Multiangle light scattering: Difference between revisions
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In [[number theory]], '''Bonse's inequality''', named after H. Bonse,<ref>{{cite journal |first=H. |last=Bonse |title={{lang|de|Über eine bekannte Eigenschaft der Zahl 30 und ihre Verallgemeinerung}} |journal=Archiv der Mathematik und Physik |volume=3 |issue=12 |year=1907 |pages=292–295 }}</ref> states that if ''p''<sub>1</sub>, ..., ''p''<sub>''n''</sub>, ''p''<sub>''n''+1</sub> are the smallest ''n'' + 1 prime numbers and ''n'' ≥ 4, then | |||
: <math> p_1 \cdots p_n > p_{n+1}^2. \, </math> | |||
== Notes == | |||
{{reflist}} | |||
== References == | |||
*{{cite book |first=J. V. |last=Uspensky |first2=M. A. |last2=Heaslet |title=Elementary Number Theory |publisher=McGraw Hill |location=New York |year=1939 |page=87 |isbn= }} | |||
*{{cite arXiv |last=Zhang |first=Shaohua |authorlink= |eprint=0908.2943 |title=A new inequality involving primes | |||
|class= |year=2009 |version=v1 |accessdate=July 7, 2012 }} | |||
[[Category:Number theory]] | |||
[[Category:Inequalities]] | |||
{{numtheory-stub}} | |||
Revision as of 03:35, 2 August 2013
In number theory, Bonse's inequality, named after H. Bonse,[1] states that if p1, ..., pn, pn+1 are the smallest n + 1 prime numbers and n ≥ 4, then
Notes
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