Only 52 Primes Have This Shape

The largest prime number anyone has ever found has 41,024,320 digits. Printed at a few thousand digits to a page, it would fill a stack of paper around thirteen thousand pages thick, and reading it aloud, one digit a second, would take about ninety-five days. Yet we know for certain it is prime without ever dividing it once. This is the story of that number: two raised to the power 136,279,841, minus one. We meet the Mersenne primes and the simple shape that makes them testable, the Lucas-Lehmer test that certifies a forty-one-million-digit number with one short squaring loop, the volunteer GPU cloud that found the record on October 12, 2024, the seventeenth-century friar whose name these numbers carry, and the ancient link to perfect numbers that reaches back to Euclid. We close on what is still open: nobody knows whether there are infinitely many Mersenne primes, and nobody has ever found an odd perfect number. Chapters: 0:00 The Question 1:36 What It Actually Is 3:14 Why Mersenne Numbers 4:40 Necessary Is Not Enough 6:04 The Test 8:01 The Hunt 9:40 The Man 11:02 The Ancient Connection 12:40 Coda Every number on screen is exact, computed and verified: the 41,024,320-digit count, the Lucas-Lehmer run, the perfect numbers 6, 28, 496, 8128, and the record's place as the 52nd known Mersenne prime. @euclideayt Music by Vincent Rubinetti Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/a...