A Proof of Twin Prime Conjecture by Statistical and Probabilistic Studies

This paper started with specific prime factor analysis of natural numbers, then found a criterion for proof of twin prime conjecture: At least one twin prime exists between the squares of consecutive primes? The statistical method was adopted to investigate this criterion over a substantial range of consecutive prime-square intervals. A graphical approach was also tried to seek the mechanism of twin prime distributions. The probabilistic study was applied to theoretically support the twin prime conjecture as well.