In the first paper on this subject, the small total of seven quadratics were shown to generate sequences of prime numbers covering all those between 0 and 100 plus 57 others. Of these, five, including Euler's and Legendre's, were already well known and documented.

Using the methods described below, the list has now been expanded to 451 quadratics of which 104 cover all the prime numbers between 0 and 1500 plus 190 beyond. The profusion of acceptable equations is now such that it is possible to tighten the control criteria as will be described below.

It is hoped that as more quadratics meeting the criteria are found, a pattern will emerge that will enable others to be "predicted" according to some "pattern law". However, it is clear that for the first term in any sequence to be prime, the quadratic constant coefficient, a₀, in the generating equation must be prime. In addition, for the second term in the sequence to be prime, the sum of all the coefficients must also be prime. Because the distribution of prime numbers is non-linear, so then will be quadratics that generate sequences of primes, according to the criteria, when based upon these two factors. Consequently, any pattern law that does subsequently emerge, can only be based upon the first two coefficients, a₂, and a₁ alone.

In this paper it will be seen that the number one, (#1), is treated as a prime number. This is contrary to classical opinion. However, it conforms to the definition of a prime number in that it can only be divided by unity and itself. The fact that "unity" and "itself" are one and the same, and the same as the number itself, is not considered sufficient reason to exclude it from the class of primes.