  A perfect polynomial over the binary field $\F_2$ is a polynomial $A \in
\F_2[x]$ that equals the sum of all its divisors. If $\gcd(A,x^2-x) \neq 1$
then we call $A$ even. The list of all even perfect polynomials over $\F_2$
with at most 3 prime factors in known. The object of this paper is to give the
list of all even perfect polynomials over $\F_2$ with four prime factors. These
are all the known perfect polynomials with four prime factors over $\F_2$.
