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I "discovered" Mersenne primes on my own when I was about 15 years old. Imagine my disappointment when I learned that some French guy beat me by four centuries.
Same man. A few years back, I proved the Poincare conjecture and then I thought I'd win 1 million dollars! But, it turned out that some Russian guy beat me to it!
Homey I have no idea what the hell hes talking about myself. I don’t Evan know why I watch this stuff like I’m gonna be sitting there in a sweater vest in a library with a tall ceiling and all of a sudden grab chalk and wright equations
a very small nitpick at 4:40 : there is a proven bijection between mersenne prime and EVEN perfect number. it excludes if odd perfect numbers... if any exist, as stated before
about Ramsey problem, the problem itself is much more general and actually explaining the general case would be easier because it is not related to hyper dimensional squares at all
4:28 Correction: There exists a bijection between EVEN perfect numbers and Mersenne primes. If there exist infinite odd perfect numbers, this doesn't necessarily mean that an infinite amount of Mersenne primes exist.
After derivation for the rational distance problem, lets say the random point you chose has coordinates (c,d) known as point z, take the points you had on the square, which are (0,1) this will have values x1 and y1 known as point 1, (1,1) which has values x2 and y2 known as point 2, (0,0) which has values x3 and y3 known as point 3, and (1,0) which has values x4 and y4 known as point 4. The distance between point 1 and point z will be a1 divided by b1, distance between point 2 and point z will be a2 divided by b2, distance between point 3 and point z will be a3 divided by b3, and distance between point 4 and point z will be a4 divided by b4. For the distance of the first point and point z, the equation 1-2c+c squared the d squared=a1 squared/b1 squared. For the distance between point 2 and point z, 2-2d-2c+c squared +d squared=a2 squared/b2 squared. For the distance between point 3 and point z, c squared+d squared=a3 squared/b3 squared. For the distance between point 4 and point z, 1-2d+c squared+d squared=a4 squared/b4 squared. If we put in the values of c and d, we would get a rational value of length, c and d should also not be irrational values.
Perfect numbers are 2 to the power of n-1 multiplied by 1 subtracted from 2 to the power of p, mersenne primes have the formula, 1 subtracted from 2 to the power of p, if p and n are whole numbers greater than 1 and smaller or equal to infinity, that means the numbers of mersenne primes and perfect numbers will also range up to infinity.
Actually in 2020 a group of mathematicians found an example that disproves the inscribed square problem. The resulting curve is quite complex and is constructed using fractals, so I can't describe it, but you can search for the solution under the names John M. Green and Johza Z. Miller
You also made a mistake. He should have swapped (0, 1) by (1, 0) (not (1,1)). Also he marked the graph Y-X instead of X-Y (horizontal Y, vertical X) which is not the common Cartesian system.
@@robertveith6383 Well that depends on whether or not you are a math teacher. A math teacher will dock me a point for that. Everyone else just knows what it's supposed to mean because we are watching the video.
The ramsay theory problem is very hard to understand. In your picture, the edges are not all the same color. They're red, blue, and black. Problem solved. 2 dimensions. It's a square.
5:31, this is not the common cartesian coordinate system, you have the x and y axes the wrong way round, y nornally goes on the vertical axis and x on the horizontal
But it is still a Cartesian coordinate system, and not a polar, cylindrical, or spherical coordinate system. The labeling of the axis is arbitrary, x being the vertical axis and y being the horizontal is just as valid as the other way around.
wait if every perfect number HAS to be able to be described as "(2^(p-1))*((2^p)-1)", wouldn't that mean there are no odd perfect numbers? because 2 to the power of any integer is even, and an even number times any integer is also even
TREE(3) has surpassed it, although it's creator, Harvey Friedman, has devised many functions that allegedly grow much faster than TREE, but never proved anything about them. And his papers look like they've been printed on some fax paper.
2^(2y+1)-2^y where y=0,1,2,3... can be use to find perfect numbers, Not all numbers produced by this formula are perfect but all perfect numbers (so far) fit this formula.
So then we can say 2 to the power of y-1 multiplied by 1 subtracted from 2 to the power of y=2 to the power of 2y+1-2 to the power of y= 2 to the power y multiplied by 1 subtracted from 2 to the power of y+1, substituting y for p. If you simplify that, you get 2 to the power of y=1/3, meaning y has a fixed value which is not possible, I may have made a mistake in calculations so feel free to tell me if you get a different result.
