ABSTRACT
This chapter considers all the known prime numbers in increasing order 2, 3, 5, 7, 11, 13, etc., onward and ever upward. Prime numbers which are separated by only one even number are found to exist up to the largest numbers tested, and are believed to exist no matter how high one go. They are called prime twins, and have been located to values far in excess of the present limit to which all prime numbers have been computed. Although there are great irregularities in the distribution of the individual primes, when the large scale distribution is considered it appears fairly smooth. In more recent years more complicated functions have been found which approximate the actual prime number distribution even more closely. One of them which is not too complicated in its definition, but is still one of the best, also goes back to Karl Friedrich Gauss.
