pgp type encription help

[Cmdr0Sunburn]

im having trouble understanding pgp type encription. from what i read u send out your public key (p*q) and the persion encripting uses a session key that is used to encript the message. then that key is encripted too and sent along with the message. but that would be easy to decpyher, just divide out the public key from the product of the public key and session key and use it to decript. this sounds just as easy as a regular cypher.
this is what i read from http://www.pgpi.org/doc/pgpintro/
is it wrong?

[TheAlchemist]

hey Cmdr0Sunburn,

i dont know the details of pgp but this is how most public key encryption algos work;
two large primes are generated
these are used to compute a key and a cyclic
a public and private key
the public key is given to a mutually trusted certificate authority and the private key stays with you.
the public key is used to encrypt messages and the private key to decrypt them(only the private key can decrypt the msg for now)

why? because we yet dont have factoring algos good enough to factor the numbers generated from the multiplication of the primes and it would take ages to try out every possible combination(in bits)

look at this www.securityfocus.com