Is it permissible for a worshipper to invoke blessings upon Prophet Muhammad silently when his name is mentioned in an audible prayer, and does the same ruling apply to all other prophets and messengers?

It is recommended for a worshipper, upon hearing the name of the Prophet, peace and blessings be upon him, to invoke blessings upon him. Analogy dictates the permissibility of invoking blessings upon the rest of the Prophets as well during prayer, due to the generality of the command stated in his saying, peace and blessings be upon him: "Invoke blessings upon Allah's Prophets and Messengers, for Allah sent them just as He sent me."