Is prayer in Madinah equivalent to a thousand prayers, considering the sanctity of all of it, and what distinguishes prayer in the Prophet's Mosque from other places of worship within Madinah?

One prayer in the Prophet's Mosque—the one that existed during his time—is equivalent to one thousand prayers in any other mosque, except for the Sacred Mosque (Masjid al-Haram).

Scholars have differed regarding what was added to his mosque after the Prophet's death. Al-Nawawi held that these additions are not included in this virtue, while Ibn Taymiyyah and Al-Muhibb Al-Tabari were of the opinion that this virtue encompasses all additions made to the mosque, and this is the preferred view among the majority of scholars.

As for the Haram of Madinah (the sacred precinct of Madinah), it is not included in this virtue mentioned in the Hadith.

In summary, the virtue mentioned regarding the superiority of prayer is specific to the Prophet's Mosque and whatever has been added to it that takes the ruling of the mosque.