Bonse's inequality

Template:Short description 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

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

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

Mathematician Denis Hanson showed an upper bound where $n\mathrm{\#}\le 3^n$.

See also

• Primorial prime

References

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