Classes of prime numbers

Good prime

A good prime is a prime number whose square is greater than the product of any two primes at the same number of positions before and after it in the sequence of primes. That is, good prime satisfies the inequality for all 1 ≤ i ≤ n−1, where pk is the kth prime. Example: the first primes are 2, 3, 5, 7 and 11. Since for 5 both the conditions are fulfilled, 5 is a good prime. There are infinitely many good primes. The first good primes are: 5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 97, 101, 127, 149, 179, 191, 223, 227, 251, 257, 269, 307, 311, 331, 347, 419, 431, 541, 557, 563, 569, 587, 593, 599, 641, 727, 733, 739, 809, 821, 853, 929, 937, 967 (sequence in the OEIS). An alternative version takes only i = 1 in the definition. With that there are more good primes: 5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 157, 163, 173, 179, 191, 197, 211, 223, 227, 239, 251, 257, 263, 269, 277, 281, 307, 311, 331, 347, 367, 373, 379, 397, 419, 431, 439, 457, 461, 479, 487, 499, 521, 541, 557, 563, 569, 587, 593, 599, 607, 613, 617, 631, 641, 653, 659, 673, 701, 719, 727, 733, 739, 751, 757, 769, 787, 809, 821, 827, 853, 857, 877, 881, 907, 929, 937, 947, 967, 977, 991 (sequence in the OEIS). (Wikipedia).

Video thumbnail

Review: Prime Numbers

via YouTube Capture

From playlist Computation with Integers

Video thumbnail

What Is A Prime Number?

Introduction to prime numbers for GCSE 9-1 maths!

From playlist Prime Numbers, HCF and LCM - GCSE 9-1 Maths

Video thumbnail

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

Video thumbnail

Prime Numbers

"Identify prime numbers."

From playlist Number: Factors, Multiples & Primes

Video thumbnail

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

Video thumbnail

Algebra - Ch. 6: Factoring (4 of 55) What is a Prime Number?

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a prime number. A prime number is a positive integer that can only be written as a product of one and itself. Its factors are “1” and itself. To donate: http://www.ilectureonline.com/

From playlist ALGEBRA CH 6 FACTORING

Video thumbnail

Prime Factors | Number | Maths | FuseSchool

Prime Factors | Number | Maths | FuseSchool Every single positive number can be broken down into prime factors. Every single positive number has a unique set of prime factors. It’s the fundamental theorem of arithmetic. Prime factors are used in cryptology to keep data safe. In this video

From playlist MATHS: Numbers

Video thumbnail

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

Video thumbnail

Very Large Primes and (Almost) Perfect Numbers -- MegaFavNumbers

This is my video submission for the #MegaFavNumbers celebration. As promised in the video, here is the very large number that was simply too big for the screen: 5282945208034002678497845769960721106385426547566030332928651387255812371024044147692699871010305634389030253300042369944654409

From playlist MegaFavNumbers

Video thumbnail

Differential Equations | Variation of Parameters.

We derive the general form for a solution to a differential equation using variation of parameters. http://www.michael-penn.net

From playlist Differential Equations

Video thumbnail

Putnam Exam | 2011: B1

We present a solution to question B1 from the 2011 William Lowell Putnam Mathematics Competition. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Putnam Exam Solutions: A1/B1

Video thumbnail

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

Video thumbnail

Differential Equations | Applications of Second Order DEs: Central Force

We use a second order differential equation to describe the motion of an object under the influence of a central force. http://www.michael-penn.net

From playlist Differential Equations

Video thumbnail

Elliptic Curves - Lecture 20a - Elliptic curves over local fields (good and bad reduction)

This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/

From playlist An Introduction to the Arithmetic of Elliptic Curves

Video thumbnail

Number Theory | Infinitely many primes of the form 4n+3.

We prove that there are infinitely many primes of the form 4n+3. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Number Theory

Video thumbnail

The Badly Behaved Prime (with James Maynard) - Numberphile Podcast

James Maynard is making waves in the world of prime numbers - we spoke to him in his office at Oxford University. James is appointed a professor - https://www.maths.ox.ac.uk/node/26989 And wins the Cole Prize - http://www.ams.org/tools/news?news_id=5602 James discusses the Twin Prime Co

From playlist James Maynard on Numberphile

Video thumbnail

Number Theory | The Multiplicativity of Euler's Totient Function

We state and prove when Euler's totient function is multiplicative. http://www.michael-penn.net

From playlist Number Theory

Video thumbnail

Multivariable Calculus | Curvature Part 2

We prove another formula that can be used to calculate curvature, give an example, and find the curvature of an arbitrary curve defined by y=f(x). http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus

Video thumbnail

Why Are There Infinitely Many Prime Numbers?

Here's why there are infinitely many prime numbers!

From playlist Summer of Math Exposition Youtube Videos

Video thumbnail

Differential Equations | Abel's Theorem

We present Abel's Theorem with a proof. http://www.michael-penn.net

From playlist Differential Equations

Related pages

Inequality (mathematics) | Prime number | Square (algebra) | Integer sequence