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]
bonse, inequality, number, theory, named, after, bonse, relates, size, primorial, smallest, prime, that, does, appear, prime, factorization, states, that, smallest, prime, numbers, then, displaystyle, cdots, middle, product, short, hand, primorial, displaystyl. 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 pn p1 pn gt pn 12 displaystyle p n p 1 cdots p n gt p n 1 2 the middle product is short hand for the primorial pn displaystyle p n of pn Mathematician Denis Hanson showed an upper bound where n 3n displaystyle n leq 3 n 2 See also editPrimorial primeNotes edit Bonse H 1907 Uber eine bekannte Eigenschaft der Zahl 30 und ihre Verallgemeinerung Archiv der Mathematik und Physik 3 12 292 295 Hanson Denis March 1972 On the Product of the Primes Canadian Mathematical Bulletin 15 1 33 37 doi 10 4153 cmb 1972 007 7 ISSN 0008 4395 References editUspensky J V Heaslet M A 1939 Elementary Number Theory New York McGraw Hill p 87 nbsp This number theory related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Bonse 27s inequality amp oldid 1102523387, wikipedia, wiki, book, books, library,
