Smallest prime with a digit sum of 911
Given that the smallest number with a digit sum of 911 is 3*10^1011=7*17*461*42703*128060437587372995319339355138356780636701102819820530493717889157422282840645351747588735187, find the smallest prime with a digit sum of 911.

[SPOILER]4*10^10110^761[/SPOILER]

[QUOTE=Stargate38;383793][STRIKE]Given that the smallest number with a digit sum of 911 is 3*10^1011=7*17*461*42703*128060437587372995319339355138356780636701102819820530493717889157422282840645351747588735187,[/STRIKE] ...[/QUOTE]
This is completely immaterial ;) How could you possibly use this? [QUOTE=Stargate38;383793]find the smallest prime with a digit sum of 911.[/QUOTE] That's how the problem should be phrased. 
[QUOTE=Batalov;383796][SPOILER]4*10^10110^761[/SPOILER][/QUOTE]
If that is the same as [spoiler]399999999999999999999999989999999999999999999999999999999999999999999999999999999999999999999999999999[/spoiler], then we agree. :) 
I didn't know it was that simple!
Thanks. That other, nonprime 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. :smile:

hmmm,
if you write 911 to a base 912 or larger then 911 itself is the smallest prime with digit sum 911 :wink: 
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 911[sub]10[/sub]=10[sub]911[/sub], though. This works for any number:
n[sub]10[/sub]=10[sub]n[/sub] 
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