@@user-oy9wf6ph7x [2^(2y+1)]-(2^y)=x which might be perfect. When y=0 then x=1, not perfect. When y=1 then x=6, perfect. When y=2 then x=28, perect. When y=3 then x=120, not perfect. When y=4 then x=496, perfect. When y=5 then x=2016, not perfect. When y=6 then x=8,128, perfect. 7 through 11 are not perfect. When y=12 then x=33,550,336, perfect. And you can continue.
@@richardl6751 But I want you to simplify the equation and tell me if you get the same thing, then we can find an explanation or a pattern in your equation.
@@user-oy9wf6ph7x It might be a little simpler to use 2^x-2^y where x=1, 3, 5, 7... and y=0, 1, 2, 3... but x still equals 2y+1. There is no pattern to prime or perfect numbers.
@@richardl6751 Then we cannot define it as a pattern which explains why the value of 2 to the power of y=1/3 which didn't make sense, therefore, it is an unstable formula, but keep on trying to morph it in an effective way and you might find the right answer, whether it boils down to the old formula, or it's a new one.
I know what the "double arrow" in the giant number at the end of the video means. But can someone tell me the meaning of the "double less-than" symbol?
Whoopsies! In the rational distance problem, there are 2 (0, 1)s. One of those is supposed to be (1, 0) Also everything is horrendously off grid But interest video nonetheless
Well since I'm not studying in mathematics. Can someone explain why is it important that we understand this type of questions? Like what does it solves?
The methods we use for solving these problems might also apply to solving other problems in the future. For example, any new methods we find for solving problems about primes can influence cryptography - giving us new methods of securing and encrypting data. The more abstract a problem is the wider the possible fields and problems its solution can be applied to.
@@HopUpOutDaBed I can see the moving sofa problem (besides the obvious y'know, moving of sofas) relating to implants like artery stents; finding a maximum workable area for a device that can still navigate the body without risking bruising or other damage. It's hard to defend the value of some of these, but I'm sure across the many many professions and sciences, one of them likely has some creative (but also probably very niche) application
1. Knowledge is good for knowledge's sake. 2. The tools you develop to solve logical puzzels and problems like these come in handy elsewhere. Ring theory was invented to solve number theory and algebra problems that seemed meaningless and now it's being used for computer graphics. Everything you see on display on a computer, unless it's bitmap, including every letter typed, is an algebraic variety carved out by polynomials that the computer is graphing in real time. And of course, it is STILL being used for number theory and algebra problems. Group theory and complex numbers were really doubted but are now an indispensable part of physics and complex numbers come into anything that has to do with electricity of fluid flow. 3. The distribution of primes is useful for cryptography. The sofa problem is a calculus of variations problem, which comes up everywhere in engineering and physics. Optimisation problems' usefulness should be obvious. Ramsey theory helps us understand general graph theory better, which is crucial for computer code. Something like queing, sorting algorithms and Google Maps wouldn't work without graph theory. The inscribed rectangle problem is solved topologically. The solution for the square problem would probably require some breakthrough in real analysis, algebraic topology or analytic geometry, which needless to say would send ripples everywhere else in math and science. The rational distance one will probably be solved with algebraic geometry, given that that is how the problems of rational points on elliptic curves get solved. I already explained why algebraic geometry is important.
@@cloudy28 true, but technically considering the largest we have is the largest it is. Also the question arise. How do we know we haven't reach the limit? But let's say we haven't found it yet.
@@asagiai4965 the largest shape we know doesnt have to be the largest shape possible. We don't know If we reached the limit because no one was able to proof it.
Great! Now you can publish your work and totally clown on all of those dumb professional mathematicians! Who needs to study prime spectra of ideals of polynomial rings for affine schemes and moduli spaces for years if a random commenter says it's easy and can be done in one sitting!
@@robertveith6383 why would you go out of your way to tell someone on the ibternet to correct their misspellings. The message was clear my hands were wet that's all.
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The sofa problem has since been solved. The shape that was thought to be optimal was now proven to be optimal.
