Name: PARI/GP
Homepage: https://pari.math.u-bordeaux.fr/
Why should this be included in the repository? While there are calculators (e.g. SpeedCrunch), statistics software (e.g. R), etc., there's nothing quite like PARI/GP available now. It's an algebra system aimed at number theory, but even if you're not using it to [dis]prove non-trivial zeros are on a critical line, it can be useful for much more basic algebra. For example, type 274 / 834 + 369 / 528 into your typical calculator and you'll probably see ~1.0274 as an answer, while gp will return an exact answer of 75403 / 73392.
Is it Open Source? Yes, GPL'ed since version 2.1.0.
Who and how many users do you anticipate will use this software? Anyone who is interested in number theory will probably want it. I suspect anyone who has ever desired more than just your basic calculator will find merit in it, and may use it as well. As for how many people that is, I have no idea.
Link to source tarball/zip file: Stable, Development, and Snapshots Directory.