In part a) of the above diagram, a new process has been created and the master process sends the first number (2) to it. Since this is the first number that the child process receives, it knows that it must be prime. It also knows that it must discard any multiples of 2, since they cannot be prime. It will pass any other numbers to the next child process.
In part b), the master process sends the value 3 to the first child. Since the first child cannot discard the number, it sends 3 to a newly created child process.
In part c), the master process sends the value 4 to the first child. The first child checks if 4 is a multiple of 2, and since it is, the first child does not send it to the next child process.