For me playing with numbers is a lot of fun and one of my frustrations it seems like a long time ago was reading through "number theory" without any numbers in it! So there would be this long dense abstruse passage of complex mathematics that lead to some conclusion and nary a number in sight! My research is NOT that way.

Here I'll put up links to some posts with some of what I think is the easiest research to write a simple computer program to watch the numbers.

That doesn't mean I've coded all these myself as most of my effort in that area was with counting prime numbers over a decade ago.

Here's something I noticed again recently--what I think is my own axiom:

somemath.blogspot.com/2010/02/prime-residue-axiom.html

It links to my prime gap equation on it as well. I introduced the prime gap equation back in 2006 so there's a post where that is done, but I think the link above helps explain things better, before you get to the prime gap equations, as it's more up to date with my more matured thinking.

Oh yeah, so what are you able to code? Well the prime gap equation lets you predict how many primes in an interval will have a certain gap, like 2 or 4 or 6. You can then go look in those intervals and see how accurate it is. If that's fun for you, then you can do it with that math.

One of my results lets you play with some cubic Diophantine equations:

somemath.blogspot.com/2013/03/generalizing-cubic-diophantine-solution.html

I haven't seen a lot on this subject with web searches. Coding it should be easy enough then it's just a matter of playing with the numbers and watching them follow the rules exactly.

Of course there's also my prime counting function, also known as a prime number counter, where I'll link to one of my other blogs:

beyondmund.blogspot.com/2013/05/simple-and-fast-prime-counter.html

There I use the sieve form and I think it's more accessible to coders as I wrote the post with that in mind, which is why it's on my other blog too.

There are LOTS of examples of math that you can code up with my research as I LOVE playing with numbers. I find it odd that you can have "number theory" which isn't shown with numbers. A fascinating area where you can consider these issues is with my explanation of what was an unsolved problem:

somemath.blogspot.com/2011/09/was-unsolved-problem.html

But I think that shows how people can get to an anti-thesis, where they feel they're doing mathematics even when it doesn't actually work with actual numbers! Huh?

Which to me is kind of a clue, you know?

I don't care how established what you're doing is, or how many mathematicians will line up and say it's great and "beautiful" mathematics: if you can't plug in some actual numbers and get a correct answer, what good is it really?

James Harris