OpenPGP is a protocol that uses various encryption algorithms in it.
For public keys, they're either RSA, DSA, or Elgamal. Note that DSA is signing-only and Elgamal is encryption-only. DSA and Elgamal are variants of Diffie-Hellman and thus their relationship to prime numbers is slightly tangential.
RSA keys are made of (typically) two prime numbers multiplied together. There are three-key variants, and more, but hardly anyone does that.
Typically, each of the primes is half the size of total key. So a 2K-bit key has two 1K-bit numbers multiplied together. Obviously, if you were doing a three-key variant that had three primes each 1K big, then the total thing would be 3K-bits long.
The security of RSA rests on the difficulty of factoring, and I'm sure you will note that a number made of three 1K-bit numbers is not substantially differently secure than one made of two. There are plenty of details to debate on that, but since that wasn't your question, I'm not going to go into that long debate. The major point is that we generally assume that an N-bit RSA key is made up of two primes each N/2 bits long.
By the way, don't make RSA keys over 4K (4096). It's obnoxious. They're big, they're slow. Any signatures you make with them will also be big. A number of implementations won't support them, and people will get irritated with you if your key breaks their software. They'll just not encrypt to you.
RFC 4880 says:
* OpenPGP does not put limits on the size of public keys. However,
larger keys are not necessarily better keys. Larger keys take
more computation time to use, and this can quickly become
impractical. Different OpenPGP implementations may also use
different upper bounds for public key sizes, and so care should
be taken when choosing sizes to maintain interoperability. As of
2007 most implementations have an upper bound of 4096 bits.
If you need more security than you'd get from a 3K-bit key, you should strongly consider using elliptic curve keys. A 3K-bit integer key is equivalent to a 256-bit ECC key. If you use the NIST P-384 curve (which has 384-bit keys), then you'll have more security than that 8K-bit RSA key and people will be much happier.
Yeah, I know that as of this writing (summer 2012), that's easier said than done.