-
What are Prime Numbers? | Math with Mr. J
Welcome to "What are Prime Numbers?" with Mr. J! Need help with prime numbers? You're in the right place!
Whether you're just starting out, or need a quick refresher, this is the video for you if you're looking for help with prime numbers. Mr. J will go through prime number examples and explain how to determine if a number is prime or not.
✅ What are Composite Numbers?:
https://youtu.be/R1CM-W8FMRA
✅ Need help with another topic?... Just search what topic you are looking for + "with Mr. J" (for example, "adding fractions with Mr. J".
About Math with Mr. J: This channel offers instructional videos that are directly aligned with math standards. Teachers, parents/guardians, and students from around the world have used this channel to help with math content in many different ways. All mat...
published: 27 Jan 2021
-
What is a prime number?
An easy intro to prime numbers and composite numbers that MAKES SENSE.
What are prime numbers?
A prime number is a number that has exactly 2 factors: two and itself.
What are composite numbers?
A composite number is one which has two or more factors.
What is the difference between a prime number and a composite number.....?
For the playlist of indicies and prime numbers.
https://www.youtube.com/playlist?list=PLjbxBzUM6SLljxglRaecKXzlXgS9ecv3f
To contribute on Patreon:
https://www.patreon.com/tecmath To donate to the tecmath channel: https://paypal.me/tecmath?locale.x=en_AU
To support tecmath on Patreon: https://www.patreon.com/tecmath
To buy tecmath mechandise: https://teespring.com/stores/tecmath-store
published: 25 Mar 2020
-
Finding Prime Numbers
For students of all ages. Gotta wrap your head around primes? Here's how you can think of it so that it makes sense, rather than just learning a bunch of numbers as prime.
Definition of primes. 1 is NOT prime.
Use the Sieve of Eratosthenes to find primes up to 50
Teachers: this is a great primer for students doing the Sieve for themselves - students often find written instructions for this confusing. Show them sieving the multiples up to and including 5 and they should find it a breeze! Get them to stop when they hit 50, then finish the film and they can check their work.
Segue - D.I.Y on paper up to 100. They must keep this work to help them remember. They will eventually learn the first primes for themselves, but it's much better and more enduring learning to work it out and be able ...
published: 03 Oct 2015
-
Math Antics - Prime Factorization
Learn More at mathantics.com
Visit http://www.mathantics.com for more Free math videos and additional subscription based content!
published: 16 Apr 2012
-
The Most Wanted Prime Number - Numberphile
Featuring Neil Sloane.
Visit https://gift.climeworks.com/numberphile to give the gift of CO₂ removal. Use code NUMBERPHILE10 for 10% off your purchase in December (sponsor)
More links & stuff in full description below ↓↓↓
Neil Sloane is the founder of The OEIS: https://oeis.org
More videos with Neil: http://bit.ly/Sloane_Numberphile
Prime Playlist: https://bit.ly/PrimePlaylist
Note the 17350-digit prime we feature is more accurately classed as a "probable prime" at this time.
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/
And suppo...
published: 15 Dec 2021
-
Prime Numbers and Composite Numbers
This math video tutorial provides a basic introduction into prime and composite numbers. It explains how to tell if a number is prime or composite using a simple method.
Subscribe:
https://www.youtube.com/channel/UCEWpbFLzoYGPfuWUMFPSaoA?sub_confirmation=1
Access to Premium Videos:
https://www.patreon.com/MathScienceTutor
https://www.facebook.com/MathScienceTutoring/
published: 15 May 2018
-
Prime Numbers Between 1 and 100
Prime numbers are positive integers greater than 1 that have no positive integer divisors other than 1 and themselves. In other words, a prime number is a number that can only be divided evenly by 1 and itself.
Prime numbers have a unique set of properties that make them important in mathematics, computer science, and cryptography. For example:
Prime numbers are the building blocks of all other integers. Every positive integer can be expressed as a product of primes in a unique way, called the prime factorization.
Prime numbers play a crucial role in cryptography, which is the study of secure communication. Many encryption algorithms rely on the difficulty of factoring large composite numbers into their prime factors.
