3 problems

Let $n$ be odd with $n\geq 3$. A minimal prime free knot diagram is a minimal free knot diagram representing a prime knot, and a trefoil descendant is a resultant trefoil obtained…

Let $K$ be a prime knot, let $c(K)$ denote its crossing number, and let $W(K)$ be its Whitehead double. Jang–Lee's conjecture. The crossing number of any prime knot coincides with…

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