Re: product of primes.
- Patrick Capelle wrote:
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).
Consider the following generalisation :
P(n) < a^n < P(p_n) < a^(p_n).
If a < 3, what's the best value for a ?