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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), 857868. https://ve42.co/Brent1991
Ochem, P., & Rao, M. (2012). Odd perfect numbers are greater than 10¹⁵⁰⁰. Mathematics of Computation, 81(279), 18691877. 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, 3147. 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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