素数定理的拓展

THE GENERALIZATION OF PRIME THEOREM

设任一偶数２ｎ，是否存在着一个仅依赖于２ｎ的函数ｆ（２ｎ）？它能表示偶数表为两个素数之和的素数解的组数。本文首先把素数定理引入奇数列（一维空间），然后拓展到二维空间。在一维空间，素数定理－素数的分布函数π（ｘ）～ｘｌｏｇｘ（ｘ∞），从素数定理得到：Ｐ（Ｎ）～１ｌｏｇｘ及Ｐ（Ｇ）～２ｌｏｇｘ。Ｐ（Ｇ）作为数据处理的工具，用它解决了命题Ｐ２ｎ（１，１）。在二维空间：素数的联合分布密度Ｐ（Ｐｘ，Ｐｙ）～１ｌｏｇｘｌｏｇｙ，由它积分得到了分布函数π（ｘ，ｙ），利用π（ｘ，ｙ）可以估计圆内素点（Ｐｘ，Ｐｙ）的个数，并且解决了命题，Ｐ２ｎ（１，１）２。Ｐ２ｎ（１，１）和Ｐ２ｎ（１，１）２的结果是用不同的方法建立的不同的数学模型，但是它们主阶的数值规律是一致的。这个问题本文得到解决。

Suppose any even integer 2n . Is there or not a function f(2n) to be on ly dependent upon 2n?It can express a number of group of prim e solutions on representation of even integer as a sum of two primes. In the paper,first,the prime theorem is led into odd sequence integer,i.e. one dimensional space Second,it is generalized into twodimensional space. In the one-dimensional space,the prime theoremprime distributed fun ction is π( x)～xlogx(x∞).P( N)～1logxin N=｛1,2,3,4...,x｝and P(G)～2logxin G=｛1,3,5,...,x｝ are from the prime theorem.P(G)is regraded as a data handling tool to solve P2n(1,1). In the twodimensional space,independence of the prime distrib ution ,the prime edge densities determine a prime joint density:P(Px,Py) ～1logxlogy.It is int egrated to get a distributed fun ction of the primes:π(x,y).A number of prime spots ( Px,Py) in a circle can be estimated by π(x,y),an d P2n(1,1)2 has a reault here. The two principal steps of the results of P2n(1,1) and P2n(1,1)2 are the two mathematical models set up by d ifferent methods. But the laws of their value are unanimous. The problem is solved. This is a direct answer to the Goldbach's con jecture.