Personal opinion / Statement
Personally, I don't really believe that these formulae and number mean anything, and that all results are probably purely coincidental. I was fun doing the exercice, nothing more.
I even give the original Koide formula's result a 50/50 chance to be coincidental, so I wouldn't bet anything on this.
Update - 2021
The model presented on this page is based on particle mass data from 2019. Using the latest data from 2020/21, the model is working less well, but I probably won't have the time to see if I can update it.
It should be noted that quark masses cannot be measured directly, as it is physically impossible to isolate quarks, so the quark masses are mostly calculated using Quantum Chromodynamics (QCD) models, so that the mass data will greatly depend on the QCD models used, even more than on the most recent data collected by experiments.
I started working on this in December 2019 in Mainz, Germany, after having read an article on the original Koide formula from 1981.
The software used to calulate the results had been developed in early 2019, and I finished work on the paper in mid 2020.
Note that the content of this paper does not represent a "theory" or anything similar. I only wanted to demonstrate that particle masses can be fitted in a specific table using specific formulae and specific primes. It's nothing more, and nothing less than that.
You may also download the paper in PDF format: