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   Coprimality of Two Randomly Chosen Integers
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   Author  Topic: Coprimality of Two Randomly Chosen Integers  (Read 940 times)
william wu
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Coprimality of Two Randomly Chosen Integers  
« on: Aug 21st, 2003, 2:17pm »
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Show that  
 
[prod]p in primes(1 - p-2) = 6[pi]-2

 
Conclude that the probability two randomly chosen integers are coprime is 6[pi]-2.
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Re: Coprimality of Two Randomly Chosen Integers  
« Reply #1 on: Aug 21st, 2003, 6:23pm »
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What a coincidence! Just a few minutes ago I used that in solution to Random Line Segment in Square riddle. However I left out the details to keep my post from being too long.
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TenaliRaman
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Re: Coprimality of Two Randomly Chosen Integers  
« Reply #2 on: Aug 22nd, 2003, 11:56am »
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hey the second question's pretty neat!!!
it had me hooked up for the last 5 hours before it dawned on me that P(coprime)=1-P(not coprime) and the first result comes into play.
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