As far as I can tell, a simple dual core processor and if you are using 2GB of RAM, you will find yourself doing quite well with it.
I've been reading the Slackware Linux Essentials, and it states that the system requirements to run Slackware are as follows:
Processor - 586
RAM - 32MB
Disk Space -1GB
Media Drive - 4x CD-Rom
Hopefully that will put it into perspective for you. Enjoy =)