Bonse's inequality
Inequality relating the primorial to square of the next prime number
In number theory, Bonse's inequality, named after H. Bonse,[1] 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
(the middle product is short-hand for the primorial of pn)
Mathematician Denis Hanson showed an upper bound where .[2]
See also
- Primorial prime
Notes
References
- Uspensky, J. V.; Heaslet, M. A. (1939). Elementary Number Theory. New York: McGraw Hill. p. 87.
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