Bell's Primeness Criterion for W(2n + 1)

On the basis of experimental work involving matrix computations , we conjecture that a criterion due to Bell for primeness of the universal enveloping algebra of a Lie superalgebra applies to the Cartan type Lie superalgebras W(n) for n = 3 but does not apply for odd n 5. The experiments lead to a rigorous proof, which we present.