In Pennsylvania, state police run the background checks. Last year, they ran nearly a million. There is no waiting period in Pennsylvania, so once you pass the background check, which can only take a few minutes, you can buy a firearm. You do not have to register your gun in Pennsylvania, but state police do keep a sales database using the serial numbers on the guns. There is no limit on how many guns you can buy.
Check out this video to find out more.