素数与其在素数序列中的位置的相关系数

本文将数理统计中的相关系数概念应用于素数领域,研究素数p_i与其在素数序列中的顺序位置i之间的相关系数,进而提出猜想,当n增大时,相关系数变化的总趋势有两种可能,或者恒上升;或者先上升,到达某个n_0以后,恒下降。

Correlation Coefficient of a Prime Number With Its Position in the Sequence of Prime Number

By employing the concept of correlation coefficient in mathematical statistics, the paper tries to present a correlation coefficient between prime numbers p_i of the first n terms and i which characterises the ordinal position of p_i in the natural sequence of prime numbers. A conjecture is formed to predict the following two trends of the correlation coefficient as n increases. 1. Increasing constantly with minor fluctuations. 2.Increasing to a certain n_0 before decreasing constantly with minor fluctuations.