I "discovered" Mersenne primes on my own when I was about 15 years old. Imagine my disappointment when I learned that some French guy beat me by four centuries.
you should feel smart for discovering something on your own that other smart people had to be told about !
I felt same dissapointment when I was playing with my calculator and accidentally discovered e and two years later found out about John Napier.
Same, had new "discoveries" and "ideas" here, but disappointed when I knew they were already had discovered long ago,...
Same man. A few years back, I proved the Poincare conjecture and then I thought I'd win 1 million dollars! But, it turned out that some Russian guy beat me to it!
@@frax5051 proving that is incredible, don't let anyone get to you.
"Rotate the hallway around the sofa" 😂😂
That I will say to the movers next time I get a new sofa...
Optimal sofa is a more complex shape than the hallway corner. Faster to transform the hallway.
I feel like the phrase "part 2" is self inflammatory considering the last one was supposed to cover every problem.
Jk I'm a big fan also second
Hmm
That sounds like a problem that's easy to solve
I gotcha point, but that really shows how many unsolved problems there are. Its hard to find them all and hard to make a video so long
On the other hand, every unsolved problem may not refer to the video but rather the series of videos, which would solve the problem
@@frozenbonkchoy4986ohhhhh right
I just heard that the sofa is finally solved!
"Unsolved math problems that sounds easy"
"Something about primes i dont grasp"
My head:
"Whoms easy is meant in the titel?"
What's not to grasp about the statements about prime numbers?
Homey I have no idea what the hell hes talking about myself. I don’t Evan know why I watch this stuff like I’m gonna be sitting there in a sweater vest in a library with a tall ceiling and all of a sudden grab chalk and wright equations
a very small nitpick at 4:40 : there is a proven bijection between mersenne prime and EVEN perfect number.
it excludes if odd perfect numbers... if any exist, as stated before
Would a discovery of an odd perfect number have any effect on the bijection or would that only be useful in the perfect numbers?
about Ramsey problem, the problem itself is much more general and actually explaining the general case would be easier because it is not related to hyper dimensional squares at all
4:28
Correction:
There exists a bijection between EVEN perfect numbers and Mersenne primes.
If there exist infinite odd perfect numbers, this doesn't necessarily mean that an infinite amount of Mersenne primes exist.
The sofa problem has been recently solved. It's a very complicated proof over 100 pages in length.
Im pretty sure they are still fact checking that
After derivation for the rational distance problem, lets say the random point you chose has coordinates (c,d) known as point z, take the points you had on the square, which are (0,1) this will have values x1 and y1 known as point 1, (1,1) which has values x2 and y2 known as point 2, (0,0) which has values x3 and y3 known as point 3, and (1,0) which has values x4 and y4 known as point 4. The distance between point 1 and point z will be a1 divided by b1, distance between point 2 and point z will be a2 divided by b2, distance between point 3 and point z will be a3 divided by b3, and distance between point 4 and point z will be a4 divided by b4. For the distance of the first point and point z, the equation 1-2c+c squared the d squared=a1 squared/b1 squared. For the distance between point 2 and point z, 2-2d-2c+c squared +d squared=a2 squared/b2 squared. For the distance between point 3 and point z, c squared+d squared=a3 squared/b3 squared. For the distance between point 4 and point z, 1-2d+c squared+d squared=a4 squared/b4 squared. If we put in the values of c and d, we would get a rational value of length, c and d should also not be irrational values.
Perfect numbers are 2 to the power of n-1 multiplied by 1 subtracted from 2 to the power of p, mersenne primes have the formula, 1 subtracted from 2 to the power of p, if p and n are whole numbers greater than 1 and smaller or equal to infinity, that means the numbers of mersenne primes and perfect numbers will also range up to infinity.
Actually in 2020 a group of mathematicians found an example that disproves the inscribed square problem. The resulting curve is quite complex and is constructed using fractals, so I can't describe it, but you can search for the solution under the names John M. Green and Johza Z. Miller
9:00 someone should tell ross/chandler about all the progress made on pivoting a sofa.
AHAHAHAHAHA YES
YESSSSSSSS
PIVOT
5:40 minor mistake. You have a (0,1) twice instead of a (1,1)
yes, on x axis there will be (1,0) instead of (0,1).
