Trying to avoid shelling out hundreds of dollars so I'm using what I can for free online. This is what I've come up with so far:
Trying to use this to demonstrate a possible way to prove the twin prime conjecture:
For every prime $p$ greater than 2, there exists one or more twin primes as follows: $(3pn-4, 3pn-2)$ where $n$ is some positive odd less than or equal to $p$.
With the free version, I can only go so far.
My questions are these:
- Would someone help test for a counter-example. Maybe refine this code to only print if a counter-example exists in the first million or so primes.
- Would someone perhaps plot
Length[twin]vs. $p$ to show that as $p$ increases, so does the number of twins found.
I realize this question requires simultaneously a lot of knowledge of primes and Mathematica, as well as requiring you to look through code to fully understand the question, so thanks in advance.