Categorization - This Section categorizes all equations types within the overall single variable polynomial group, into four classes, one of which meets the criteria and three that do not. It also shows that some of the non-conforming equations generate sub-sets of equations that do conform. The conversion of these (Sub-Prime and Symmetrical and Non-Symmetrical V Prime equations) non-conforming equations, to those that do meeet the criteria, (Full Prime), is demonstrated.

The Challenge and Conclusions - This final Section invites readers to participate in an exercise to find those equations that while meeting the criteria, generate all the prime numbers between 101 and 200 that have not been covered by those discussed in the earlier Sections. There are eight numbers not accounted for that will require a maximum of seven equations to generate them. To assist in this exercise a prime number listing program can be downloaded to check the numbers generated by any potential equation. The program is a Visual Basic program and is supplied as a .ZIP file incorporating four files. The main program is PRIMES.EXE and can be located anywhere convenient in the directory structure. The remaining three Visual Basic support files should be placed in the WINDOWS/SYSTEM directory, (the Registry is not altered). The Zip file is available here:- PRIMES.ZIP.

Appendix A and References - The Appendix provides a listing of redundant equations in the form of :- (i) "Repeaters", equations that meet the criteria but simply repeat primes found by other equations. (ii) "Sub-Prime" equations that do not meet the criteria but generate a sub-set of a Full Prime equation. (iii) Symmetrical and Non-Symmetrical V Prime equations that have been converted to Full Prime.