I have been working on a number theory conjecture. I wrote these programs to create practical proofs for my conjecture. I aim at checking each individual number up to a decent range to give a solid backing to my conjecture. Since I am dealing with large scale prime numbers, I had tons of complexity issues. As I was only learning python, I have had to make more than 25 versions of the same programs, each time lowering the complexities. I have tried to identify patterns in the number of representations. However, currently, I'm focussed on achieving single representations for given numbers. Feel free to contribute if you have less complex ways to achieve this.
P.S. The conjecture will be published shortly.