  In this paper, we prove the mirror symmetry conjecture between the
Saito-Givental theory of exceptional unimodular singularities on
Landau-Ginzburg B-side and the Fan-Jarvis-Ruan-Witten theory of their mirror
partners on Landau-Ginzburg A-side. On the B-side, we compute the genus-zero
generating function from a perturbative formula of primitive forms introduced
by the first three authors recently. This computation matches the
orbifold-Grothendieck-Riemann-Roch and WDVV calculations in FJRW theory on the
A-side. The coincidence of the full data at all genera is established by
reconstruction techniques. Our result establishes the first examples of LG-LG
mirror symmetry of all genera for weighted homogeneous polynomials of central
charge greater than one (i.e. which contain negative degree deformation
parameters).
