I've a somewhat silly question, if i have a series of processes that are created ... these are not necessarily some sort of inheritance, the pid of the processes have to be numbers continuous or random pids ?
Depends on your platform, but you shouldn't be dependent on any specific order to your pid's.
On Windows, pid's are usually allocated in increasing numbers, but as processes exit the pid's can be recycled and you will see cases where a newer process has a lower pid than an older process. Also, pid's come out of the same namespace as tid's, so you won't see pid's increasing by 4 as you launch new processes.
From your perspective they will be random. The system manages those numbers and assigns them as processes are created. A quick look at the PID's currently on my system shows that they are all divisible by 4...
This is determined by the Operating System.
In general, they are usually sequentially assigned by the OS. However, this behavior is not something to base decisions upon, since most operating system specifications state that the process ID allocation is not deterministic (ie: it could be random, and could change in a future version, etc).
On Linux, pids are generally allocated sequentially on a system-wide basis, but they will wrap around periodically, and there may be 'gaps' caused by other unrelated processes. In an extreme case, you might have a 'gap' wide enough to cause this wrap-around. So don't assume any particular ordering - instead explicitly keep track of your parent or child process' PIDs.
If you're creating those childs you'll know the pid, the pid depends on the OS scheduler, you don't care about this stuff.
Here's how to test what your system does:
for i in $(seq 20); do ps; done | grep ps
The PIDs of the "ps" commands are consecutive processes, or as close to consecutive as any other caller could reasonably expect to be able to spawn.
My cygwin terminal on Windows allocates them randomly-ish, my web host allocates them sequentially (with occasional gaps which presumably are for processes run by other users or servers).
Some consider sequential PID allocation to be a slight possible security concern, since it may leak information between users of a multi-user system.
On AIX, you will often see bigger (e.g. 7-digit) PIDs and they are not necessarily allocated semi-sequentially (though I seemed to be cycling in increments of 2 when I tested; there was another user on the machine, so it may not mean much).
Fresh login on an AIX 5.3 machine:
$ ps
PID TTY TIME CMD
1060910 pts/27 0:00 -ksh
1155224 pts/27 0:00 ps
$