Simultaneous numerical solutions of the second and first order partial differential equations describing the first order decomposition of seven explosives are presented. The solutions were used to compare the critical rates of heat production per unit mass of each material. The lower such a rate is the more sensitive is the explosive. The relative sensitivities of Tetryl, PETN, RDX, TNT, HMX and TATB are as might have been predicted. However, PBX9404 shows apparently enhanced thermal sensitivity compared with these six explosives. This provides a warning that some modern low vulnerability composite explosives based partly on propellant ingredients might constitute enhanced thermal threats.