Arithmetic functions | Prime numbers
A prime gap is the difference between two successive prime numbers. The n-th prime gap, denoted gn or g(pn) is the difference between the (n + 1)-th and then-th prime numbers, i.e. We have g1 = 1, g2 = g3 = 2, and g4 = 4. The sequence (gn) of prime gaps has been extensively studied; however, many questions and conjectures remain unanswered. The first 60 prime gaps are: 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 14, 4, 6, 2, 10, 2, 6, 6, 4, 6, 6, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4, 6, 2, 10, 6, 6, 6, 2, 6, 4, 2, ... (sequence in the OEIS). By the definition of gn every prime can be written as (Wikipedia).
Prime Gaps and The Crazy Sequences of Steps
When we try to avoid multiples of numbers using sequences we find a very unique way to create a prime list that has its own properties and curiosities. These sequences are state machines that can become very complex to generate but should be very simple to read.
From playlist Summer of Math Exposition Youtube Videos
Prime Gaps As Large As You Want (and Larger!) // [NUMBER THEORY]
This is one of the most stunningly cool things I've learned about the prime numbers: it's trivial to construct infinitely large gaps between them. Subscribe: https://bit.ly/polymathematic | Enable ALL push notifications đź”” To be sure, we want to be careful about the sense in which we're u
From playlist Math Mini
Prove that the gap of successive prime numbers can be arbitrarily large
A simple number theory proof problem regarding prime number distribution: Prove that the gap of successive prime numbers can be arbitrarily large Please Like, Share and Subscribe!
From playlist Elementary Number Theory
Infinitely Large Prime Gaps! #mathclass #shorts Check out the main channel @polymathematic ! We currently cannot prove that there are infinitely many prime gaps of size 2 (also known as "twin primes"), though we certainly think that there are. But it turns out it's trivial to prove that
From playlist polymathematic #shorts
How to find prime numbers #shorts
In this short we talk about finding prime numbers. Full video at https://youtu.be/CEyZRhi45pE
From playlist #shorts mathematicsonline
Terence Tao - 1/3 Bounded gaps between primes Download
Terence Tao - Bounded gaps between primes
From playlist École d'été 2014 - Théorie analytique des nombres
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
Gaps between primes – James Maynard – ICM2018
Number Theory Invited Lecture 3.2 Gaps between primes James Maynard Abstract: We discuss recent advances on weak forms of the Prime k-tuple Conjecture, and its role in proving new estimates for the existence of small gaps between primes and the existence of large gaps between primes.
From playlist Number Theory
Terence Tao - Large and Small Gaps in the Primes [2015]
Slides for this talk: https://drive.google.com/file/d/1Nkwt96VXvHZxCEGg5qlcgAXZFPLme_kq/view?usp=sharing Latinos in the Mathematical Sciences Conference 2015 APRIL 9 - 11, 2015 Large and small gaps in the primes Terence Tao University of California, Los Angeles (UCLA) There are many
From playlist Number Theory
LATMATH: Terence Tao - "Large and Small Gaps in the Primes"
Latin@s in the Mathematical Sciences Conference 2015 "Large and Small Gaps in the Primes" Terence Tao, UCLA Institute for Pure and Applied Mathematics, UCLA April 9, 2015 For more information: https://www.ipam.ucla.edu/programs/special-events-and-conferences/latinos-in-the-mathematical-
From playlist Latin@s in the Mathematical Sciences 2015
Large Gaps between Primes - Numberphile
James Maynard on discoveries about large gaps between prime numbers. More links & stuff in full description below ↓↓↓ More Maynard videos: http://bit.ly/JamesMaynard Prime Playlist: http://bit.ly/primevids The 20 August paper: https://arxiv.org/abs/1408.4505 The 21 August paper: https://
From playlist James Maynard on Numberphile
Twin Prime Conjecture - Numberphile
Dr James Maynard is a leading figure in recent progress on the Twin Prime Conjecture. More links and stuff below ↓↓↓ More Twin Primes from Numberphile: https://youtu.be/vkMXdShDdtY and https://youtu.be/D4_sNKoO-RA Prime Number Playlist: http://bit.ly/primevids Riemann Hypothesis videos:
From playlist James Maynard on Numberphile
James Maynard: Large gaps between primes in subsets
Abstract: All previous methods of showing the existence of large gaps between primes have relied on the fact that smooth numbers are unusually sparse. This feature of the argument does not seem to generalise to showing large gaps between primes in subsets, such as values of a polynomial. W
From playlist Number Theory
János Pintz: Polignac numbers and the consecutive gaps between primes
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Number Theory
Almost Primes in Short Intervals
Short Talks by Postdoctoral Members Topic: Almost Primes in Short Intervals Speaker: Joni Teräväinen Affiliation: Member, School pf Mathematics September 30, 2022
From playlist Short Talks by Postdoctoral Members
Introduction to number theory lecture 5. Primes.
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We discuss some basic properties of primes and prove the fundamental theorem of arithmetic.
From playlist Introduction to number theory (Berkeley Math 115)
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