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    5. 乘法質數生成器
    質數生成器

    乘法質數生成器

    5.0分,1 ratings
    Author 特野
    Publisher 特野 /韓特野
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    Released
    2017/06/15
    Language
    Traditional Chinese
    File format
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    Pages
    21
    ID
    98620
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    質數(Prime number),又稱素數,指在大於1的自然數中,除了1和該數自身外,無法被其他自然數整除的整數。
    此文件的目的是以乘法的思維來探討如何在任意整數【2,N】範圍內不用除法器來建立N範圍內的質數表。
    依據定義,質數只能被1以及自身整除。反之,在N的範圍內所有非質數的整數必定符合下列的表示法:
    P1T1 P2T2 P3T3 P4T4 . . . . .PnTn
    其中:
     P1 ~ Pn為在N範圍內的所有質數,且1 P1 P2 P3 P4 . . . . . . Pn
     T1 ~ Tn為任意正整數,且允許T1到Tn之間出現相同值。
     當n等於1時,T1值必須大於1。
    質數表生成器的基本構想: 首先建立一個整數列表 【2, 3, 4, 5, 6, 7, 8, 9,. . . . . ,N】,然後將P1T1P2T2P3T3P4T4 . . . . .PnTn 所有的可能組合的乘積從我們建立的整數列表中移除,便可以得到N範圍內的質數表。
    此方法與依據質數的定義所建立的質數表,其之間最大的差異是:做1次乘法便可刪除1個“非質數”。不像傳統做法:判斷“非質數”至少得做一次除法(凡質數2的整倍數),而判斷質數得做多次數的除法才能完成。
    透過“乘法”思維方式 ,本文將包含整個發展演算法過程中所面臨的困難以及解決之道,並且提供C語言的程式範本。雖然我們將很遺憾發現此種方法仍存在難題,只能有待有心人去解決。筆者期待有朝一日,此演算法能超越傳統方法。

    歷史版本
    ========================================
    2017/06/15 初版
    2017/06/22 修訂版:更正錯誤。
    2017/06/24 修訂版:優化演算法。
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    Released
    2017/06/15
    Language
    Traditional Chinese
    File format
    PDF: Fit in large screen
    Provide Adobe DRM
    Provide PDF
    Offer DRM free license
    Yes
    ID
    98620

    質數

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    揭開整數分割的神秘面紗 - 乘法公式

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    演算法 - 整數分割

    乘法質數生成器

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