Prime numbers are used extensively in number theory, which is the br...
published: 19 Feb 2020
-
Why do prime numbers make these spirals? | Dirichlet’s theorem and pi approximations
A curious pattern, approximations for pi, and prime distributions.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/spiral-thanks
Based on this Math Stack Exchange post:
https://math.stackexchange.com/questions/885879/meaning-of-rays-in-polar-plot-of-prime-numbers/885894
Want to learn more about rational approximations? See this Mathologer video.
https://youtu.be/CaasbfdJdJg
Also, if you haven't heard of Ulam Spirals, you may enjoy this Numberphile video:
https://youtu.be/iFuR97YcSLM
Dirichlet's paper:
https://arxiv.org/pdf/0808.1408.pdf
Timestamps:
0:00 - The spiral mystery
3:35 - Non-prime spirals
6:10 - Residue classes
7:20 - Why the galactic ...
published: 08 Oct 2019
4:46
What are Prime Numbers? | Math with Mr. J
Welcome to "What are Prime Numbers?" with Mr. J! Need help with prime numbers? You're in the right place!
Whether you're just starting out, or need a quick ref...
Welcome to "What are Prime Numbers?" with Mr. J! Need help with prime numbers? You're in the right place!
Whether you're just starting out, or need a quick refresher, this is the video for you if you're looking for help with prime numbers. Mr. J will go through prime number examples and explain how to determine if a number is prime or not.
✅ What are Composite Numbers?:
https://youtu.be/R1CM-W8FMRA
✅ Need help with another topic?... Just search what topic you are looking for + "with Mr. J" (for example, "adding fractions with Mr. J".
About Math with Mr. J: This channel offers instructional videos that are directly aligned with math standards. Teachers, parents/guardians, and students from around the world have used this channel to help with math content in many different ways. All material is absolutely free.
Click Here to Subscribe to the Greatest Math Channel On Earth: https://goo.gl/XHTrfY
Follow Mr. J on Twitter: @MrJMath5
Email:
[email protected]
Music: https://www.bensound.com/royalty-free-music
Hopefully this video is what you're looking for when it comes to prime numbers.
https://wn.com/What_Are_Prime_Numbers_|_Math_With_Mr._J
Welcome to "What are Prime Numbers?" with Mr. J! Need help with prime numbers? You're in the right place!
Whether you're just starting out, or need a quick refresher, this is the video for you if you're looking for help with prime numbers. Mr. J will go through prime number examples and explain how to determine if a number is prime or not.
✅ What are Composite Numbers?:
https://youtu.be/R1CM-W8FMRA
✅ Need help with another topic?... Just search what topic you are looking for + "with Mr. J" (for example, "adding fractions with Mr. J".
About Math with Mr. J: This channel offers instructional videos that are directly aligned with math standards. Teachers, parents/guardians, and students from around the world have used this channel to help with math content in many different ways. All material is absolutely free.
Click Here to Subscribe to the Greatest Math Channel On Earth: https://goo.gl/XHTrfY
Follow Mr. J on Twitter: @MrJMath5
Email:
[email protected]
Music: https://www.bensound.com/royalty-free-music
Hopefully this video is what you're looking for when it comes to prime numbers.
- published: 27 Jan 2021
- views: 784834
4:37
What is a prime number?
An easy intro to prime numbers and composite numbers that MAKES SENSE.
What are prime numbers?
A prime number is a number that has exactly 2 factors: two and...
An easy intro to prime numbers and composite numbers that MAKES SENSE.
What are prime numbers?
A prime number is a number that has exactly 2 factors: two and itself.
What are composite numbers?
A composite number is one which has two or more factors.
What is the difference between a prime number and a composite number.....?
For the playlist of indicies and prime numbers.
https://www.youtube.com/playlist?list=PLjbxBzUM6SLljxglRaecKXzlXgS9ecv3f
To contribute on Patreon:
https://www.patreon.com/tecmath To donate to the tecmath channel: https://paypal.me/tecmath?locale.x=en_AU
To support tecmath on Patreon: https://www.patreon.com/tecmath
To buy tecmath mechandise: https://teespring.com/stores/tecmath-store
https://wn.com/What_Is_A_Prime_Number
An easy intro to prime numbers and composite numbers that MAKES SENSE.
What are prime numbers?
A prime number is a number that has exactly 2 factors: two and itself.
What are composite numbers?
A composite number is one which has two or more factors.
What is the difference between a prime number and a composite number.....?
For the playlist of indicies and prime numbers.
https://www.youtube.com/playlist?list=PLjbxBzUM6SLljxglRaecKXzlXgS9ecv3f
To contribute on Patreon:
https://www.patreon.com/tecmath To donate to the tecmath channel: https://paypal.me/tecmath?locale.x=en_AU
To support tecmath on Patreon: https://www.patreon.com/tecmath
To buy tecmath mechandise: https://teespring.com/stores/tecmath-store
- published: 25 Mar 2020
- views: 299717
3:38
Finding Prime Numbers
For students of all ages. Gotta wrap your head around primes? Here's how you can think of it so that it makes sense, rather than just learning a bunch of number...
