Smallest prime with a digit sum of 911

Stargate38 · 2014-09-24, 22:54

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

4*10^101-10^76-1

Batalov · 2014-09-25, 00:05

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.

ewmayer · 2014-09-25, 02:56

Quote:

Originally Posted by Batalov

4*10^101-10^76-1

If that is the same as

399999999999999999999999989999999999999999999999999999999999999999999999999999999999999999999999999999,

then we agree. :)

Stargate38 · 2014-09-25, 13:51

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.

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

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 911₁₀=10₉₁₁, though. This works for any number:

n₁₀=10_n

2014-09-24, 22:54	#1
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 2²×7×23 Posts	Smallest prime with a digit sum of 911 Given that the smallest number with a digit sum of 911 is 310^101-1=71746142703*128060437587372995319339355138356780636701102819820530493717889157422282840645351747588735187, find the smallest prime with a digit sum of 911.

2014-09-25, 13:51	#5
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 2²·7·23 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

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2014-09-24, 23:45	#2
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 10010001101111₂ Posts	4*10^101-10^76-1

2014-09-28, 05:26	#6
MatWur-S530113 Apr 2007 Spessart/Germany 2·3⁴ 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 2²×7×23 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=10_n