  We prove that, for every natural number $k$, every sufficiently large
3-connected cubic planar graph has a cycle whose length is in $[k,2k+9]$. We
also show that this bound is close to being optimal by constructing, for every
even $k\geq 4$, an infinite family of 3-connected cubic planar graphs that
contain no cycle whose length is in $[k,2k+1]$.
