20140924, 22:54  #1 
"Daniel Jackson"
May 2011
14285714285714285714
2^{3}·3^{4} Posts 
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.

20140924, 23:45  #2 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
41·229 Posts 
4*10^10110^761

20140925, 00:05  #3  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
41×229 Posts 
Quote:
That's how the problem should be phrased. 

20140925, 02:56  #4 
∂^{2}ω=0
Sep 2002
República de California
3×5^{3}×31 Posts 

20140925, 13:51  #5 
"Daniel Jackson"
May 2011
14285714285714285714
2^{3}×3^{4} Posts 
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.
Last fiddled with by Stargate38 on 20140925 at 13:52 Reason: fix emoticon 
20140928, 05:26  #6 
Apr 2007
Spessart/Germany
10100010_{2} Posts 
hmmm,
if you write 911 to a base 912 or larger then 911 itself is the smallest prime with digit sum 911 
20140929, 14:18  #7 
"Daniel Jackson"
May 2011
14285714285714285714
2^{3}·3^{4} 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 911_{10}=10_{911}, though. This works for any number:
n_{10}=10_{n} 
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