You also made a mistake. He should have swapped (0, 1) by (1, 0) (not (1,1)). Also he marked the graph Y-X instead of X-Y (horizontal Y, vertical X) which is not the common Cartesian system.
@@lior1222 Oh yeah the (1,0) is missing not the (1,1)
It is *not* a "minor" mistake.
@@robertveith6383 Well that depends on whether or not you are a math teacher. A math teacher will dock me a point for that. Everyone else just knows what it's supposed to mean because we are watching the video.
Hasnt the sofa problem just been proved
The ramsay theory problem is very hard to understand. In your picture, the edges are not all the same color. They're red, blue, and black. Problem solved. 2 dimensions. It's a square.
5:31, this is not the common cartesian coordinate system, you have the x and y axes the wrong way round, y nornally goes on the vertical axis and x on the horizontal
But it is still a Cartesian coordinate system, and not a polar, cylindrical, or spherical coordinate system. The labeling of the axis is arbitrary, x being the vertical axis and y being the horizontal is just as valid as the other way around.
Who know that moving a sofa could be so complicated
NEW MERSENNE PRIME J DROPPED
Collatz conjecture
ζ(2)=π^2 /6
3ζ(2)/2=π^2 /4
=π^2 /2^2
π⇔1
1/4+1
1/4+4/4
5/4
//5 is an odd number//
3×5+1=16
16=2^3→1
All natural numbers
Collatz conjecture
reduces to 1.
wait if every perfect number HAS to be able to be described as "(2^(p-1))*((2^p)-1)", wouldn't that mean there are no odd perfect numbers? because 2 to the power of any integer is even, and an even number times any integer is also even
Its believed that if an odd perfect number exists, it would have a different form than the even perfect numbers.
Good coverage!
About rational distances ... It seems related to the provlem of finding the function of prime numbers
12:10 once held? You can't leave us hanging with that implication
TREE(3) has surpassed it, although it's creator, Harvey Friedman, has devised many functions that allegedly grow much faster than TREE, but never proved anything about them. And his papers look like they've been printed on some fax paper.
TREE 3
5:43 an error in the coordinates
2^(2y+1)-2^y where y=0,1,2,3... can be use to find perfect numbers, Not all numbers produced by this formula are perfect but all perfect numbers (so far) fit this formula.
So then we can say 2 to the power of y-1 multiplied by 1 subtracted from 2 to the power of y=2 to the power of 2y+1-2 to the power of y= 2 to the power y multiplied by 1 subtracted from 2 to the power of y+1, substituting y for p. If you simplify that, you get 2 to the power of y=1/3, meaning y has a fixed value which is not possible, I may have made a mistake in calculations so feel free to tell me if you get a different result.
@@user-oy9wf6ph7x [2^(2y+1)]-(2^y)=x which might be perfect.
When y=0 then x=1, not perfect.
When y=1 then x=6, perfect.
When y=2 then x=28, perect.
When y=3 then x=120, not perfect.
When y=4 then x=496, perfect.
When y=5 then x=2016, not perfect.
When y=6 then x=8,128, perfect.
7 through 11 are not perfect.
When y=12 then x=33,550,336, perfect.
And you can continue.
@@richardl6751 But I want you to simplify the equation and tell me if you get the same thing, then we can find an explanation or a pattern in your equation.
@@user-oy9wf6ph7x It might be a little simpler to use 2^x-2^y where x=1, 3, 5, 7... and y=0, 1, 2, 3... but x still equals 2y+1. There is no pattern to prime or perfect numbers.
@@richardl6751 Then we cannot define it as a pattern which explains why the value of 2 to the power of y=1/3 which didn't make sense, therefore, it is an unstable formula, but keep on trying to morph it in an effective way and you might find the right answer, whether it boils down to the old formula, or it's a new one.
Whats the outro music?
Your x and y axes are swapped
what do you make your videos on cheers
Song at the end?
"the usual xy coordinates"
*immediately flips axes relative to the usual*
5:40 1 graph paper square not equalling to 1 unit is slightly annoying to me lol
I know what the "double arrow" in the giant number at the end of the video means. But can someone tell me the meaning of the "double less-than" symbol?
"a
It doesn't have a precise meaning. It just emphasises how much smaller a is.
