Suppose a pipeline of p processes operates on a stream of integers, 2, 3, 4, . . ., passed from one process to the next. Each process remembers the first number, N, it receives and passes to the next process all remaining numbers in the sequence that are not multiples of N. When the last process receives a number, the algorithm stops. (This algorithm is a parallel version of the sequential sieve of Eratosthenes algorithm.)

a. Determine the task of this algorithm.

b. Develop a program for a sequential version of this algorithm.

c. Develop a program to simulate the pipeline version.

d. Write an analysis of the amounts of computation and communication for the sequential and pipeline versions and of the speedup.