Add to ORKGWe study some new aspects of the twin prime distribution, focusing especially on how the prime pairs are distributed in arithmetic progressions when they are classified according to the residues of their first members. A modified totient function is seen to play a significant role in this study - we analyze this function and use it to construct a new heuristics for the twin prime conjecture. For the twin primes, we also discuss a sieve similar to Eratosthenes' sieve and a formula similar to the Legendre's formula for the prime counting function. We end our work with a discussion on three types of biases in the distribution of twin primes. Where possible, we compare our results with the corresponding results from the distribution of primes.C...