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。






-

Popular posts from this blog

名間水力發電廠 目录 沿革 設施 鄰近設施 註釋 外部連結 导航菜单23°50′10″N 120°42′41″E / 23.83611°N 120.71139°E / 23.83611; 120.7113923°50′10″N 120°42′41″E / 23.83611°N 120.71139°E / 23.83611; 120.71139計畫概要原始内容臺灣第一座BOT 模式開發的水力發電廠－名間水力電廠名間水力發電廠 水利署首件BOT案原始内容《小檔案》名間電廠 首座BOT水力發電廠原始内容名間電廠BOT - 經濟部水利署中區水資源局编编

Image
東螺溪清水溪加走寮溪阿里山溪東埔蚋溪獅尾堀清水溪清水溝溪水里溪陳有蘭溪郡坑溪十八重溪那馬嘎班溪松柏坑溪卓棍溪瓠瓢坑溪益則坑溪玉崙溪丹大溪郡大溪巒大溪卡社溪栗栖溪萬大溪萬大北溪萬大南溪霧社溪塔羅灣溪馬赫坡溪萬大發電廠大觀發電廠日月潭第一發電所明潭發電廠...
Read more

Prove that NP is closed under karp reduction?Space(n) not closed under Karp reductions - what about NTime(n)?Class P is closed under rotation?Prove or disprove that $NL$ is closed under polynomial many-one reductions$mathbfNC_2$ is closed under log-space reductionOn Karp reductionwhen can I know if a class (complexity) is closed under reduction (cook/karp)Check if class $PSPACE$ is closed under polyonomially space reductionIs NPSPACE also closed under polynomial-time reduction and under log-space reduction?Prove PSPACE is closed under complement?Prove PSPACE is closed under union?

Image
Is a conference paper whose proceedings will be published in IEEE Xplore counted as a publication? Prove that NP is closed under karp reduction? Is it important to consider tone, melody, and musical form while writing a song? How is it possible to have an ability score that is less than 3? Can I make popcorn with any corn? Mathematical cryptic clues tikz: show 0 at the axis origin Minkowski space can i play a electric guitar through a bass amp? Why not use SQL instead of GraphQL? How can I prevent hyper evolved versions of regular creatures from wiping out their cousins? How old can references or sources in a thesis be? Do VLANs within a subnet need to have their own subnet for router on a stick? How to add double frame in tcolorbox? How much RAM could one put in a typical 80386 setup? "You are your self first supporter", a more proper way to say it How is the claim "I am in New York only if I am in America" the same as "If I am ...
Read more

Is my guitar’s action too high? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Strings too stiff on a recently purchased acoustic guitar | Cort AD880CEIs the action of my guitar really high?Μy little finger is too weak to play guitarWith guitar, how long should I give my fingers to strengthen / callous?When playing a fret the guitar sounds mutedPlaying (Barre) chords up the guitar neckI think my guitar strings are wound too tight and I can't play barre chordsF barre chord on an SG guitarHow to find to the right strings of a barre chord by feel?High action on higher fret on my steel acoustic guitar

Image
Is the Mordenkainen's Sword spell underpowered? Escaping $ in listings environment Short story about astronauts fertilizing soil with their own bodies No invitation for tourist visa but I want to visit Do regular languages belong to Space(1)? Can I take recommendation from someone I met at a conference? How to name indistinguishable henchmen in a screenplay? Found this skink in my tomato plant bucket. Is he trapped? Or could he leave if he wanted? How can I prevent/balance waiting and turtling as a response to cooldown mechanics Can I feed enough spin up electron to a black hole to affect it's angular momentum? Why does BitLocker not use RSA? Is my guitar’s action too high? Does GDPR cover the collection of data by websites that crawl the web and resell user data Trying to enter the Fox's den How to achieve cat-like agility? "Destructive power" carried by a B-52? Should man-made satellites feature an intelligent inverted "cow c...
Read more