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Old 2006-03-07, 03:17   #1
Citrix
 
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Jun 2003

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Default Primorial puzzle

Find the number of numbers under P# that are not divisible by any of the primes under p. (including p)

I am interested in an exact number not an approximate prediction.

Describe such an algorithm.

Have fun!!!
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Old 2006-03-07, 04:51   #2
grandpascorpion
 
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Default Priminusal

The odds of the number being p unsmooth is: 1/2*2/3*4/5*6/7 ... (p-1)/p

The denominator = p#. You multiply the probability by the sample size to get the count of numbers. The sample is size is p#. So, p#'s cancel and you are left with:

The answer is 1* 2 * 4 * 6 ... *(p-1). I dub this the Priminusal
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Old 2006-03-07, 06:08   #3
Citrix
 
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Any other methods, I know that is the answer? I have a method in mind that leads to this formula, anyone want to guess?

Citrix


edit:-
Does the ratio approach a value?
1/2*2/3*4/5*6/7 ... (p-1)/p

Last fiddled with by Citrix on 2006-03-07 at 06:16
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Old 2006-03-07, 15:07   #4
grandpascorpion
 
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Why in the world would you need another answer or method? This is basic stuff.

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