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 for all $n\ge 4$, if $p_1,\dots ,p_n,p_{n+1}$ are the first $n+1$ prime numbers, then

$p_n\mathrm{\#}=\prod _{i=1}^n{p}_i>p_{n+1}^2.$

Barkley Rosser showed an upper bound where $n\mathrm{\#}\le 2.83^n$.

See also

• Primorial prime

References

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