Tutte and Kauffman polynomials detect primeness of knots and links

Let $P$ be a polynomial invariant of a knot or link $KL$. Say that $P$ is factorizable for a connected sum when it satisfies

$$P(L_1\mathbin{\#}L_2)=P(L_1)P(L_2).$$

Primeness-detection conjecture. The Tutte polynomial and the Kauffman two-variable polynomial detect primeness: they are not factorizable for prime $KL$s.

The claim is motivated by computations showing that other polynomial invariants can factor for some prime knots or links, whereas the authors found no such exceptions for these two polynomials. The supplied material does not establish whether the claim has since been resolved.