-
The Sum of All Prime Twins
In number theory, Brun's theorem states that the sum of the reciprocals of the twin primes (pairs of prime numbers which differ by 2) converges to a finite value known as Brun's constant. Brun's theorem was proved by Viggo Brun in 1919, and it has historical importance in the introduction of sieve methods.
published: 25 Mar 2023
-
Twin Primes & Bruns Theorem
Twin primes are prime numbers separated by 2. Viggo Bruns theorem states that sum of reciprocals of twin primes is convergent. This video demonstrates how to test this theorem, using ZCubes. You will observe that the computation is simple and easy in ZCubes, as it takes only 4 lines of code.
More videos about ZCubes : http://wiki.zcubes.com/ZCubes_Videos
ZCubes is an omnifunctional platform using which you can compute, do analytics, create graphs, draw, paint, create presentations, web pages and do much more.
Visit the website http://www.zcubes.com and launch ZCubes on your browser. Experience omnifunctionality.
published: 21 Feb 2020
-
Brun sieve
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Brun sieve
In the field of number theory, the Brun sieve (also called Brun's pure sieve) is a technique for estimating the size of "sifted sets" of positive integers which satisfy a set of conditions which are expressed by congruences.It was developed by Viggo Brun in 1915.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=vTnkK2wnYIc
published: 22 Jan 2016
-
The High Schooler Who Solved a Prime Number Theorem
In his senior year of high school, Daniel Larsen proved a key theorem about Carmichael numbers — strange entities that mimic the primes. “It would be a paper that any mathematician would be really proud to have written,” said one mathematician.
Read more at Quanta Magazine: https://www.quantamagazine.org/teenager-solves-stubborn-riddle-about-prime-number-look-alikes-20221013
- VISIT our Website: https://www.quantamagazine.org
- LIKE us on Facebook: https://www.facebook.com/QuantaNews
- FOLLOW us Twitter: https://twitter.com/QuantaMagazine
Quanta Magazine is an editorially independent publication supported by the Simons Foundation https://www.simonsfoundation.org/
published: 13 Oct 2022
-
reciprocals of twin primes
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Research Gate profile: https://www.researchgate.net/profile/Michael_Penn5
Google Scholar ...
published: 12 Feb 2024
-
Twin Prime Gap Explained [2014]
What’s the difference between 70 million and 246? For a team of mathematicians, the difference is more than just a number. It’s the story of how a relatively unknown researcher cracked an impenetrable math problem, setting off a mad dash to set a new record in the timeless study of prime numbers.
research article: https://link.springer.com/article/10.1186%2Fs40687-014-0012-7
https://resmathsci.springeropen.com/
published: 01 Jan 2018
-
Probabilistic Methods 11-2: Brun's Sieve and the Poisson Paradigm
In the second video of Week 11, we state and the Poisson paradigm and Brun's sieve. We prove the latter and apply it and Janson's to study first the probability G(n,p) is triangle-free near its threshold and then the threshold that every vertex is in a triangle.
published: 01 Apr 2021
-
Brun's Constant: Unlocking the Mystery
Unlocking the Mystery of Brun's Constant • Discover the secrets behind Brun's Constant, a mathematical mystery that has fascinated scholars for centuries. Join us on a journey of exploration and unravel the enigma of this intriguing mathematical constant.
00:00 • Introduction - Brun's Constant: Unlocking the Mystery
00:28 • What is Brun's Constant?
01:01 • Why is Brun's Constant Important?
01:33 • The Value and Mystery of Brun's Constant
published: 07 Jan 2024
-
Burnside's Lemma (Part 1) - combining group theory and combinatorics
A result often used in math competitions, Burnside's lemma is an interesting result in group theory that helps us count things with symmetries considered, e.g. in some situations, we don't want to count things that can be transformed into one another by rotation different, like in this case - how many ways are there to paint a cube's faces when we are given three colors, if two coloring patterns are considered the same when they differ just by a rotation?
