Where does the British Prime Minister officially reside?

Downing Street in London has been the official residence of the British Prime Minister since 1735. Number 10 Downing Street, specifically, is more than just a house; it's a symbol of British political power. Originally, King George II offered the house to Sir Robert Walpole, often considered Britain's first Prime Minister, as a gift. Walpole accepted it, but only on the condition that it would be an official residence for future Prime Ministers. While Buckingham Palace is the official residence of the monarch and Windsor Castle is another royal residence with a long history, neither has ever been the Prime Minister's home. 18 Oxford Street is simply a street address and has no political significance. The Prime Minister needs to be close to Parliament, and 10 Downing Street provides that proximity, along with offices for staff and meeting rooms, making it the practical and symbolic center of British government. It's not just a place to live; it's where the Prime Minister conducts the business of running the country.
Imagine the Prime Minister's home as a famous address, like a well-known street number in London.