Prime ONLY protects against inactivity suspensions.
Although the Prime users have the resource usage limits set higher then those that use the basic free service, there's still limits at place.
This is a snippet from the log noting your account to be using one full CPU and then some of a second CPU:
Wed 07 Sep 2011 08:34:14 / 1315398854:
cpu: 110.000
mem: 0.200
ctm: 00:00:01
commands: (1 total)
...
SCRIPT_FILENAME=/home/[cpaneluserhere]/public_html/search.php
....
That is the highest notation that I saw, there's a few log notes ranging from 50% of one CPU to the above mentioned notation as well.