Let $M = 2\Bbb{N} + 1$ be the monoid of odd naturals. It contains all odd primes. If for some $2n \in \Bbb{N}$ we have that there exists no prime solution to $2n - p = q$, then that's the same thing as saying the submonoid $N$ generated by all $2n - q, n \in \Bbb{N}, q \in \Bbb{P}$ such that $q...

I'm vaguely aware that people have proved that by starting with any number, and iterating through the Collatz algorithm one will eventually reach a number divisible by 4. But I am looking for the proof that one will eventually reach a number divisible by 8 for every odd number n divisible by 3. T...

Is the following paper a correct proof of the Collatz conjecture? I read through it one time. At least it seems to have demonstrated the simple, yet clear, mathematical induction logic, though I have not checked all the detailed analytical formula yet. https://www.mdpi.com/2227-7390/10/12/1972