Bonse's inequality

In number theory, Bonse's inequality, named after H. Bonse, relates the size of a primorial to the smallest prime that does not appear in its prime factorization. It states that if p1, ..., pn, pn+1 are the smallest n + 1 prime numbers and n ≥ 4, then


 * $$ p_n\# = p_1 \cdots p_n > p_{n+1}^2. $$

(the middle product is short-hand for the primorial $$ p_n\# $$ of pn)

Mathematician Denis Hanson showed an upper bound where $$n\#\leq 3^n$$.