There is usually also something called Pólya Enumeration Theorem, which is a generalization of Burnside's lemma, and can be used to tackle a wider set of problems, but most problems that Pólya Enumeration Theorem can be applied to can also be tackled by Burnside's lemma, so this is usually more important. The theorem simply extracts the ...
published: 20 Aug 2020
-
Monster Group (John Conway) - Numberphile
The Monster Group explained. Conway playlist: http://bit.ly/ConwayNumberphile
More links & stuff in full description below ↓↓↓
Featuring John Conway (Princeton University) and Tim Burness (University of Bristol).
Brown papers and Numberphile artwork: http://bit.ly/brownpapers
More Conway on this topic: http://youtu.be/xOCe5HUObD4
And Conway on Game of Life, etc: http://bit.ly/JohnConway
A little extra bit from Tim: http://youtu.be/MXKiih4JJvQ
Support us on Patreon: http://www.patreon.com/numberphile
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http:/...
published: 09 May 2014
5:05
The Sum of All Prime Twins
In number theory, Brun's theorem states that the sum of the reciprocals of the twin primes (pairs of prime numbers which differ by 2) converges to a finite valu...
In number theory, Brun's theorem states that the sum of the reciprocals of the twin primes (pairs of prime numbers which differ by 2) converges to a finite value known as Brun's constant. Brun's theorem was proved by Viggo Brun in 1919, and it has historical importance in the introduction of sieve methods.
https://wn.com/The_Sum_Of_All_Prime_Twins
In number theory, Brun's theorem states that the sum of the reciprocals of the twin primes (pairs of prime numbers which differ by 2) converges to a finite value known as Brun's constant. Brun's theorem was proved by Viggo Brun in 1919, and it has historical importance in the introduction of sieve methods.
- published: 25 Mar 2023
- views: 6397
2:32
Twin Primes & Bruns Theorem
Twin primes are prime numbers separated by 2. Viggo Bruns theorem states that sum of reciprocals of twin primes is convergent. This video demonstrates how to te...
Twin primes are prime numbers separated by 2. Viggo Bruns theorem states that sum of reciprocals of twin primes is convergent. This video demonstrates how to test this theorem, using ZCubes. You will observe that the computation is simple and easy in ZCubes, as it takes only 4 lines of code.
More videos about ZCubes : http://wiki.zcubes.com/ZCubes_Videos
ZCubes is an omnifunctional platform using which you can compute, do analytics, create graphs, draw, paint, create presentations, web pages and do much more.
Visit the website http://www.zcubes.com and launch ZCubes on your browser. Experience omnifunctionality.
https://wn.com/Twin_Primes_Bruns_Theorem
Twin primes are prime numbers separated by 2. Viggo Bruns theorem states that sum of reciprocals of twin primes is convergent. This video demonstrates how to test this theorem, using ZCubes. You will observe that the computation is simple and easy in ZCubes, as it takes only 4 lines of code.
More videos about ZCubes : http://wiki.zcubes.com/ZCubes_Videos
ZCubes is an omnifunctional platform using which you can compute, do analytics, create graphs, draw, paint, create presentations, web pages and do much more.
Visit the website http://www.zcubes.com and launch ZCubes on your browser. Experience omnifunctionality.
- published: 21 Feb 2020
- views: 361
2:04
Brun sieve
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Brun sieve
In the field of numbe...
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Brun sieve
In the field of number theory, the Brun sieve (also called Brun's pure sieve) is a technique for estimating the size of "sifted sets" of positive integers which satisfy a set of conditions which are expressed by congruences.It was developed by Viggo Brun in 1915.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=vTnkK2wnYIc
https://wn.com/Brun_Sieve
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Brun sieve
In the field of number theory, the Brun sieve (also called Brun's pure sieve) is a technique for estimating the size of "sifted sets" of positive integers which satisfy a set of conditions which are expressed by congruences.It was developed by Viggo Brun in 1915.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=vTnkK2wnYIc
- published: 22 Jan 2016
- views: 309
5:15
The High Schooler Who Solved a Prime Number Theorem
In his senior year of high school, Daniel Larsen proved a key theorem about Carmichael numbers — strange entities that mimic the primes. “It would be a paper th...
