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:
https://www.youtube.com/watch?v=T0xKHwQH-4I&pp=ygUPcGVyZmVjdCBudW1iZXJz
https://www.youtube.com/watch?v=q8n15q1v4Xo&pp=ygUPcGVyZmVjdCBudW1iZXJz
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 - https://www.youtube.com/watch?v=y0paHEA8-gA
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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