Whoopsies! In the rational distance problem, there are 2 (0, 1)s. One of those is supposed to be (1, 0)
Also everything is horrendously off grid
But interest video nonetheless
5:39 I think you swapped the x and y axis
8:38 Usain sofa
Perfect numbers go hand-to- hand with Mersenne primes. As [2^(p-1)][2^(p)-1] is the form of all found perfect numbers.
Correction:2^(p-1)*(2^p-1) if 2^p-1 is prime
2^(p-1) × (2^p -1) can never be odd so...
69 is NOT perfect because the sum of its proper divisors is 27, which is a different number
8:32 Geometry dash 2.207 ?
5:38 yowch the coordinates are off 💀
Well since I'm not studying in mathematics. Can someone explain why is it important that we understand this type of questions? Like what does it solves?
It solves the problem of mathematicians having something to do
Why climb a mountain? Because it's there.
The methods we use for solving these problems might also apply to solving other problems in the future. For example, any new methods we find for solving problems about primes can influence cryptography - giving us new methods of securing and encrypting data. The more abstract a problem is the wider the possible fields and problems its solution can be applied to.
@@HopUpOutDaBed I can see the moving sofa problem (besides the obvious y'know, moving of sofas) relating to implants like artery stents; finding a maximum workable area for a device that can still navigate the body without risking bruising or other damage.
It's hard to defend the value of some of these, but I'm sure across the many many professions and sciences, one of them likely has some creative (but also probably very niche) application
1. Knowledge is good for knowledge's sake.
2. The tools you develop to solve logical puzzels and problems like these come in handy elsewhere. Ring theory was invented to solve number theory and algebra problems that seemed meaningless and now it's being used for computer graphics. Everything you see on display on a computer, unless it's bitmap, including every letter typed, is an algebraic variety carved out by polynomials that the computer is graphing in real time. And of course, it is STILL being used for number theory and algebra problems. Group theory and complex numbers were really doubted but are now an indispensable part of physics and complex numbers come into anything that has to do with electricity of fluid flow.
3. The distribution of primes is useful for cryptography. The sofa problem is a calculus of variations problem, which comes up everywhere in engineering and physics. Optimisation problems' usefulness should be obvious. Ramsey theory helps us understand general graph theory better, which is crucial for computer code. Something like queing, sorting algorithms and Google Maps wouldn't work without graph theory. The inscribed rectangle problem is solved topologically. The solution for the square problem would probably require some breakthrough in real analysis, algebraic topology or analytic geometry, which needless to say would send ripples everywhere else in math and science. The rational distance one will probably be solved with algebraic geometry, given that that is how the problems of rational points on elliptic curves get solved. I already explained why algebraic geometry is important.
Isn't the sofa problem already answered.
Nope
@@fatih3806 but didn't we technically have the largest sofa right now?
@@asagiai4965 it's not proven to be the largest one possible, which means larger ones might still be found in the future
@@cloudy28 true, but technically considering the largest we have is the largest it is.
Also the question arise. How do we know we haven't reach the limit?
But let's say we haven't found it yet.
@@asagiai4965 the largest shape we know doesnt have to be the largest shape possible. We don't know If we reached the limit because no one was able to proof it.
69 isn't a perfect number
thinkers die thinking
Best way to go.
just solved the rational distance problem i think, not that difficult
Great! Now you can publish your work and totally clown on all of those dumb professional mathematicians! Who needs to study prime spectra of ideals of polynomial rings for affine schemes and moduli spaces for years if a random commenter says it's easy and can be done in one sitting!
Well tell us how
I don't belive you, becquse tgousands of siencetists didn't but you did
@@wooweejeezlouise -- Go back and correct your misspellings.
@@robertveith6383 why would you go out of your way to tell someone on the ibternet to correct their misspellings. The message was clear my hands were wet that's all.
Sheeiiit
Bro 1 is a perfect number
for a perfect number both the number itself and it's factors are added, aka 1+1 = 2, so no it's not
Dr. Doom, from MARVEL comics, knows how to answer and solve all of these problems. If he didn’t, he would look pretty foolish, wouldn’t he?
Bot.
(2^(82589933)-1)(2^(82589932)) is perfect because 2^(82589933)-1 is mersenne
Cool. It's even, though.