In his senior year of high school, Daniel Larsen proved a key theorem about Carmichael numbers — strange entities that mimic the primes. “It would be a paper that any mathematician would be really proud to have written,” said one mathematician.
Read more at Quanta Magazine: https://www.quantamagazine.org/teenager-solves-stubborn-riddle-about-prime-number-look-alikes-20221013
- VISIT our Website: https://www.quantamagazine.org
- LIKE us on Facebook: https://www.facebook.com/QuantaNews
- FOLLOW us Twitter: https://twitter.com/QuantaMagazine
Quanta Magazine is an editorially independent publication supported by the Simons Foundation https://www.simonsfoundation.org/
https://wn.com/The_High_Schooler_Who_Solved_A_Prime_Number_Theorem
In his senior year of high school, Daniel Larsen proved a key theorem about Carmichael numbers — strange entities that mimic the primes. “It would be a paper that any mathematician would be really proud to have written,” said one mathematician.
Read more at Quanta Magazine: https://www.quantamagazine.org/teenager-solves-stubborn-riddle-about-prime-number-look-alikes-20221013
- VISIT our Website: https://www.quantamagazine.org
- LIKE us on Facebook: https://www.facebook.com/QuantaNews
- FOLLOW us Twitter: https://twitter.com/QuantaMagazine
Quanta Magazine is an editorially independent publication supported by the Simons Foundation https://www.simonsfoundation.org/
- published: 13 Oct 2022
- views: 2268335
15:11
reciprocals of twin primes
🌟Support the channel🌟
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https://wn.com/Reciprocals_Of_Twin_Primes
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mathmajor: https://www.youtube.com/channel/UCC6Wl-xnWVS9FP0k-Hj5aiw
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🌟My Links🌟
Personal Website: http://www.michael-penn.net
Instagram: https://www.instagram.com/melp2718/
Twitter: https://twitter.com/michaelpennmath
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Research Gate profile: https://www.researchgate.net/profile/Michael_Penn5
Google Scholar profile: https://scholar.google.com/citations?user=W5wkSxcAAAAJ&hl=en
🌟How I make Thumbnails🌟
Canva: https://partner.canva.com/c/3036853/647168/10068
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🌟Suggest a problem🌟
https://forms.gle/ea7Pw7HcKePGB4my5
- published: 12 Feb 2024
- views: 18658
2:35
Twin Prime Gap Explained [2014]
What’s the difference between 70 million and 246? For a team of mathematicians, the difference is more than just a number. It’s the story of how a relatively un...
What’s the difference between 70 million and 246? For a team of mathematicians, the difference is more than just a number. It’s the story of how a relatively unknown researcher cracked an impenetrable math problem, setting off a mad dash to set a new record in the timeless study of prime numbers.
research article: https://link.springer.com/article/10.1186%2Fs40687-014-0012-7
https://resmathsci.springeropen.com/
https://wn.com/Twin_Prime_Gap_Explained_2014
What’s the difference between 70 million and 246? For a team of mathematicians, the difference is more than just a number. It’s the story of how a relatively unknown researcher cracked an impenetrable math problem, setting off a mad dash to set a new record in the timeless study of prime numbers.
research article: https://link.springer.com/article/10.1186%2Fs40687-014-0012-7
https://resmathsci.springeropen.com/
- published: 01 Jan 2018
- views: 10379
35:30
Probabilistic Methods 11-2: Brun's Sieve and the Poisson Paradigm
In the second video of Week 11, we state and the Poisson paradigm and Brun's sieve. We prove the latter and apply it and Janson's to study first the probability...
