  We prove that in any unitary CFT, a twist gap in the spectrum of operator
product expansion (OPE) of identical scalar primary operators (i.e. $\phi\times
\phi$) implies the existence of a family of primary operators
$\mathcal{O}_{\tau, \ell}$ with spins $\ell \rightarrow \infty$ and twists
$\tau \rightarrow 2 \Delta_{\phi}$ in the same OPE spectrum. A similar
twist-accumulation result is proven for any two-dimensional Virasoro-invariant,
modular-invariant, unitary CFT with a normalizable vacuum and central charge $c
> 1$, where we show that a twist gap in the spectrum of Virasoro primaries
implies the existence of a family of Virasoro primaries $\mathcal{O}_{h,
\bar{h}}$ with $h \rightarrow \infty$ and $\bar{h} \rightarrow \frac{c -
1}{24}$ (the same is true with $h$ and $\bar{h}$ interchanged). We summarize
the similarity of the two problems and propose a general formulation of the
lightcone bootstrap.
