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).
Introduction to prime numbers for GCSE 9-1 maths!
From playlist Prime Numbers, HCF and LCM - GCSE 9-1 Maths
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Why Are There Infinitely Many Prime Numbers?
Here's why there are infinitely many prime numbers!
From playlist Summer of Math Exposition Youtube Videos
Differential Equations | Abel's Theorem
We present Abel's Theorem with a proof. http://www.michael-penn.net
From playlist Differential Equations