In the second video of Week 11, we state and the Poisson paradigm and Brun's sieve. We prove the latter and apply it and Janson's to study first the probability G(n,p) is triangle-free near its threshold and then the threshold that every vertex is in a triangle.
https://wn.com/Probabilistic_Methods_11_2_Brun's_Sieve_And_The_Poisson_Paradigm
In the second video of Week 11, we state and the Poisson paradigm and Brun's sieve. We prove the latter and apply it and Janson's to study first the probability G(n,p) is triangle-free near its threshold and then the threshold that every vertex is in a triangle.
- published: 01 Apr 2021
- views: 583
2:38
Brun's Constant: Unlocking the Mystery
Unlocking the Mystery of Brun's Constant • Discover the secrets behind Brun's Constant, a mathematical mystery that has fascinated scholars for centuries. Join ...
Unlocking the Mystery of Brun's Constant • Discover the secrets behind Brun's Constant, a mathematical mystery that has fascinated scholars for centuries. Join us on a journey of exploration and unravel the enigma of this intriguing mathematical constant.
00:00 • Introduction - Brun's Constant: Unlocking the Mystery
00:28 • What is Brun's Constant?
01:01 • Why is Brun's Constant Important?
01:33 • The Value and Mystery of Brun's Constant
https://wn.com/Brun's_Constant_Unlocking_The_Mystery
Unlocking the Mystery of Brun's Constant • Discover the secrets behind Brun's Constant, a mathematical mystery that has fascinated scholars for centuries. Join us on a journey of exploration and unravel the enigma of this intriguing mathematical constant.
00:00 • Introduction - Brun's Constant: Unlocking the Mystery
00:28 • What is Brun's Constant?
01:01 • Why is Brun's Constant Important?
01:33 • The Value and Mystery of Brun's Constant
- published: 07 Jan 2024
- views: 12
13:45
Burnside's Lemma (Part 1) - combining group theory and combinatorics
A result often used in math competitions, Burnside's lemma is an interesting result in group theory that helps us count things with symmetries considered, e.g. ...
A result often used in math competitions, Burnside's lemma is an interesting result in group theory that helps us count things with symmetries considered, e.g. in some situations, we don't want to count things that can be transformed into one another by rotation different, like in this case - how many ways are there to paint a cube's faces when we are given three colors, if two coloring patterns are considered the same when they differ just by a rotation?
There is usually also something called Pólya Enumeration Theorem, which is a generalization of Burnside's lemma, and can be used to tackle a wider set of problems, but most problems that Pólya Enumeration Theorem can be applied to can also be tackled by Burnside's lemma, so this is usually more important. The theorem simply extracts the core of what we are doing and put it in a nice generating function, which can be useful, but the notation and the computations required are very troublesome, and does not fit well too well with the theme of this channel.
Non-mathematical applications like counting the number of isomers of an organic molecule (organic chemistry) and the number of trichords (music theory) are usually tackled by the theorem mentioned above, but this can really be tackled by Burnside's lemma, just with a bit more care. We will explore how this can be applied in those situations in the next video.
By the way, this lemma is not actually first discovered by Burnside, and the Pólya Enumeration theorem is also not first discovered by Pólya, but this phenomenon is also prevalent throughout mathematics and science, known as Stigler's law of eponymy.
This is not a part of the "Essence of Group Theory" video series, because it is not "essence", but an application of the orbit-stabilizer theorem, which is in Chapter 2 of the video series: https://youtu.be/BfgMdi0OkPU
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
SUBSCRIBE and see you in the next video!
If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe!
Social media:
Facebook: https://www.facebook.com/mathemaniacyt
Instagram: https://www.instagram.com/_mathemaniac_/
Twitter: https://twitter.com/mathemaniacyt
For my contact email, check my About page on a PC.
See you next time!