For students of all ages. Gotta wrap your head around primes? Here's how you can think of it so that it makes sense, rather than just learning a bunch of numbers as prime.
Definition of primes. 1 is NOT prime.
Use the Sieve of Eratosthenes to find primes up to 50
Teachers: this is a great primer for students doing the Sieve for themselves - students often find written instructions for this confusing. Show them sieving the multiples up to and including 5 and they should find it a breeze! Get them to stop when they hit 50, then finish the film and they can check their work.
Segue - D.I.Y on paper up to 100. They must keep this work to help them remember. They will eventually learn the first primes for themselves, but it's much better and more enduring learning to work it out and be able to look back and review through understanding rather than trying to cram it by rote.
https://wn.com/Finding_Prime_Numbers
For students of all ages. Gotta wrap your head around primes? Here's how you can think of it so that it makes sense, rather than just learning a bunch of numbers as prime.
Definition of primes. 1 is NOT prime.
Use the Sieve of Eratosthenes to find primes up to 50
Teachers: this is a great primer for students doing the Sieve for themselves - students often find written instructions for this confusing. Show them sieving the multiples up to and including 5 and they should find it a breeze! Get them to stop when they hit 50, then finish the film and they can check their work.
Segue - D.I.Y on paper up to 100. They must keep this work to help them remember. They will eventually learn the first primes for themselves, but it's much better and more enduring learning to work it out and be able to look back and review through understanding rather than trying to cram it by rote.
- published: 03 Oct 2015
- views: 1205983
6:40
Math Antics - Prime Factorization
Learn More at mathantics.com
Visit http://www.mathantics.com for more Free math videos and additional subscription based content!
Learn More at mathantics.com
Visit http://www.mathantics.com for more Free math videos and additional subscription based content!
https://wn.com/Math_Antics_Prime_Factorization
Learn More at mathantics.com
Visit http://www.mathantics.com for more Free math videos and additional subscription based content!
- published: 16 Apr 2012
- views: 2736207
8:35
The Most Wanted Prime Number - Numberphile
Featuring Neil Sloane.
Visit https://gift.climeworks.com/numberphile to give the gift of CO₂ removal. Use code NUMBERPHILE10 for 10% off your purchase in Decemb...
Featuring Neil Sloane.
Visit https://gift.climeworks.com/numberphile to give the gift of CO₂ removal. Use code NUMBERPHILE10 for 10% off your purchase in December (sponsor)
More links & stuff in full description below ↓↓↓
Neil Sloane is the founder of The OEIS: https://oeis.org
More videos with Neil: http://bit.ly/Sloane_Numberphile
Prime Playlist: https://bit.ly/PrimePlaylist
Note the 17350-digit prime we feature is more accurately classed as a "probable prime" at this time.
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/
And support from The Akamai Foundation - dedicated to encouraging the next generation of technology innovators and equitable access to STEM education - https://www.akamai.com/company/corporate-responsibility/akamai-foundation
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
Videos by Brady Haran
Patreon: http://www.patreon.com/numberphile
Numberphile T-Shirts and Merch: https://teespring.com/stores/numberphile
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
https://wn.com/The_Most_Wanted_Prime_Number_Numberphile
Featuring Neil Sloane.
Visit https://gift.climeworks.com/numberphile to give the gift of CO₂ removal. Use code NUMBERPHILE10 for 10% off your purchase in December (sponsor)
More links & stuff in full description below ↓↓↓
Neil Sloane is the founder of The OEIS: https://oeis.org
More videos with Neil: http://bit.ly/Sloane_Numberphile
Prime Playlist: https://bit.ly/PrimePlaylist
Note the 17350-digit prime we feature is more accurately classed as a "probable prime" at this time.
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/
And support from The Akamai Foundation - dedicated to encouraging the next generation of technology innovators and equitable access to STEM education - https://www.akamai.com/company/corporate-responsibility/akamai-foundation
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
Videos by Brady Haran
Patreon: http://www.patreon.com/numberphile
Numberphile T-Shirts and Merch: https://teespring.com/stores/numberphile
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
- published: 15 Dec 2021
- views: 515844
6:23
Prime Numbers and Composite Numbers
This math video tutorial provides a basic introduction into prime and composite numbers. It explains how to tell if a number is prime or composite using a simp...
This math video tutorial provides a basic introduction into prime and composite numbers. It explains how to tell if a number is prime or composite using a simple method.
