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-   -   Smallest prime with a digit sum of 911 (https://www.mersenneforum.org/showthread.php?t=19719)

 Stargate38 2014-09-24 22:54

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.

 Batalov 2014-09-24 23:45

[SPOILER]4*10^101-10^76-1[/SPOILER]

 Batalov 2014-09-25 00:05

[QUOTE=Stargate38;383793][STRIKE]Given that the smallest number with a digit sum of 911 is 3*10^101-1=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.

 ewmayer 2014-09-25 02:56

[QUOTE=Batalov;383796][SPOILER]4*10^101-10^76-1[/SPOILER][/QUOTE]

If that is the same as

[spoiler]399999999999999999999999989999999999999999999999999999999999999999999999999999999999999999999999999999[/spoiler],

then we agree. :)

 Stargate38 2014-09-25 13:51

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. :smile:

 MatWur-S530113 2014-09-28 05:26

hmmm,

if you write 911 to a base 912 or larger then 911 itself is the smallest prime with digit sum 911 :wink:

 Stargate38 2014-09-29 14:18

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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