Jones's conjecture on nontrivial knots with trivial Jones polynomial

Let $K$ be a knot, and let $V(K)$ denote its Jones polynomial. A knot is non-trivial if it is not isotopic to the unknot. Jones's conjecture. There exists a non-trivial knot $K$ such that

$$V(K)=1.$$

The statement is presented as still open, although Khovanov homology detects the unknot, showing that the analogous question for Khovanov homology has a negative answer.