I would really like to get some constructive feed back on this prime-seeking algorithm. Computationally it's no better than the rest. However, it does offer some unique insight. I have partitioned the set of naturals between prime and composites using a rigorous structural schema that I prove in the following thesis: https://sites.google.com/site/primenumbertheory/home/the-prime-thesis Let me know what you think. I appreciate any further insight the community can offer me. Shalom.