  A knot $K$ is called $(m,n)$-fertile if for every prime knot $K'$ whose
crossing number is less than or equal to $m$, there exists an $n$-crossing
diagram of $K$ such that one can get $K'$ from the diagram by changing its
over-under information. We give an obstruction for knot to be $(m,n)$-fertile.
As application, we prove the finiteness of $(c(K)+f,c(K)+p)$-fertile knots for
all $f,p$. We also discuss the nubmer of Seiefrt circle and writhe of minimum
crossing diagrams.
