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.