Primecoin is actually one of the only projects of its kind because it actually gives a purpose to Proof of Work mining. In all Proof of Work cryptocurrencies the miner's computer must solve certain problems set forth for the purpose of validating blocks, the use case ends there. The "problems" are not needed for anything else. XPM is actually a scientific initiative which turns these hashes into powerful tools that search for prime numbers.
While adding a purpose to the massive hashing power that cryptocurrencies consume is admirable, those interested in making a Primecoin investment should be aware that this project is quite niche. Their social media accounts are dead for the most part, and there is no ongoing development for this currency. While there are some community members still hanging around, and there might even be some people mining it, it's unlikely it will see any future advancements.
Investors can buy Primecoin on a good number of exchanges. They have a lot of listings, and even some popular options are present here. While they have quite a few pairings, only two of them have enough liquidity to be able to successfully support a trade, unfortunately. Traders will need to utilize either Bitcoin or the US Dollar Tether.
In order to safely store your assets, you'll need to download the official wallet from the coin's website. They have installation packages for Windows or Linux. There does not seem to be a download available for Mac, so if you're a Mac user you'll need to find a workaround or emulator that is capable of hosting one of the other wallets. In any case, cryptocurrency enthusiasts should make sure to always back up their wallet file in order to protect their investment. If your host device becomes inoperable, this will be the only way to restore access to your wallet.