#mathemaniac #grouptheory #abstractalgebra #burnside #mathematics
https://wn.com/Burnside's_Lemma_(Part_1)_Combining_Group_Theory_And_Combinatorics
A result often used in math competitions, Burnside's lemma is an interesting result in group theory that helps us count things with symmetries considered, e.g. in some situations, we don't want to count things that can be transformed into one another by rotation different, like in this case - how many ways are there to paint a cube's faces when we are given three colors, if two coloring patterns are considered the same when they differ just by a rotation?
There is usually also something called Pólya Enumeration Theorem, which is a generalization of Burnside's lemma, and can be used to tackle a wider set of problems, but most problems that Pólya Enumeration Theorem can be applied to can also be tackled by Burnside's lemma, so this is usually more important. The theorem simply extracts the core of what we are doing and put it in a nice generating function, which can be useful, but the notation and the computations required are very troublesome, and does not fit well too well with the theme of this channel.
Non-mathematical applications like counting the number of isomers of an organic molecule (organic chemistry) and the number of trichords (music theory) are usually tackled by the theorem mentioned above, but this can really be tackled by Burnside's lemma, just with a bit more care. We will explore how this can be applied in those situations in the next video.
By the way, this lemma is not actually first discovered by Burnside, and the Pólya Enumeration theorem is also not first discovered by Pólya, but this phenomenon is also prevalent throughout mathematics and science, known as Stigler's law of eponymy.
This is not a part of the "Essence of Group Theory" video series, because it is not "essence", but an application of the orbit-stabilizer theorem, which is in Chapter 2 of the video series: https://youtu.be/BfgMdi0OkPU
Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6
If you want to know more interesting Mathematics, stay tuned for the next video!
SUBSCRIBE and see you in the next video!
If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe!
Social media:
Facebook: https://www.facebook.com/mathemaniacyt
Instagram: https://www.instagram.com/_mathemaniac_/
Twitter: https://twitter.com/mathemaniacyt
For my contact email, check my About page on a PC.
See you next time!
#mathemaniac #grouptheory #abstractalgebra #burnside #mathematics
- published: 20 Aug 2020
- views: 27180
15:54
Monster Group (John Conway) - Numberphile
The Monster Group explained. Conway playlist: http://bit.ly/ConwayNumberphile
More links & stuff in full description below ↓↓↓
Featuring John Conway (Princeton...
The Monster Group explained. Conway playlist: http://bit.ly/ConwayNumberphile
More links & stuff in full description below ↓↓↓
Featuring John Conway (Princeton University) and Tim Burness (University of Bristol).
Brown papers and Numberphile artwork: http://bit.ly/brownpapers
More Conway on this topic: http://youtu.be/xOCe5HUObD4
And Conway on Game of Life, etc: http://bit.ly/JohnConway
A little extra bit from Tim: http://youtu.be/MXKiih4JJvQ
Support us on Patreon: http://www.patreon.com/numberphile
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady Haran
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
Numberphile T-Shirts: https://teespring.com/stores/numberphile
Other merchandise: https://store.dftba.com/collections/numberphile
https://wn.com/Monster_Group_(John_Conway)_Numberphile
The Monster Group explained. Conway playlist: http://bit.ly/ConwayNumberphile
More links & stuff in full description below ↓↓↓
Featuring John Conway (Princeton University) and Tim Burness (University of Bristol).
Brown papers and Numberphile artwork: http://bit.ly/brownpapers
More Conway on this topic: http://youtu.be/xOCe5HUObD4
And Conway on Game of Life, etc: http://bit.ly/JohnConway
A little extra bit from Tim: http://youtu.be/MXKiih4JJvQ
Support us on Patreon: http://www.patreon.com/numberphile
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady Haran
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
Numberphile T-Shirts: https://teespring.com/stores/numberphile
Other merchandise: https://store.dftba.com/collections/numberphile
- published: 09 May 2014
- views: 758381