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Re: product of primes.

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  • Patrick Capelle
    Patrick Capelle wrote: (snip) If we define P(x) as the product of the primes which are smaller or equal to x, we have : P(n)= p_1 * p_2 * p_3 * ... * p_i ,
    Message 1 of 10 , Sep 23, 2005
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      Patrick Capelle wrote:
      (snip)
      If we define P(x) as the product of the primes which are smaller or
      equal to x, we have :
      P(n)= p_1 * p_2 * p_3 * ... * p_i , with p_i <= n.
      P(p_n)= p_1 * p_2 * p_3 * ... * p_n.

      We have the following inequalities for n > 2 :
      P(n) < 3^n < P(p_n) < 3^(p_n).
      (snip)


      Consider the following generalisation :
      P(n) < a^n < P(p_n) < a^(p_n).

      Question :
      If a < 3, what's the best value for a ?


      Regards,
      Patrick Capelle.
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