《数论探秘》电子版

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以上是1000000内的素数表，用埃拉托斯特尼筛法（Sieve of Eratosthenes）编的程序，不到几秒钟就算出来了

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如下为程序运行截图，不知道那个7713是啥意思：（可能是7713行，数据小的时候每行超过10个，数据大的时候可能是每行就是10个，1000000内有78498个素数，最大的是999983，其中有8169对孪生素数，不打表的话程序1秒内就可以算完当然用的是埃拉托斯特尼筛法，用vb编的程序计时是不打表0.1秒）（对了，78498-7713*10=1368，19*72=1368，就是其中有72行是19+10=29个一行的，其余是10个一行的，也可能是其中72行是10+10=20个一行的，又72行是10+9=19个一行的，剩余是10个一行的）

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最新版数论探秘的目录：
第一章  孪生素数猜想和哥德巴赫猜想的初等证明
第一节  几个概念......................................................1
第二节  孪生素数猜想的证明和哥德巴赫猜想的证明..........................3
第三节  抛物线数列中的孪生素数对和相邻素数对的差的定理..................6
第四节  孪生素数对总个数及其分布规律....................................10
第五节  差为2,4,6,8，……的相邻素数对是无穷多的........................12
第六节  抛物线数列中素因子的周期性和同一周期中的对称性.................12
第二章  哥德巴赫猜想成立的必要条件和充分条件
第一节  哥德巴赫猜想成立的条件.........................................13
第二节  哥德巴赫猜想解的个数的绝对下限.................................14
第三节  偶数哥德巴赫猜想解中的最小素数的求证...........................24
第四节  偶数的哥猜拆分素数和对的下限公式及程序等.......................29
第三章  素数分布规律和哥德巴赫猜想的验证
第一节  素数的分布规律.................................................30
第二节  哥德巴赫猜想的验证.............................................32
第三节  某数内相邻素数的最大间距的公式及推导...........................33
第四章  研究素数的几个常用公式
第一节  几个常用公式...................................................37
第二节  我证明的定理...................................................39
第三节  关于素数对个数的几个命题.......................................40
第四节  关于精确的素数个数公式和素数对个数公式及哥德巴赫猜想解个数公式的
推导和探索.....................................................41
第五节  差为2m的素数对个数的比例以及特殊K生素数探索……………………48
第五章  费尔马大定理的初等证明
第一节  费尔马大定理的初等证明.........................................49
第二节  证明a^(2/3),b^(2/3),c^(2/3)之中(abc为勾股数)必有1个无理数....69
第三节  勾股小题（1）..................................................72
第四节  勾股小题（2）..................................................72
第六章  知识储备
第一节  费尔马小定理.........................................74
第二节  欧拉原理等...........................................74
第三节  中国剩余定理和求乘法的逆元...........................75
第七章  知识扩展
第一节  傅立叶变换与大整数的快速计算.........................81
第二节  朋友的一元三次方程根式解的研究.......................88
第三节  RSA密码体制及大整数的快速分解和快速素性测试.........90
第四节  梅森素数和费马数的密码特性等.........................95
第五节  李明波孪中猜想的证明.................................97
第八章  几个趣味问题
第一节  素数小题.............................................108
第二节  电话号码问题.........................................109
第三节  传令兵走多远等....................................... 109
第四节  勾股定理的平民证法....................................114
后记.............................................................117
附录1，素数表.....................................................119
附录2，两个可调用程序............................................127
附录3，李明波给美国人的挑战书.....................................132
个人简介.........................................................133

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哥德巴赫猜想不仅容易理解证明也根本不难：
      有多种初等证明方法可以证明，哥德巴赫猜想是远远成立的：
1，由差定理（更容易证明）证明和定理（就是哥德巴赫猜想）成立。
2，设偶数2A的方根为M则其方根M内的素数的个数的下限是m=M/lnM，则偶数2A的哥德巴赫猜想解的个数的绝对下限就是m-1，这是对无穷大的偶数都成立的，随着偶数的增大实际解的个数远远大于m-1 ， 所以，哥德巴赫猜想远远成立。
3，据构成哥德巴赫猜想解的素数与偶数的方根的大小，把解分为两类：小根拆和大根拆，大于4的偶数，仅仅有73个偶数只有大根拆而不含有小根拆，其他的都是既有小根拆也有大根拆，而4=2+2.

所以，哥德巴赫猜想远远成立，容易证明，仅仅初等数学就可以证明，中学以上的学历都i可以完全解决。

至今不能解决的原因仅仅有两个：一是数学家喜欢本末倒置从解析数论下手解决问题，二是中国数学界到处是汉奸破环了中国数学界的学术氛围！！

     所以，哥德巴赫猜想的证明并不难，方法并不是唯一的，还有很多其他方法，所谓的解析数论的方法并不是必须的，用初等数论的方法是完全能够彻底解决的！！

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数论探秘电子书：
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