Subscribe:
https://www.youtube.com/channel/UCEWpbFLzoYGPfuWUMFPSaoA?sub_confirmation=1
Access to Premium Videos:
https://www.patreon.com/MathScienceTutor
https://www.facebook.com/MathScienceTutoring/
https://wn.com/Prime_Numbers_And_Composite_Numbers
This math video tutorial provides a basic introduction into prime and composite numbers. It explains how to tell if a number is prime or composite using a simple method.
Subscribe:
https://www.youtube.com/channel/UCEWpbFLzoYGPfuWUMFPSaoA?sub_confirmation=1
Access to Premium Videos:
https://www.patreon.com/MathScienceTutor
https://www.facebook.com/MathScienceTutoring/
- published: 15 May 2018
- views: 446825
6:28
Prime Numbers Between 1 and 100
Prime numbers are positive integers greater than 1 that have no positive integer divisors other than 1 and themselves. In other words, a prime number is a numbe...
Prime numbers are positive integers greater than 1 that have no positive integer divisors other than 1 and themselves. In other words, a prime number is a number that can only be divided evenly by 1 and itself.
Prime numbers have a unique set of properties that make them important in mathematics, computer science, and cryptography. For example:
Prime numbers are the building blocks of all other integers. Every positive integer can be expressed as a product of primes in a unique way, called the prime factorization.
Prime numbers play a crucial role in cryptography, which is the study of secure communication. Many encryption algorithms rely on the difficulty of factoring large composite numbers into their prime factors.
Prime numbers are used extensively in number theory, which is the branch of mathematics that deals with the properties of numbers. Many famous unsolved problems in mathematics involve prime numbers, such as the twin prime conjecture and the Goldbach conjecture.
Some examples of prime numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
2 is the only even prime number.
Play store app: https://play.google.com/store/apps/details?id=com.maths24x7&hl=en_US&gl=US
Website: https://maths24x7.com
Don't forget to share it in your friend's circle and in your WhatsApp groups.
How to find prime numbers between 1 and 200
The prime number between 1 and 100 ideal maths lab with models and projects
Link for prime numbers between 1 and 100 -
1. https://youtu.be/yUc3WaE4ua4
2. https://youtu.be/1gW6ec3hyN0
Download app Maths24x7 https://play.google.com/store/apps/details?id=com.maths24x7&hl=en_US&gl=US
Website: https://maths24x7.com
Prime no 1 to 500
There are 95 prime numbers between 1 and 500
Prime numbers from 1 to 200 https://youtu.be/-AwJvtTIsx8
Prime Numbers Between 1 and 100 https://youtu.be/ZnQtXUtE44c
Prime no 1 to 500 https://youtu.be/wPwERA_Izys
Prime number between 1 and 100 ideal maths lab with models and projects https://youtu.be/1gW6ec3hyN0
https://wn.com/Prime_Numbers_Between_1_And_100
Prime numbers are positive integers greater than 1 that have no positive integer divisors other than 1 and themselves. In other words, a prime number is a number that can only be divided evenly by 1 and itself.
Prime numbers have a unique set of properties that make them important in mathematics, computer science, and cryptography. For example:
Prime numbers are the building blocks of all other integers. Every positive integer can be expressed as a product of primes in a unique way, called the prime factorization.
Prime numbers play a crucial role in cryptography, which is the study of secure communication. Many encryption algorithms rely on the difficulty of factoring large composite numbers into their prime factors.
Prime numbers are used extensively in number theory, which is the branch of mathematics that deals with the properties of numbers. Many famous unsolved problems in mathematics involve prime numbers, such as the twin prime conjecture and the Goldbach conjecture.
Some examples of prime numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
2 is the only even prime number.
Play store app: https://play.google.com/store/apps/details?id=com.maths24x7&hl=en_US&gl=US
Website: https://maths24x7.com
Don't forget to share it in your friend's circle and in your WhatsApp groups.
How to find prime numbers between 1 and 200
The prime number between 1 and 100 ideal maths lab with models and projects
Link for prime numbers between 1 and 100 -
1. https://youtu.be/yUc3WaE4ua4
2. https://youtu.be/1gW6ec3hyN0
Download app Maths24x7 https://play.google.com/store/apps/details?id=com.maths24x7&hl=en_US&gl=US
Website: https://maths24x7.com
Prime no 1 to 500
There are 95 prime numbers between 1 and 500
Prime numbers from 1 to 200 https://youtu.be/-AwJvtTIsx8
Prime Numbers Between 1 and 100 https://youtu.be/ZnQtXUtE44c
Prime no 1 to 500 https://youtu.be/wPwERA_Izys
Prime number between 1 and 100 ideal maths lab with models and projects https://youtu.be/1gW6ec3hyN0
- published: 19 Feb 2020
- views: 3625523
22:21
Why do prime numbers make these spirals? | Dirichlet’s theorem and pi approximations
A curious pattern, approximations for pi, and prime distributions.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of su...
