: Mathématiques: Bonse's inequality

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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, ..., p_n, p_n+1 are the smallest n + 1 prime numbers and n ≥ 4, then
${\\displaystyle p_{n}\\#=p_{1}\\cdots p_{n}>p_{n+1}^{2}.}$
(the middle product is short-hand for the primorial ${\\displaystyle p_{n}\\#}$ of p_n) Mathematician Denis Hanson showed an upper bound where ${\\displaystyle n\\#\\leq 3^{n}}$ .
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Bonse%27s_inequality)