I'm developing an algorithm that will enable me to factor integer numbers using the methods of partial differential equations.
Attached I've provided a copy of my Mathematica Notebook factorization algorithm.
In this particular case, the algorithm factors the number: "18,167 = (37*491)".
At the bottom of the Notebook the computed (i.e. estimated) values of the variables are shown. The key aspects to observe are as follows:
(1) x -> 491.000000000000000094330715800440587325 (2) y -> 37.000000000000000000000000000000000000 (3) (xy) -> 18167.000000000000003490236484616301731
The answers shown above are correct. I have hardcoded (i.e. set) "y". To implement the minimization, I'm using the "NMinimize" function. The estimated values of "x" and "xy" appear to have "floor" on the accuracy of the number of computed digits. Ideally, I would like for the "accuracy" to be 50, 60, or more decimal digits to the right of the decimal-place.
Despite having set "AccuracyGoal -> 40, PrecisionGoal -> 40, WorkingPrecision -> 40" and etc. I'm unable to improve the accuracy. The accuracy appears to be limited to approximate "machine precision".
Yes, I have tried to vary "AccuracyGoal, PrecisionGoal, WorkingPrecision, and Method". I appear unable to improve the decimal-place accuracy.
At present, I'm using Mathematica 11.3. I can upgrade if needed.
I'm open to any advice and recommendations to extend the decimal digits to the right of the decimal-place.
Thanks, Edward
Attachments:
