Bonse不等式 腳註 參考資料 导航菜单arXiv:0908.2943v1编辑或修订

數論相關的定理不等式


數論質數階乘質因數分解質數




Bonse不等式（英语：Bonse's inequality）為數論中的不等式，得名自H. Bonse,[1]，有關質數階乘和未在其質因數分解中出現的最小質數之間的大小關係。若p1, ..., pn, pn+1 為最小n + 1個質數，且n ≥ 4，則


pn+12<p1⋯pndisplaystyle p_n+1^2<p_1cdots p_n,



以下列出一些質數之間的關係，前四行不在Bonse不等式的範圍內


4=22>0displaystyle 4=2^2>0

9=32>2=2displaystyle 9=3^2>2=2

25=52>2⋅3=6displaystyle 25=5^2>2cdot 3=6

49=72>2⋅3⋅5=30displaystyle 49=7^2>2cdot 3cdot 5=30

121=112<2⋅3⋅5⋅7=210displaystyle 121=11^2<2cdot 3cdot 5cdot 7=210

169=132<2⋅3⋅5⋅7⋅11=2310displaystyle 169=13^2<2cdot 3cdot 5cdot 7cdot 11=2310

289=172<2⋅3⋅5⋅7⋅11⋅13=30030displaystyle 289=17^2<2cdot 3cdot 5cdot 7cdot 11cdot 13=30030

……



腳註




  1. ^ Bonse, H. Über eine bekannte Eigenschaft der Zahl 30 und ihre Verallgemeinerung. Archiv der Mathematik und Physik. 1907, 3 (12): 292–295. 



參考資料



  • Uspensky, J. V.; Heaslet, M. A. Elementary Number Theory. New York: McGraw Hill. 1939: 87. 


  • Zhang, Shaohua. A new inequality involving primes. 2009. arXiv:0908.2943v1.  引文使用过时参数version (帮助); 不支持的参数使用了arXiv (帮助)


Nuvola apps edu mathematics-p.svg  這是與数论相關的小作品。你可以通过编辑或修订扩充其内容。






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