(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.