It’s 32768 by default, you can read the value on your system in /proc/sys/kernel/pid_max.
And you can set the value higher on 64-bit systems (up to 222 = 4,194,304) with:
echo 4194304 > /proc/sys/kernel/pid_max
Read more here:
http://www.cs.wisc.edu/condor/condorg/linux_scalability.html (via archive.org)