Exploring the Collatz Conjecture: 2000 to Now

[Joseph Parranto]

I have been interested in the attempts to prove this Conjecture since 2000 and like many others (eg Ken Conrow) I have tried to find a convincing solution. Today I read on this forum what looks like a proof that there cannot be an internal cycle beyond 4:2:1 but I don't think the author realizes it as that. Of course that still doesn't "prove" the whole conjecture because it does not address an infinitely long trajectory. I wonder if anyone else has done so. I have created a system to account for every integer possible and its first ascent step that may answer the density problem in nearly every proof offered so far.

 

[mfb]

Write a paper, submit it to a journal. Ideally show it to some colleagues before to check it.
That's how mathematics is done. This forum can't help in that part of the process. If the proof is published we can discuss it here.

Just to be realistic: The most likely result is some error somewhere.

 

[fresh_42]

Here are 344 pages, all dedicated to this problem:
https://www.maa.org/press/maa-reviews/the-ultimate-challenge-the-3x1-problem
How are the odds, you've found something new?
The most promising contribution someone can do, is probably to take part in:
http://boinc.thesonntags.com/collatz/
They started above $2,361,183,346,958,000,000,001.$

„Don’t try to solve these problems!“ (Richard Guy, 1983)

 

[WWGD]

Or maybe try "parallel" problems, like , say, a "5x+1" version, to gather insights into the Collatz.

 

[JED777]

Hello all: I have the Collatz Conjecture infinite matrix that binds all numbers to it. By it, I can take any random number that I think of and determine where it resides in the matrix and what "Exchange" path it is destined to. It proves that no number can go infinitely higher and will return to 1, the base unit of our base 10 numbering system. I am now working on the second part of the proof that there can be no loops, with exception of the loop seen if we operate the number 1 in the conjecture. I am very close. I am about to copyright the Matrix and publish it so that mathematicians far better than me can take this even beyond the Collatz Conjecture. Prime numbers show interesting infinite slopes they must adhere to inside the matrix. Sorry, and not to disappoint, but I avoided using Calculus since so many before me found no solution by it. I will take mfb's advice above and submit it to a Journal as well. Just giving all interested the news of my on-and-off year long work on this, which lead me to the epiphany of this wonderful infinite matrix. Best wishes, JED

 

[JED777]

Or maybe try "parallel" problems, like , say, a "5x+1" version, to gather insights into the Collatz.

I can tell you that the 5x+1 function will deliver you to loops.

 

[fresh_42]

I will take mfb's advice above and submit it to a Journal as well.

This is a bad worded. "As well" let's me assume you will publish it here. However, this is not allowed until it will have been published in a renowned scientific journal first. It would cause its removal and eventually a ban of your account, if you confuse the order. We explicitly do not discuss personal theories and we take this rule very serious. We are certainly the wrong place to discuss any work on the Collatz conjecture which hasn't been reviewed before.

To avoid any misunderstandings, I will close this thread.