300k updates in script running slow in sql*plus

I have a script that has around 300k update statements against a table with 500k rows. It seems to be taking about 1 second per update statement. So it might take 80 hours to run, 300k/60/60=83.3. I attempted to speed it up by putting around 10k rows within begin/end; and run as anonymous pl/sql block but it doesn't seem to be running any faster. Any ideas on how I might speed this up? This is an 18.14.0.0.0 database running on Solaris. I'm running sqlplus locally on the db server to avoid the network round trips. The update statements look like