This research aims to generate primitive weird numbers using mathematical and programming methods. The n function was used to create these numbers within a specific range where p and q are primes, b > a > 2 also K ≥ 1. Programming was implemented in Python to generate these numbers. A function  G(x) for generating prime numbers was also used, modified to create weird numbers, and implemented programmatically. The findings of this research have been verified through previous research, and finally, tables and graphs of the resulting numbers were plotted. Furthermore, Number theory is regarded as the core of cryptosystem science, where there are several distributions of various types in the sequence of the natural numbers. This work concentrated on finding a bit of enhancement of the general form of the wired numbers in order to use them in cryptosystem work.