  We have presented a multivariate polynomial function termed as factor
elimination function,by which, we can generate prime numbers. This function's
mapping behavior can explain the irregularities in the occurrence of prime
numbers on the number line. Generally the different categories of prime numbers
found till date, satisfy the form of this function. We present some absolute
and probabilistic conditions for the primality of the number generated by this
method. This function is capable of leading to highly efficient algorithms for
generating prime numbers.
