Is the hadith, "Fasting Ramadan in Makkah is equivalent to fasting a thousand months elsewhere," authentic?

It is not true that fasting Ramadan in Mecca is equivalent to one hundred thousand fasts. A weak hadith, which is not authentic, has been narrated regarding this. The established multiplication is only for prayer: prayer in the Sacred Mosque (Masjid al-Haram) is equivalent to one hundred thousand prayers, and in the Prophet's Mosque (Masjid an-Nabawi) to one thousand prayers. As for other good deeds like fasting, charity, and remembrances, they do have merit in Mecca, but there is no proven evidence specifying the quantity of their multiplication, except for prayer.