My take is that I read this thread and didn't see the OP giving any kind of specific reason to buy a prime, which makes it difficult to give any kind of recommendation.
In general, any purchase of a new lens will be made to address a specific need. In some cases it's just to get a focal length range you don't have already. Like, if I don't have a telephoto lens I might look at a 70-200 or a 100-400, or a long prime.
But if we assume the OP is looking for a prime within the range of some undisclosed zoom lenses he already has, then we need to think about what the OP is looking for from the prime and then ideas may come to mind.
Often, people buy primes within their zoom range just to get a faster maximum aperture. For the OP's stated interest of portrait photography this might make sense, and there are several excellent lenses between 50mm and 135mm (even the 200/2.8L is a consideration if you like very tight framing) for this work.
The OP also likes landscape work. Reasons to select a prime for this work might be to get a lens with very low distortion, or better flare performance, or perhaps to get a lens that is sharper from corner to corner. The problem is, not all primes have these desirable features, so to suggest something here we really need to know what zoom lens you are using for this work, and what specific optical issues you do not like about it. Even then, depending on the focal length range you like for landscapes, there might be zoom lenses that are excellent choices. Primes are not always the best option.