If your pc's are fairly robust and having unique id's is of VITAL importance (it seems it is) then you ought to consider the use of GUID data type as the primary key for patient. I don't know what the chances of duplication is (probably around 0.00000000000001%), but it's far better than your suggestion from that perspective. This is just an example to illustrate my point, but if you can monkey with the autonumber sequence, so can anyone else down the road. If that happens, will you duplicate? Who knows?
The GUID data type is a large number, but it's the way it is built that pretty much guarantees uniqueness. Part of the value is clock based, part comes from the identification of the hard drive (serial number? I forget exactly). What is the chance that 2 hard drives that have the same contributing id doing something at the exact same clock millisecond? As if that were not enough, there are more parts to the ID number.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.