\subsubsection{Sieve of Eratosthenes}
Perhaps the simplest example is provided by the old algorithm for
computing the sequence of primes.

Assume that the timed sequence of natural numbers, starting with
{\tt 2} is produced on {\tt Val}. The program asserts that each
such number {\tt N} is prime by default --- unless there is
reason to believe that it is not. If the default is not defeated,
an agent {\tt sieve} is set up that declares every subsequent
number {\tt X} {\tt not\_prime} if it is a multiple of {\tt N}.

\begin{ccprogram}
\agent primes(Val, Output):: 
    always\ N\$\(Val:N -> not\_prime ~> [\{Output:N\}, always\    sieve(N, Val)]..

\agent sieve(N, Val) :: 
    X\$(Val:X -> X\ mod\ N {={}}:{={}} 0 -> \{not\_prime\})..
\end{ccprogram}

The overall program is obtained by coupling with the {\tt
counter} from the previous section:
\begin{ccprogram}
\agent primes(Primes) :: 
  Val^[primes(Val, Primes), counter(2,Val)]..
\end{ccprogram}
\noindent The program may be run in a harness (using {\tt watching}) in the
same way as {\tt fib}.