  The aim of this paper is to prove Golyshev's conjecture in the cases of Fano
threefolds $V_{10}$ and $V_{14}$. This conjecture states modularity of D3
equations for smooth Fano threefolds with Picard group Z. More precisely, we
find counting matrices of prime two-pointed Gromov-Witten invariants for them.
For this we use the method that lets us find Gromov-Witten invariants of
complete intersections in varieties whose invariants are (partially) known.
