20060307, 03:17  #1 
Jun 2003
3054_{8} Posts 
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!!! 
20060307, 04:51  #2 
Jan 2005
Transdniestr
503 Posts 
Priminusal
The odds of the number being p unsmooth is: 1/2*2/3*4/5*6/7 ... (p1)/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 ... *(p1). I dub this the Priminusal 
20060307, 06:08  #3 
Jun 2003
2^{2}·5·79 Posts 
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 ... (p1)/p Last fiddled with by Citrix on 20060307 at 06:16 
20060307, 15:07  #4 
Jan 2005
Transdniestr
503 Posts 
Why in the world would you need another answer or method? This is basic stuff.

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