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I got sucked into this problem as an undergraduate in mathematics. I similarly wanted to limit my search space and my initial work lead me down the path of prim
by pg_bot 7y ago
I got sucked into this problem as an undergraduate in mathematics. I similarly wanted to limit my search space and my initial work lead me down the path of prime factorization. If every prime number follows this pattern then logically every number also follows this pattern. Then you get to the hard part which is why or why not would a prime number follow this pattern. So then you go looking for the reasons why prime cycles can or cannot exist, your brain melts, and then you work on something else. Fun times though.
- cyborgx7 7y agoAs a computer science (Informatics) student, I shy away from any path in a prove that makes me make some kind of statement about primes. They are the death of every approach they are involved in, to me. From my one hour of thinking about this problem, I think sums of finite sequences are a much more promising approach. But obviously you'd know way more about all of this than me.
- RockIslandLine 7y agoSieve of Aristothenes + induction seem most likely to me. "For every binary sequence of length X, the Collatz iteration ends at 1. Adding more zeros clearly does not change the result, therefor adding more ones is the only path which might disprove the conjecture." Eventually you build up to a catalog of proven sequences that all other numbers must necessarily step into at some point.
- AstralStorm 7y agoYou just made it as hard as proving generalized Riemann hypothesis. Not good progress with that task. Might as well start working on Goldbach conjecture.
- mkl 7y ago*Eratosthenes, best known for being the first person to calculate the circumference of the Earth.
- Gene_Parmesan 7y agoMany of the smartest mathematicians who have ever lived have spent collective man-decades thinking about this problem. Any idea any of us can come up with in an hour of thought will have been considered and rejected a thousand times already by others. This is partly why it's such a trap. It's like trisecting an angle or squaring a circle -- easy to state the problem, easy to start playing around with it. In my amateur opinion, any proof related to Collatz would be similar in complexity and non-obviousness as the proof of Fermat by Wiles, if such a proof is even possible.
- cyborgx7 7y agoI know, I know. But I kind of want to figure out why what I'm thinking doesn't work. I want to run up against these problems myself.
- khawkins 7y agoFor most, it's far more fruitful to jump on https://math.stackexchange.com/ https://math.stackexchange.com/ and work on questions there. Low impact, but high probability it is within anyone's realm of capabilities. Answering 100 questions people want to know is bigger impact than making 0% progress towards a problem you have no realistic chance of solving.
- egdod 7y agoThere are tons of theorems that are most easily proved by showing that some statement holds for primes, and extending it through some sort of multiplicative structure to all numbers.
- bluGill 7y agoI don't think primes are a factor - if it was 3n+1 is also prime, and it is easy to shown 3n+1 can be factorized into 2 and something else.
- AstralStorm 7y agoThe starting number has to be a prime, and the result is that you would cycle to that number and no further. Alternative result would mean literal mathematical chaos. The number would be an origin point of an attractor. Approaches to find such a counterexample would require something akin to guessing a fractal. Trying to evaluate the Lyapunov exponent of this system could be fun. Applying Poincare-Bendixson and Bendixson-Dulac to a dual system that is so defined as to reject the final limit cycle and is differentiable, perhaps... Too big math for me. It smells of Hilbert's sixteenth problem.
- WhompingWindows 7y agoCan you write more about prime cycles and your brain melting? That sounds neat.
- undershirt 7y agoi wandered into a talk at MAA ~2006, where an old professor spoke deadpan on how he “wasted his life” on this problem. it was a poignant comedy, and he delivered it well. dont fuck with this problem.