It is known that the general Ramanujan–Nagell equation $x^2+D=y^n$ Have no solution for $ D<100 $ see the table in the paper
CLASSICAL AND MODULAR APPROACHES TO EXPONENTIAL DIOPHANTINE EQUATIONS II. THE LEBESGUE–NAGELL EQUATION by YANN BUGEAUD, MAURICE MIGNOTTE, SAMIR SIKSEK
My question is there some work for the case when $D>100$?