If you've registered then you should have been sent an e-mail with the software key. Mines was 4 digits.
The serial number is the one printed on the back of the CD/DVD cover which you input during installation. You may have already done this, but just in case start Readiris, click on Register and you'll be taken to their web site, fill your details on the registration form which should already have the 15 digit serial number inserted. Once registration is complete you receive the software key almost immediately.