999999999999999999999999999999999999999999999999999999999999,

then we agree. :)
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Old 2014-09-25, 13:51   #5
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Smile 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
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Old 2014-09-28, 05:26   #6
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hmmm,

if you write 911 to a base 912 or larger then 911 itself is the smallest prime with digit sum 911
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Old 2014-09-29, 14:18   #7
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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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