The Oldest Unsolved Problem in Math

From 1veritasium, 2veritasium, or sciencium.

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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:

These sources were particularly helpful:
Perfect numbers via MacTutor –
Cai, T. (2022). Perfect numbers and fibonacci sequences. World Scientific. –
Dunham, W. (2022). Euler: The master of us all (Vol. 22). American Mathematical Society. –

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. –
Perfect number via Wikipedia –
Introduction to Arithmetic via HalthiTrust –
Nicomachus of Gerasa via MacTutor –
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. –
Ibn Fallus via Wikipedia –
Mersenne prime via Wikipedia –
List of Known Mersenne Prime Numbers –
Marin Mersenne via MacTutor –
Leonhard Euler via Wikipedia –
Frank Nelson Cole via Wikipedia –
GIMPS History via –
EFF Cooperative Computing Awards via EFF –
Jonathan Pace via Primewiki –
Book with just one number sells out in Japan via BastillePost –
Predicted distribution of Mersenne primes via John D. Cook –
Euler’s Odd Perfect Numbers Theorem via Cantor’s Paradise –
A Perfect (Math) Mystery via Medium –
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. –
Ochem, P., & Rao, M. (2012). Odd perfect numbers are greater than 10¹⁵⁰⁰. Mathematics of Computation, 81(279), 1869-1877. –
Mathematicians Open a New Front on an Ancient Number Problem via Quantamagazine –
Descartes number via Wikipedia –
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. –
Pomerance’s Heuristic that Odd Perfect Numbers are Unlikely via –

Images & Video:
Clip of Piergiorgio Odifreddi –
Euclid’s Elements 1 via Claymath –
Euclid’s Elements 2 via Claymath –
Euclid’s Elements 3 via Claymath –
Diophanti –
Gauss book –
Euler’s Archive 1 –
Euler’s Archive 2 –

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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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