Number theoretic algorithms | Prime numbers | Cryptographic algorithms
In computational number theory, a variety of algorithms make it possible to generate prime numbers efficiently. These are used in various applications, for example hashing, public-key cryptography, and search of prime factors in large numbers. For relatively small numbers, it is possible to just apply trial division to each successive odd number. Prime sieves are almost always faster. Prime sieving is the fastest known way to deterministically enumerate the primes. There are some known formulas that can calculate the next prime but there is no known way to express the next prime in terms of the previous primes. Also, there is no effective known general manipulation and/or extension of some mathematical expression (even such including later primes) that deterministically calculates the next prime. (Wikipedia).
MegaFavNumbers: Plus One Primes, 154,641,337, and 62,784,382,823
My entry in the #MegaFavNumbers series looks at a particularly striking example of a very specific family of primes -- and how it connects to what digits can be the final digit of primes in different bases.
From playlist MegaFavNumbers
Interesting Facts About the Last Digits of Prime Numbers
This video explains some interesting facts about the last digits of prime numbers.
From playlist Mathematics General Interest
Prime Numbers and their Mysterious Distribution (Prime Number Theorem)
Primes are the building blocks of math. But just how mysterious are they? Our study of prime numbers dates back to the ancient Greeks who first recognized that certain numbers can't be turned into rectangles, or that they can't be factored into any way. Over the years prime numbers have
From playlist Prime Numbers
Why Are There Infinitely Many Prime Numbers?
Here's why there are infinitely many prime numbers!
From playlist Summer of Math Exposition Youtube Videos
Kids of the 80s and 90s had a lot of prime years, but kids of the 2010s won't be so lucky.
Check out the main channel @polymathematic ! As a child born in the 80s, I had a lot of great prime years: 1993, 1997, 1999, 2003. But we're in the midst of the largest prime desert since the mid-20th century at present, and after a couple twin prime years in 2027 and 2029, it will only g
From playlist polymathematic #shorts
Prime Factoring - GCSE Mathematics Revision (Foundation)
What are prime numbers? Learn how to find the prime factors of a number and write it as a product of prime factors. ❤️ ❤️ ❤️ Support the channel ❤️ ❤️ ❤️ https://www.youtube.com/channel/UCf89Gd0FuNUdWv8FlSS7lqQ/join
From playlist Number
Introduction to prime numbers for GCSE 9-1 maths!
From playlist Prime Numbers, HCF and LCM - GCSE 9-1 Maths
MegaFavNumbers :- Evenly Primest Prime 232,222,222,222,233,333,333,222,222,222,222,222,322,222,223
#MegaFavNumber
From playlist MegaFavNumbers
Commutative algebra 28 Geometry of associated primes
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give a geometric interpretation of Ass(M), the set of associated primes of M, by showing that its closure is the support Su
From playlist Commutative algebra
Mod-03 Lec-12 Second Order Linear Equations
Ordinary Differential Equations and Applications by A. K. Nandakumaran,P. S. Datti & Raju K. George,Department of Mathematics,IISc Bangalore.For more details on NPTEL visit http://nptel.ac.in.
From playlist IISc Bangalore: Ordinary Differential Equations and Applications | CosmoLearning.org Mathematics
Nakayama's Lemma - April 12 2021
This is a video from by Abstract Algebra 4 course that took place in Spring 2021.
From playlist Course on Rings and Modules (Abstract Algebra 4) [Graduate Course]
Part II: Differential Equations, Lec 5: Variations of Parameters
Part II: Differential Equations, Lecture 5: Variations of Parameters Instructor: Herbert Gross View the complete course: http://ocw.mit.edu/RES18-008F11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Calculus Revisited: Calculus of Complex Variables
Prime Numbers - What is Known and Unknown, by Keith Conrad
This talk by Keith Conrad (UConn) was part of UConn's Number Theory Day 2017.
From playlist Number Theory Day
Mod-03 Lec-13 Second Order Linear Equations Continued I
Ordinary Differential Equations and Applications by A. K. Nandakumaran,P. S. Datti & Raju K. George,Department of Mathematics,IISc Bangalore.For more details on NPTEL visit http://nptel.ac.in.
From playlist IISc Bangalore: Ordinary Differential Equations and Applications | CosmoLearning.org Mathematics
Lec 08. Einstein's General Relativity and Gravitation: General Relativity 4
UCI Physics 255 Einstein's General Relativity and Gravitation (Spring 2014) Lec 08. Einstein's General Relativity and Gravitation -- General Relativity -- Part 4 View the complete course: http://ocw.uci.edu/courses/einsteins_general_relativity_and_gravitation.html Instructor: Herbert W. Ha
From playlist Einstein's General Relativity and Gravitation
CTNT 2022 - 100 Years of Chebotarev Density (Lecture 2) - by Keith Conrad
This video is part of a mini-course on "100 Years of Chebotarev Density" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - 100 Years of Chebotarev Density (by Keith Conrad)
7 is the only Prime followed by a Cube.
Feel like exploring more curious facts about prime numbers? Why not try out Brilliant then? =D https://brilliant.org/FlammableMaths Hagoromo chalk :D https://stemerch.com/collections/school-teaching-supplies Infimum Merch :0 https://papaflammy.creator-spring.com/listing/infimum? Today we
From playlist Number Theory
Encoding with Prime Numbers and Second Ratios - #MegaFavNumbers
It's still Sept 2nd somewhere! I've been fascinated by Prime Numbers and sequences of prime numbers over the last 3 years or so. I've had two sequences approved for inclusion in the oeis.org related to prime numbers, https://oeis.org/A295746 and https://oeis.org/A295973 In this video, ins
From playlist MegaFavNumbers
Lie Groups and Lie Algebras: Lesson 19 - Infinitesimal transformation example
Lie Groups and Lie Algebras: Lesson 19 - Infinitesimal transformation example In this lecture we demonstrate how a transformation group generator can transform a function on the geometric space when the transformation is infinitesimal. For this we use Gilmores 2-parameter scale/shift exa
From playlist Lie Groups and Lie Algebras