Thank you for posting this! ]]>

Please, could you add the eror message “ModuleNotFoundError: ” in your “it fails” description?

It safes a lot of time for searching.

Thank you!

]]>I tested the method 2 in my local, but the same error occures.

I uses python selenium and wanna to run the script inside the php web app.

but when I run the script inside php, it says it can not find the selenium module.

I changed the www-data to my user name of ubuntu.

Let me know what is the solution.

Thank you. ]]>

Very interesting. Thank you for bringing this to my attention.

You wrote:

“Considering Collatz function producing random numbers and over sufficient number of iterations,.”…

In my post about this (http://nocurve.com/virtual-lab/contemplating-the-collatz-conjecture-3n1/) , I mentioned that as far as I can tell, this is the problematic part of the proof is that while it appears to be the case that the Collatz function produces random numbers, this is exactly what needs to be proved to employ the probabilistic proof.

abstract:

A new approach towards probabilistic proof of the convergence of the Collatz conjecture is described via identifying a sequential correlation of even natural numbers by divisions by that follows a recurrent pattern of the form , where represents divisions by 2 more than once. The sequence presents a probability of 50:50 of division by 2 more than once as opposed to division by 2 once over the even natural numbers. The sequence also gives the same 50:50 probability of consecutive Collatz even elements when counted for division by 2 more than once as opposed to division by 2 once and a ratio of 3:1. Considering Collatz function producing random numbers and over sufficient number of iterations, this probability distribution produces numbers in descending order that lead to the convergence of the Collatz function to 1, assuming that the only cycle of the function is 1-4-2-1. ]]>