Is it authentically reported that "a prayer in the Sacred Mosque is equivalent to one hundred prayers in the Prophet's Mosque"?

There is no narration with the exact wording, "a prayer in the Sacred Mosque is equal to a hundred prayers in the Prophet's Mosque." However, a similar meaning is conveyed with a close wording by Ahmad and Ibn Hibban from Abdullah ibn Al-Zubair, that the Prophet (peace be upon him) said: "(A prayer in) this mosque of mine is better than a thousand prayers in any other mosque, except the Sacred Mosque. And a prayer in the Sacred Mosque is better than a hundred prayers in this (mosque)," meaning the mosque in Medina. The chain of narration for this hadith is authentic, and the phrase mentioned in the question is a narration of this hadith by meaning. Narration by meaning is permissible according to scholars if the meaning does not change and the narrator is knowledgeable of the language and meanings.