5 problems

Let $K_1$ and $K_2$ be the knots occurring in Theorem; the theorem has an extra assumption that $K_1$ and $K_2$ are not 2-bridge. Generalised strong primeness conjecture. The concl…

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 conjecture. The authors conjecture that $K_{-4}$ is also prime.

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