I would like to convert my equations in a MathCad worksheet directly into a higher language (C or C++, or other) to run on a super computer. Is there a software or second source software that can do this directly?
Sorry, but there is no way to automatically do this.
In Mathcad Prime 3.1 SDK shows an example demonstrates how you can read SExpressions and translate them to use PTC Mathcad Prime as a C++ class generator.
With the Mathcad Prime 3.1 SDK can I convert worksheets directly to C? It seems many of the commands between C and Mathcad are similar.
I haven't even looked at the Prime 3.1 SDK, but I am >99.99% certain that the answer to your question is "no".
I used https://github.com/std8590/xmcd2cs to convert 90% of my Mathcad xmcd files to C#.