A curious pattern, approximations for pi, and prime distributions.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/spiral-thanks
Based on this Math Stack Exchange post:
https://math.stackexchange.com/questions/885879/meaning-of-rays-in-polar-plot-of-prime-numbers/885894
Want to learn more about rational approximations? See this Mathologer video.
https://youtu.be/CaasbfdJdJg
Also, if you haven't heard of Ulam Spirals, you may enjoy this Numberphile video:
https://youtu.be/iFuR97YcSLM
Dirichlet's paper:
https://arxiv.org/pdf/0808.1408.pdf
Timestamps:
0:00 - The spiral mystery
3:35 - Non-prime spirals
6:10 - Residue classes
7:20 - Why the galactic spirals
9:30 - Euler’s totient function
10:28 - The larger scale
14:45 - Dirichlet’s theorem
20:26 - Why care?
Corrections:
18:30: In the video, I say that Dirichlet showed that the primes are equally distributed among allowable residue classes, but this is not historically accurate. (By "allowable", here, I mean a residue class whose elements are coprime to the modulus, as described in the video). What he actually showed is that the sum of the reciprocals of all primes in a given allowable residue class diverges, which proves that there are infinitely many primes in such a sequence.
Dirichlet observed this equal distribution numerically and noted this in his paper, but it wasn't until decades later that this fact was properly proved, as it required building on some of the work of Riemann in his famous 1859 paper. If I'm not mistaken, I think it wasn't until Vallée Poussin in (1899), with a version of the prime number theorem for residue classes like this, but I could be wrong there.
In many ways, this was a very silly error for me to have let through. It is true that this result was proven with heavy use of complex analysis, and in fact, it's in a complex analysis lecture that I remember first learning about it. But of course, this would have to have happened after Dirichlet because it would have to have happened after Riemann!
My apologies for the mistake. If you notice factual errors in videos that are not already mentioned in the video's description or pinned comment, don't hesitate to let me know.
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
------------------
These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
https://wn.com/Why_Do_Prime_Numbers_Make_These_Spirals_|_Dirichlet’S_Theorem_And_Pi_Approximations
A curious pattern, approximations for pi, and prime distributions.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/spiral-thanks
Based on this Math Stack Exchange post:
https://math.stackexchange.com/questions/885879/meaning-of-rays-in-polar-plot-of-prime-numbers/885894
Want to learn more about rational approximations? See this Mathologer video.
https://youtu.be/CaasbfdJdJg
Also, if you haven't heard of Ulam Spirals, you may enjoy this Numberphile video:
https://youtu.be/iFuR97YcSLM
Dirichlet's paper:
https://arxiv.org/pdf/0808.1408.pdf
Timestamps:
0:00 - The spiral mystery
3:35 - Non-prime spirals
6:10 - Residue classes
7:20 - Why the galactic spirals
9:30 - Euler’s totient function
10:28 - The larger scale
14:45 - Dirichlet’s theorem
20:26 - Why care?
Corrections:
18:30: In the video, I say that Dirichlet showed that the primes are equally distributed among allowable residue classes, but this is not historically accurate. (By "allowable", here, I mean a residue class whose elements are coprime to the modulus, as described in the video). What he actually showed is that the sum of the reciprocals of all primes in a given allowable residue class diverges, which proves that there are infinitely many primes in such a sequence.
Dirichlet observed this equal distribution numerically and noted this in his paper, but it wasn't until decades later that this fact was properly proved, as it required building on some of the work of Riemann in his famous 1859 paper. If I'm not mistaken, I think it wasn't until Vallée Poussin in (1899), with a version of the prime number theorem for residue classes like this, but I could be wrong there.
In many ways, this was a very silly error for me to have let through. It is true that this result was proven with heavy use of complex analysis, and in fact, it's in a complex analysis lecture that I remember first learning about it. But of course, this would have to have happened after Dirichlet because it would have to have happened after Riemann!
My apologies for the mistake. If you notice factual errors in videos that are not already mentioned in the video's description or pinned comment, don't hesitate to let me know.
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
------------------
These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
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- published: 08 Oct 2019
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