The search for efficient algorithms to produce primes is motivated largely by the needs of cryptologists and number theorists. Many open problems in these areas rely on very large tables of primes for their solution. The Sieve of Erathosthenes is a well known method for generating tables of primes up to a given natural number, N. Significant work has been published that improves on the original sieve to generate primes, some in sublinear time. This project will investigate six variations on the sieve to generate large tables of primes efficiently using parallel architectures. Initial testing and implementation of the algorithms will be based on selected mapping and communication structures that are determined to be optimal. The most effective architecture will be identified for each algorithm. Preliminary data will give insight into the scope of memory limitations that must be addressed in order to generate primes to N = 10^18. Break even points between the various algorithms will be provided because it is important to determine how feasible it is to reach a certain point given a particular algorithm. ***
