ABSTRACT
Every integer can be broken down into constituent parts in a variety of ways such that, in a sense, each has a distinct personality. In this manner some groups of integers fall rather naturally into ‘families’ which have a particular characteristic in common. Mathematicians have been searching for centuries for a simple method which would enable them to determine, without great effort, whether or not a particular number is prime. It is true that methods do exist, but none materially shortens the work of testing from basic first principles, which implies checking the possible divisibility by all primes less than the square root of the number. It would be so much nicer if a formula could be derived to generate prime numbers; even if it wasn’t able to give them all. Many suggestions have been forthcoming over the centuries, but none has been successful although some have come enticingly close, only to fail on closer inspection.
