How to get functions about prime numbers in Excel 2013?

I have very limited experience in number theory like that. I do know that the algorithms for these kind of functions are fairly complex, but also fairly well established.

The short but useless answer to your question is, yes, it can be done. The difficult part is how best to approach it.

One approach would be to take code from the internet (most of it seems to be in C, some of the older stuff is in Fortran), adapt and compile it into a dll in such a way that Excel can call those functions as user-defined functions.

Another approach would be to take the same C code, convert it to VBA, then you can use those VBA UDF's in your spreadsheet.

For some of these (like pi(x) or prime(n)) the "easiest" approach might be to compute the results using the Mathematica function and build a table of results. This table could then be imported into Excel and used as a simple lookup table.

I realize it is not much help, but this will at least bump your question back to the top and see if anyone else has any additional suggestions.