Integer sequences | Classes of prime numbers
In mathematics, a primorial prime is a prime number of the form pn# ± 1, where pn# is the primorial of pn (i.e. the product of the first n primes). Primality tests show that pn# − 1 is prime for n = 2, 3, 5, 6, 13, 24, ... (sequence in the OEIS)pn# + 1 is prime for n = 0, 1, 2, 3, 4, 5, 11, ... (sequence in the OEIS) The first term of the second sequence is 0 because p0# = 1 is the empty product, and thus p0# + 1 = 2, which is prime. Similarly, the first term of the first sequence is not 1, because p1# = 2, and 2 − 1 = 1 is not prime. The first few primorial primes are 2, 3, 5, 7, 29, 31, 211, 2309, 2311, 30029, 200560490131, 304250263527209, 23768741896345550770650537601358309 (sequence in the OEIS) As of October 2021, the largest known primorial prime (of the form pn# − 1) is 3267113# − 1 (n = 234,725) with 1,418,398 digits, found by the PrimeGrid project. As of 2022, the largest known prime of the form pn# + 1 is 392113# + 1 (n = 33,237) with 169,966 digits, found in 2001 by Daniel Heuer. Euclid's proof of the infinitude of the prime numbers is commonly misinterpreted as defining the primorial primes, in the following manner: Assume that the first n consecutive primes including 2 are the only primes that exist. If either pn# + 1 or pn# − 1 is a primorial prime, it means that there are larger primes than the nth prime (if neither is a prime, that also proves the infinitude of primes, but less directly; each of these two numbers has a remainder of either p − 1 or 1 when divided by any of the first n primes, and hence all its prime factors are larger than pn). (Wikipedia).
A Beautiful Algorithm for the Primes
What's the fastest algorithm for generating the prime sequence? Watch a frat bro hunch over a notebook and find out! . . . Walkthrough (pause, then use “,” and “.” keys to step): https://www.youtube.com/watch?v=GxgGMwLfTjE&t=4s Computing the primes up to 40,000 (also pause and use "," and
From playlist Summer of Math Exposition 2 videos
My #MegaFavNumbers - 9,699,690, primorial and prime
Something needs to clarify: 3:32 does not include 9,699,667(19#-23) and 9,699,713(19#+23) Also, Let me promote my game here: https://rmf2077.itch.io/why-is-6-afraid-of-7-9-s-revenge (Need a keyboard to play) This game is an action game about numbers! #MegaFavNumbers
From playlist MegaFavNumbers
Prealgebra Lecture 4.3: How to Multiply and Divide Fractions
https://www.patreon.com/ProfessorLeonard Prealgebra Lecture 4.3: Multiplying and Dividing Fractions
From playlist Prealgebra (Full Length Videos)
937 is a PRIME-arily Awesome Number!
937 is a surprising remarkable number - find out why here! Sponsored by Squarespace - get your own beautiful website at: http://squarespace.com/drawcuriosity Use CODE 'DC' to get 10% off at check out I've been wanting to make another video on maths for ages, so boom, here you go, recreati
From playlist Mathematics
Prealgebra Lecture 4.2: Prime Factorization and Simplification of Fractions
https://www.patreon.com/ProfessorLeonard Prealgebra Lecture 4.2: Prime Factorization and Simplification of Fractions
From playlist Prealgebra (Full Length Videos)
J and Bex vs Primorial 15 | MegaFavNumbers
Solving boolean expressions, and how 614,889,782,588,491,410 became my #megafavnumber ! table of contents: 00:00 intro: primorial 15 01:23 the problem to solve (factoring in bex) 03:31 solving the problem in J 06:03 the problem in bex 07:38 scaling the problem 08:39 visualizing x*y=6 in
From playlist MegaFavNumbers
∃ the AVERAGE prime number (n#)^(⅟n) → e
■ Instagram & Telegram: @jodirac ■ Handle: @jodirac-2 ▬ Davie504 ▬ https://youtu.be/onN0mOLjtm4 Bye for now! ͜ Jo͠ thumbnails: ■ Dr Peyam ■ COOL Euler ■ Mathologer ■ The number e explained in depth for (smart) dummies ■ 3Blue1Brown ■ What's so special about Euler's number e? ■ Numberph
From playlist Summer of Math Exposition Youtube Videos
This video will teach students how to convert from fractions to decimals. In particular, I show students how to set up a long division problem using a fraction. Next, I demonstrate the technique of adding zeroes so that an accurate decimal can be found. Thank you for watching and please s
From playlist PreAlgebra
From playlist Cryptography
This video focuses on how to multiply decimals. In particular, I teach students the concept of moving the decimal appropriately when multiplying decimal terms. In addition, show students how to use estimation strategies in the event that they forget the technique for multiplying decimals.
From playlist PreAlgebra
We designed special dice using math, but there’s a catch
How would you order the players randomly? Tell us in the comments. :) Some proposals that already appeared in the comments section: - Put cards with player names in a sack, shuffle, then take them out one by one to get the order. - Simulate the above process using dice (see the comments
From playlist Prob and Stats
Driving Downtown - Dallas' Main Street 4K - USA
40+ Popular Streets In Major Cities - Driving Downtown Streets - Full Playlist Here! - https://www.youtube.com/playlist?list=PLvEhUAlWIdM2lTX9dNZ3TfJvN-HGA2lTL Driving Downtown Streets - Main Street - Dallas Texas USA - Episode 46. Starting Point: Main Street - https://goo.gl/maps/3PEqD6
From playlist Location by State - Texas USA - J Utah
Driving Downtown - Dallas 4K - USA
Driving Downtown - Dallas Texas USA - Episode 39. Starting Point: https://goo.gl/maps/Kt22kujAN242 . Dallas is a major city in the state of Texas and is the largest urban center of the fourth most populous metropolitan area in the United States. The city proper ranks ninth in the U.S. and
From playlist Location by State - Texas USA - J Utah
Exploring the constraints to increase genome complexity in RNA viruses by Santiago F. Elena
The Third Bangalore School on Population Genetics and Evolution DATE:05 March 2018 to 17 March 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore. No living organism escapes evolutionary change. Evolutionary biology thus connects all biological disciplines. To understand the processes dri
From playlist Third Bangalore School on Population Genetics and Evolution
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
Prealgebra Lecture 4.2 Part 2: Prime Factorization and Simplification of Fractions
From playlist Prealgebra Playlist 1
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 p
From playlist Indicies (Exponents) and Primes
In this video, I use the coordinate method or Chain Rule method to solve a PDE. It is based on defining clever coordinates and using the Chain Rule to turn the PDE into one that's much easier to solve. Enjoy! Check out my PDE Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmDo
From playlist Partial Differential Equations