Nakanishi's 4-move conjecture for knots

A 4-move is the local operation on a link diagram that replaces four consecutive half-twists between two strands by the opposite four half-twists. Nakanishi's 4-move conjecture. Every knot can be reduced to the trivial knot by 4-moves. This conjecture is an early move-equivalence conjecture in knot theory, formulated by Nakanishi in 1979 before the 3-move conjecture was formally stated; the supplied evidence says it is disproved by the $2$-cable of the figure-eight knot with a half-twist, a knot with 17 crossings.