Note on pri from ps man page:
"pri PRI priority of the process. Higher number means lower priority"
Consider PID 26073 here
$ renice +15 26073
26073: old priority 5, new priority 15 # I am making this process more nice
$ ps -t 1 -o pid,ppid,%cpu,stat,cmd,bsdstart,time,pri
PID PPID %CPU STAT CMD START TIME PRI
9115 18136 0.0 Ss bash 17:10 00:00:01 19
26073 9115 12.0 RN+ p4 sync 19:06 00:02:56 4
STAT = RN+ which means : Running , low-prio ( nice to others), foreground. PRI=4 (1)
$ sudo renice -10 26073
26073: old priority 15, new priority -10 # I am making this process less nice
$ ps -t 1 -o pid,ppid,%cpu,stat,cmd,bsdstart,time,pri
PID PPID %CPU STAT CMD START TIME PRI
9115 18136 0.0 Ss bash 17:10 00:00:01 19
26073 9115 12.0 S<+ p4 sync 19:06 00:03:15 29
STAT = S<+ which means : Interruptible sleep , high-prio ( not nice to others), foreground. PRI=29 (2)
In case 2 the process priority increased or to say it another way the process became higher priority.
But this contradicts what definition of pri says from man page ( that higher number means lower priority)