Unsolved problems in number theory | Articles containing proofs | Integer sequences | Mersenne primes | Perfect numbers | Classes of prime numbers
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If n is a composite number then so is 2n − 1. Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form Mp = 2p − 1 for some prime p. The exponents n which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, ... (sequence in the OEIS) and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ... (sequence in the OEIS). Numbers of the form Mn = 2n − 1 without the primality requirement may be called Mersenne numbers. Sometimes, however, Mersenne numbers are defined to have the additional requirement that n be prime.The smallest composite Mersenne number with prime exponent n is 211 − 1 = 2047 = 23 × 89. Mersenne primes were studied in antiquity because of their close : the Euclid–Euler theorem asserts a one-to-one correspondence between even perfect numbers and Mersenne primes. Many of the largest known primes are Mersenne primes because Mersenne numbers are easier to check for primality. As of October 2022, 51 Mersenne primes are known. The largest known prime number, 282,589,933 − 1, is a Mersenne prime. Since 1997, all newly found Mersenne primes have been discovered by the Great Internet Mersenne Prime Search, a distributed computing project. In December 2020, a major milestone in the project was passed after all exponents below 100 million were checked at least once. (Wikipedia).
From playlist Cryptography
My #MegaFavNumbers is 2^82589933-1 // The largest Mersenne prime…..yet
This video is part of the #MegaFavNumbers series where a tonne of math youtubers like @numberphile @standupmaths and @3blue1brown share their favourite MEGA numbers, i.e. numbers over a million. Check out the full playlist here: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPs
From playlist MegaFavNumbers
New World's Biggest Prime Number (PRINTED FULLY ON PAPER) - Numberphile
Matt Parker on the latest Mersenne Prime to take the title of "world's biggest prime". He had it printed! More links & stuff in full description below ↓↓↓ More from this interview very soon, including details of how the prime was found. PART TWO: https://youtu.be/lEvXcTYqtKU PART THREE o
From playlist Matt Parker (standupmaths) on Numberphile
How they found the World's Biggest Prime Number - Numberphile
Featuring Matt Parker... More links & stuff in full description below ↓↓↓ See part one at: https://youtu.be/tlpYjrbujG0 Part three on Numberphile2: https://youtu.be/jNXAMBvYe-Y Matt's interview with Curtis Cooper: https://youtu.be/q5ozBnrd5Zc The previous record: https://youtu.be/QSEKzFG
From playlist Matt Parker (standupmaths) on Numberphile
Why Do We Need a 23 Million Digit Prime Number?
Finding the biggest prime number might not only have applications in computing, it could also win you some serious money. Here’s how. The ‘Ham Sandwich Theorem’ Will Change How You See the Universe… Seriously - https://youtu.be/uhNqEs7vDGg Read More: How a FedEx employee discovered th
From playlist Elements | Seeker
Veering from the Pattern in Mersenne Primes | #MegaFavNumbers | Pwime Numbewednesdays | Ep. 0
What's your favourite number over a million? Mine just had to be about primes: numbers that look prime, but aren't! Thanks to Prof. James Grime for motivating my first-ever YouTube video. Check out his playlist of #MegaFavNumbers. Let's go exploring! Next video: https://youtu.be/XnAzl
From playlist MegaFavNumbers
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
More resources available at www.misterwootube.com
From playlist The Nature of Proof
Frank Merle - 1/4 Comportement asymptotique des solutions de l'équation des ondes critique
Les principales questions abordées dans cette série de cours concernent l'existence locale et globale en temps, explosion en temps fini et la résolution en solitons des solutions de l'équation des ondes non linéaire énergie critique. Les lectures ne demanderont pas de pré-requis.
From playlist Frank Merle - Comportement asymptotique des solutions de
The Biggest Known Prime Number - Keith Conrad [2018]
Slides for this talk: https://ctnt-summer.math.uconn.edu/wp-content/uploads/sites/1632/2018/05/mersennetalkCTNT.pdf May 29: Keith Conrad (UConn) Title: The Biggest Known Prime Number. Abstract: There are infinitely many primes, but at any moment there is a biggest known prime. Earlier t
From playlist Number Theory
CTNT 2018 - "The Biggest Known Prime Number" by Keith Conrad
This is lecture on "The Biggest Known Prime Number", by Keith Conrad, during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2018 - Guest Lectures
Perfect Numbers and Mersenne Primes
Perfect numbers and Mersenne primes might seem like unrelated branches of math, but work by Euclid and Euler over 2000 years apart showed they are so deeply connected that a one-to-one correspondence exists between the even perfect numbers and the Mersenne primes. The existence of odd perf
From playlist Mathstars
Perfect Number Proof - Numberphile
This video follows on from: http://youtu.be/T0xKHwQH-4I More links & stuff in full description below ↓↓↓ Objectivity: https://www.youtube.com/c/objectivityvideos Mersenne Primes and Perfect Numbers, featuring Matt Parker. Matt is the author of Things to Make and Do in the Fourth Dimensio
From playlist Director's Cut on Numberphile
Perfect Numbers and Mersenne Primes - Numberphile
We are re-visiting Perfect Numbers and Mersenne Primes, this time with Matt Parker. More links & stuff in full description below ↓↓↓ Part Two of this interview at: http://youtu.be/q8n15q1v4Xo More on Prime Numbers: https://bit.ly/PrimePlaylist More on Perfect Numbers: http://bit.ly/Perfec
From playlist Matt Parker (standupmaths) on Numberphile
Squarespace (10% off): http://squarespace.com/numberphile Matt Parker on 383 and Woodall Primes. More links below. PrimeGrid: http://www.primegrid.com Centenary of Woodall Primes T-Shirt, Hoodie, and Mug: US customers - https://teespring.com/woodall-primes-US EU customers - https://teesp
From playlist Matt Parker (standupmaths) on Numberphile
Featuring Simon Singh - catch him on the latest Numberphile Podcast too... https://youtu.be/kOttzKC33Vk More links & stuff in full description below ↓↓↓ Catch the Numberphile Podcast at: http://bit.ly/Numberphile_Pod_Playlist or at https://www.numberphile.com/podcast/ More videos with Si
From playlist Simon Singh on Numberphile
Frank Merle - 4/4 Comportement asymptotique des solutions de l'équation des ondes critique
Les principales questions abordées dans cette série de cours concernent l'existence locale et globale en temps, explosion en temps fini et la résolution en solitons des solutions de l'équation des ondes non linéaire énergie critique. Les lectures ne demanderont pas de pré-requis.
From playlist Frank Merle - Comportement asymptotique des solutions de