According to a story that I read, Mr Sullivan was waiting for a flight in London and heard a bunch of girls screaming at the airport. He concluded correctly that American girls would probably scream too. Shortly after, he directed his team to get The Beatles on his show.
Around 8:12 pm ET, Paul McCartney sang "Close your eyes....." and Beatlemania was on. All together, The Beatles performed twice that night and 73 million people watched them.
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