Special thanks to our Patreon supporters! Join this list to help us keep our videos free, forever:
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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:
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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44 Replies to “The Oldest Unsolved Problem in Math”
David Hume > Descartes
Good stuff
I don't understand math, no matter how hard I try. This blows my mind.
nice👍
"If you just want a problem to think about
Why does this matter?
How much do I need to invest to be cruising on a yacht in a month?
11:11 erm what the sigma
38,346.568
What's the logic of this ? I mean the word "odd" means it's something unusual that we don't know anything about it . While the word " perfect " means something that is surely the best form of a thing that we know…..so how can "odd" and "perfect " be in the same line? am I right?
What's the logic of this ? I mean the word "odd" means it's something unusual that we don't know anything about it . While the word " perfect " means something that is surely the best form of a thing that we know…..so how can "odd" and "perfect " be in the same line? am I right?
I get confused by the numbers base thing. All this applies to a decimal system. Or is that a stupid question?
137438691328
So what I'm gathering is this similar to PIE not having an end digit? Would that be correct?
Let me crack this case; 1's an odd perfect number. 😅
The SIGMA function?
Tides though, i want to know if magnetism can be a parralell with gravity on a small scale, like a sphere of rotating ferrofluid in gravity free vacume. And is a gravity "free" place an impossible senario. And can you actually be motionless in the universe, no of course, but if you could in relation to universe would it be in a similar state as "light" speed and does light speed really exist for a photon or time rather and how to you stop and freeze one and what would that look like while spinning and hurdling through space and how fast are we going in relation to farthest galixies earth if we could look at eachother? And what is the 5 and 6th dimension and are dreams and consciousness a dimension ( they are) but how why and can it be proven in the cartesion ero sum idea
Also do an episode anout infinity. The difference between numerical and tangible, bigger and larger infinities, and just the infinate infinities that egsist, like the polygon thats a perfect circle, the reason 1 and 3 divisions have infinate issues and pi itself shows that a circle is an infinste polygon etc etc 😮
Will you do an episodes on tides? It's always puzzled me how there is an opposing tide on the other side of earth. The explanations for this never felt right. It made sense in a balance phenom but not with gravity explanation. Please 😊
Will AI crack the problem?
Will AI eclipse all the great mathematicians?
SIGMA FUNCTION?!
Due to the very nature of divisibility, the short and obvious answer is no. There is no prime perfect number. A prime number can only divide by two numbers, which is itself and the number one. The process that determines if a number is a perfect number involves analyzing the structure of that number's division. That aspect in and of itself is direct and logical proof that perfect numbers are simply not prime, and I would go as far as to say that any advanced mathematician who continues the search after more than one instance of an attempt involving a number that requires a thick book just to write the one number should probably look at pursuing a different occupation.
Didn't some girl in middle school solve this already?
The answer is one
🚀 Bitcoin is making a strong comeback! Who’s still holding since $20k?
Another argument for why this problem is worth solving (or at least attempting to do so) is that even if it is ultimately useless, the methods used to solve it may themselves be useful constructs for solving other /useful/ problems.
The nearby answer is 945 and 2205 using DeepSeek AI
Tried asking chatgpt. It couldn't answer 😂
Yooo someone needs to keep this away from Vsause
If Euler said it was hard, I'm not going to work on it.
29:30 Doing the meth is the only way to know for sure
~ average psychonaut
These days I would've thought it to be 2 + 2 = 5
i think im starting to admire the mathematicians
Falcon was here
but what would someone even bother to try finding a number who doesn't exist
Thanks!
Einstein, Euclid and Euler are some of the best minds that human civilisation has ever produced !
Sumerians used base 12 number system, eg, 60 sec=I min, 360°= circle, 2×12=24 hr day. How does it work?
In some territories math ain't mathing😂🎉heaven and earth will pass away, but my word will never pass away. You cant cheat God😅
After wa5ching 5 minutes of the video and a random theory based off the bare minimum infoi say the answer is 105409255339
It's genuinely perplexing how someone with a PhD in Education, specifically physics education research, presents himself with such unwavering authority across a vast spectrum of intricate scientific and mathematical domains. One would be forgiven for mistaking him for a seasoned theoretical physicist or a groundbreaking mathematician, regularly publishing in the most esteemed peer-reviewed journals, given the conviction with which he tackles subjects he often appears to grasp only superficially.
This isn't just about a confident presentation style; there have been instances that raise serious questions about the depth and accuracy of his understanding. The episode where he seemed to challenge the very foundation of the first law of thermodynamics, a cornerstone of physics, immediately comes to mind. It wasn't a nuanced discussion of edge cases, but rather a seemingly fundamental disagreement that left many experts scratching their heads.
Furthermore, Veritasium's track record isn't without blemishes. The need for retractions and significant corrections on past videos speaks volumes about the level of rigor sometimes applied in the pursuit of engaging content. This pattern fuels the suspicion that captivating demonstrations and sensationalized claims can, at times, take precedence over meticulous accuracy.
It begs the question: why is there this persistent tendency among some science communicators to project an image of profound expertise that doesn't necessarily align with their formal training or demonstrated track record in actual scientific discovery? While the role of science communication is undoubtedly vital, it shouldn't come at the cost of misrepresenting one's own level of expertise or, more importantly, misconstruing established scientific principles. There's a significant difference between effectively conveying existing scientific knowledge and presenting oneself as a leading voice within those fields, especially when the latter isn't supported by a history of original, peer-reviewed research.
@veritasium Mersenne Prime #52 (136,279,841) ÷ digits 41,024,320= 3.32… #51 (82,589,933) ÷ digits 24,862,048=3.32…#50 (77,232,917)÷ digits 23,249,425=3.32…#49(74,207,281) ÷ digits 22,338,618= 3.32… #48 (57,885,161)÷ digits 17,425,170= 3.32 #23 (11,213) digits 3,376=3.32…Anyways, not gonna write them all out. Watched your video and got curious played with the numbers…Found that pattern
Wait what 2 days ago I remember this video being up for some time?
And I don’t know the math! 🥺🤦🏽♂️