It was 50 years ago today (January 6th, 1973) that Carly Simon scored her sole chart-topper to date, when “You’re So Vain” hit Number One on the Billboard Hot 100 for the first of three weeks.

The song, which was produced by Richard Perry and included on Simon’s 1972 third album No Secrets, featured solo Beatles sideman Klaus Voormann playing the distinctive bass part, Jim Gordon from Derek & The Dominos on drums, and Jimmy Ryan on guitars. Mick Jagger sang the instantly identifiable backing vocal.

Throughout the years Simon has refused to say publicly who exactly “You’re So Vain” was written about and has sometimes said that it was a composite of several different men. She has confirmed that the second verse was indeed about actor Warren Beatty — but not the entire song.

At the 2003 Possible Dreams charity auction in Martha’s Vineyard, Simon auctioned off the identity of the person who “You’re So Vain” was about. NBC’s Dick Ebersol had the winning bid of $50,000 and learned the secret — but was sworn to secrecy by Simon, as part of the deal. Simon has also reportedly revealed to both Taylor Swift and Howard Stern who the song is about.

Carly Simon recalled recording the backing vocals to “You’re So Vain” with Mick Jagger and Harry Nilsson: “Y’know, Harry and I were in there, we were doing it, it didn’t quite have the right character, because it wasn’t tough. I didn’t ask Mick to come over because I needed a tough voice. Mick just showed up, and so we invited him to join us. And so the three of us were singing it together. And it sounded too sweet. The three-part harmony didn’t work, but Harry was the first to notice it, and Harry said, ‘Well, why don’t the two of you try it together?’ Y’know that’s how it happened — but more than anything Harry wanted to go out and have a drink (laughs).”

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