This is old and very basic algebra, but I don't ever remember seeing it in writing, and I am curious if an alternative definition of a prime, below, has been useful in the search for primes or the study of the distribution of primes.
Definition: Let j be any positive integer. If j is not the difference between two NON consecutive perfect squares, then it is prime. Of course, the difference between two CONSECUTIVE perfect squares gives all the odd numbers, whether prime or composite.
just curious. Bill