# Collatz Conjecture

Guy Torbet

August 3, 2021

## What is it?

The Collatz Conjecture can be defined simply as:

$F(x) = \begin{cases} \dfrac{n}{2} &\text{if }{n} \equiv 0 \\ 3{n}+1 &\text{if }{n} \equiv 1 \\ \end{cases}$

With any number being passed in recursivly converging on 1 (apparently).

Still unsolved, but verified for everynumber under 268, so gotta start around 3 quintillion.

By adding 1 to your number x, you shuffle its prime factors in a certain way. Its easy to see that x and x+1 share no factors in common, but what else can you say about the factors of x+1 by looking at the factors of x? This, I believe, is the main issue at heart here. The issue of "what the fuck does addition of 1 do to the prime factorization of a number".

there's a pretty shitty "proof" here, written in Java, obviously.

Pretty much, someone thought they were smart by finding out that x must eventually hit some kind of 2k, good read if you're looking for some satire though.

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