How would I go about generating this... I want to keep my primary key sequential and have a 12 digit unique pin generated for each new object added to the database.
All solutions so far lack one thing essential to your application: Security!
You said you will be using these numbers as a (product) verification code - so you really, really want this to be unpredictable, otherwise it will get exploited.
Neither MySQL's built-in RANDOM
function nor any of the random functions PHP provides today are secure random functions. They behave pseudo-randomly, alright, but they all are predictable!
Your only chance is to whip up something of your own using /dev/urandom
on a *nix machine or leveraging the Crypto API on Windows. OpenSSL does provide secure random numbers based on these mechanisms - you could reuse this either in a C extension for PHP or by reading the output from a command line script called from PHP. See also this answer.
About your requirement for the numbers to be sequential - is this really so important? It does complicate things enormously. Otherwise you would be good to go with a simple secure 6 byte random number encoded to a string using hex encoding (yielding a 12 character string). Although I would recommend making it 10 bytes and 20 characters to be safer.
But if you want to be sequential, which I interpret as monotonously increasing (because a simple +1 would be trivially predictable), this makes things just so much more complicated. And you don't gain anything from this complexity, the only thing that might happen is that you break the security by inventing some obscure scheme that is easily exploitable.
My suggestion: Add another column that acts as a plain old auto-incremented ID and add the code as a random number constructed as above as a separate column. As far as I see, there's no need to require the product activation code to be the ID at the same time.