The Oldest Unsolved Problem in Math

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A massive thank you to Prof. Pace Nielsen for all his time and help with this video.

A big thank you to Dr. Asaf Karagila, Pascal Ochem, Prof. Tianxin Cai, and Prof. William Dunham for their expertise and help.

To try GIMPS out yourself: https://ve42.co/GIMPS

These sources were particularly helpful:

Perfect numbers via MacTutor - https://ve42.co/MTPerfect

Cai, T. (2022). Perfect numbers and fibonacci sequences. World Scientific. - https://ve42.co/Cai2022

Dunham, W. (2022). Euler: The master of us all (Vol. 22). American Mathematical Society. - https://ve42.co/Dunham2022

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References:

• Perfect Numbers and Mersenne Primes -...

• Perfect Number Proof - Numberphile

Dickson, L. E. (1919). History of the Theory of Numbers.. (Vol. 1). Carnegie Institution of Washington.

Knill, O. (2007). The oldest open problem in mathematics. NEU Math Circle, December2. - https://ve42.co/Knill2007

Perfect number via Wikipedia - https://ve42.co/WikiPerfect

Introduction to Arithmetic via HalthiTrust - https://ve42.co/IntroArithmetic

Nicomachus of Gerasa via MacTutor - https://ve42.co/MTNicomachus

Sonja, B. (1988). The First Perfect Numbers and Three Types of Amicable Numbers in a Manuscript on Elementary Number Theory by Ibn Fellûs. Erdem, c. IV, 11. - https://ve42.co/Sonja1988

Ibn Fallus via Wikipedia - https://ve42.co/WikiFallus

Mersenne prime via Wikipedia - https://ve42.co/WikiMP

List of Known Mersenne Prime Numbers - https://ve42.co/ListOfMP

Marin Mersenne via MacTutor - https://ve42.co/MTMersenne

Leonhard Euler via Wikipedia - https://ve42.co/WikiEuler

Frank Nelson Cole via Wikipedia - https://ve42.co/WikiFNCole

GIMPS History via Mersenne.org - https://ve42.co/GIMPSHistory

EFF Cooperative Computing Awards via EFF - https://ve42.co/EFFAwards

Jonathan Pace via Primewiki - https://ve42.co/PWikiPace

Book with just one number sells out in Japan via BastillePost - https://ve42.co/PrimeBook

Predicted distribution of Mersenne primes via John D. Cook - https://ve42.co/JDCookMP

Euler’s Odd Perfect Numbers Theorem via Cantor's Paradise - https://ve42.co/EulerOPN

A Perfect (Math) Mystery via Medium - https://ve42.co/Machado2024

Brent, R. P., Cohen, G. L., & te Riele, H. J. (1991). Improved techniques for lower bounds for odd perfect numbers. Mathematics of Computation, 57(196), 857-868. - https://ve42.co/Brent1991

Ochem, P., & Rao, M. (2012). Odd perfect numbers are greater than 10¹⁵⁰⁰. Mathematics of Computation, 81(279), 1869-1877. - https://ve42.co/Ochem2012

Mathematicians Open a New Front on an Ancient Number Problem via Quantamagazine - https://ve42.co/QuantaSpoofs

Descartes number via Wikipedia - https://ve42.co/WikiDescartesNumber

Andersen, N., Durham, S., Griffin, M. J., Hales, J., Jenkins, P., Keck, R., ... & Wu, D. (2022). Odd, spoof perfect factorizations. Journal of Number Theory, 234, 31-47. - https://ve42.co/Andersen2022

Pomerance’s Heuristic that Odd Perfect Numbers are Unlikely via OddPerfect.org - https://ve42.co/Heuristic

Images & Video:

Clip of Piergiorgio Odifreddi - • Odifreddi da Gramellini: piccola lezi...

Euclid’s Elements 1 via Claymath - https://ve42.co/CM1

Euclid’s Elements 2 via Claymath - https://ve42.co/CM2

Euclid’s Elements 3 via Claymath - https://ve42.co/CM3

Diophanti - https://ve42.co/Diophanti

Gauss book - https://ve42.co/GaussDis

Euler’s Archive 1 - https://ve42.co/Euler1

Euler’s Archive 2 - https://ve42.co/Euler2

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Directed by Casper Mebius

Written by Casper Mebius and Derek Muller

Edited by Peter Nelson

Illustrated by Jakub Misiek

Animated by Fabio Albertelli, Ivy Tello, David Szakaly, Alondra Vitae, Alex Drakoulis, and Leigh Williamson

Filmed by Derek Muller, Raquel Nuno, and Peter Nelson

Additional research by Aaron Santos, Camilla Machado, and Gregor Čavlović

Produced by Casper Mebius, Gregor Čavlović, Han Evans, and Derek Muller

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