  The prime number problem falls within the realm of number theory,
specifically elementary number theory. Current research approaches have
unnecessarily complicated this matter. In contrast to more advanced
mathematical tools, the methods of elementary number theory can effectively
address the twin prime problem. The primary contribution of this article lies
in establishing a set that systematically includes all twin prime pairs without
omissions. This set's distribution is governed by a precise general solution
formula. Furthermore, an analysis of the distribution set reveals
characteristics of parity balance, enabling us to determine whether twin prime
pairs are finite. Finally, our method can be extended to the general case of
twin primes, such as the Polignac's conjecture.
