Learned about the Great Internet Mersenne Prime Search (GIMPS) this morning. There's just something about prime numbers, I think I'll add my computer to the search this evening.
Mersenne primes are of the form 2^p - 1, and currently the largest known prime is a Mersenne prime found by GIMPS. Exciting stuff!
#prime #PrimeNumber #mersenne #MersennePrime #math #gimps #mathematics #maths
Luke Durant hat die bislang längste #Primzahl gefunden: 2 hoch 136.279.841–1. Eine Zahl mit über 41 Mio. Dezimalstellen! Durant hat die Zahl im Rahmen des #GIMPS-Projekts entdeckt, das auf verteilte #Computerkapazitäten setzt und neuerdings vor allem #GPU mit den langwierigen Rechnungen für Primzahlen beschäftigt.
Das ZDF hat den Versuch für Kinder erklärt: https://www.zdf.de/kinder/logo/mathe-primzahl-rekord-100.html
Die VDI Nachrichten beschreiben das Ganze für Erwachsene: https://www.vdi-nachrichten.com/technik/forschung/bisher-groesste-primzahl-entdeckt-wie-gpus-dabei-halfen/
Photo: DALL-E Open Ai.
Anunciado el descubrimiento del número primo más grande conocido hasta la fecha:
2^136279841-1 = 88169432750...
Un número con más de 41 millones de dígitos en base 10.
Descubierto por el proyecto #GIMPS (Great Internet Mersenne Prime Search); un proyecto colaborativo, iniciado por George Woltman en 1996, donde cualquier persona puede dedicar tiempo de cómputo de su computadora para buscar el próximo número #primo más grande. http://www.mersenne.org
GIMPS busca números primos de tipo #Mersenne. Estos son de la forma 2^p-1, donde p es un número primo ya conocido. Por ejemplo: si tomamos p=3, que es primo, su número primo de Mersenne asociado es: 2^3-1=8-1=7.
El nuevo primo de Mersenne fue descubierto por Luke Durant, un investigador de California, y ex empleado de NVIDIA.
El 11/10 el número fue detectado como "probablemente primo" mediante un algoritmo probabilístico, conocido como "test de primalidad de #Fermat". Al día siguiente fue confirmado como primo, aplicando el test de primalidad determinístico de Lucas-Lehmer. Los cálculos fueron hechos en una #GPU NVIDIA A100 y NVIDIA H100, respectivamente.
Si bien sabemos que la cantidad de números primos es infinita, y podemos calcular muchos números primos, hasta la fecha se conocen solamente 52 números primos de tipo Mersenne, que son los que busca el proyecto GIMPS.
El anterior primo de Mersenne más grande conocido había sido descubierto hace 6 años, también en el marco del proyecto GIMPS.
Los números primos son muy relevantes en la tecnología actual de la información y la comunicación, particularmente en los algoritmos de cifrado y descifrado de mensajes.
Nota al pie: puede ocurrir que un número de Mersenne 2^p-1 no sea primo, aunque p sea primo. Por ejemplo: si bien p=11 es primo, su número de Mersenne asociado es: 2^11 − 1 = 2047 = 23 * 89, que no es primo.
GIMPS: нам нужны твои процессор и видеокарта
Приветствую всех любителей математики и больших простых чисел, а особенно - интересующихся, но ещё не погрузившихся в эту тему. Пару недель назад было найдено очередное простое число Мерсенна - и я, пользуясь тем, что это событие подогрело интерес к проектам распределённым вычислений, хочу рассказать вам подробнее, что из себя представляет Great Internet Mersenne Prime Search. И, конечно же, по возможности, убедить присоединиться. Итак, Великий Интернет-поиск Простых Чисел
https://habr.com/ru/articles/853816/
#gimps #mersenne_prime #probable_prime #распределённые_вычисления #простые_числа
Rekord der Zahlenwelt: Ein Hobby-Primzahljäger in Kalifornien hat eine neue Rekord-Primzahl entdeckt – eine Zahl mit mehr als 41 Millionen Stellen. #Primzahl #Mathematik #Mersenne #GIMPS
https://www.scinexx.de/news/technik/groesste-bekannte-primzahl-entdeckt/
Two more videos about the new largest discovered prime number from Numberphile!
"New Largest Known Prime with Matt Parker (Full Interview)": https://youtube.com/embed/oE8puWQ4taQ
"The Largest Known Prime Number - Numberphile Podcast": https://youtube.com/embed/E6iz4Vs5jcc
#MersennePrime #Math #Mathematics #GIMPS #Maths #Numberphile #PrimeNumbers
Een stukje in 720 tekens (exclusief spaties) over het nieuwe #priemgetal van 41.024.320 cijfers dat deze week werd onthuld. @nrc_nl #GIMPS #mersenneprime
https://www.nrc.nl/nieuws/2024/10/26/4102432041024320-a4870396
Wake up Fedi!! New #MersennePrime and largest discovered prime number just dropped, and it’s over 41 million digits long!! 🥳🎉
GIMPS Press Release: https://www.mersenne.org/primes/?press=M136279841
Stand-Up Maths Video: https://youtube.com/embed/zsyGRDrDfbI
When technology meets mathematics: The A100 GPU powers the discovery of the latest giant in the prime number world! 🚀💻✨🔍💡🧮💥🎉
The "new" largest prime was discovered today (October 21, 2024)! It's a Mersenne prime \( (2^p-1 )\), which is easier to find because it can utilize a specialized "faster" primality test (known as LLT, i.e., Lucas-Lehmer test). On October 11, an NVIDIA A100 GPU in Dublin, Ireland, reported that M136279841 is probably prime. On October 12, an NVIDIA H100 in San Antonio, Texas, USA, confirmed primality with a Lucas-Lehmer test.
\[\Huge 2^{136,279,841}-1\]
It took nearly 6 years for the Great Internet Mersenne Prime Search (GIMPS )software to find it after the previous largest known prime. It was also the first Mersenne prime found using GPUs.
#Prime #PrimeNumber #LargestPrime #LargestKnownPrime #MersennePrimeA100 #TensorCore #LLT #LucasLehmerTest #PrimalityTest #GPGPUs #GIMPS
https://www.mersenne.org/primes/?press=M136279841
https://www.livescience.com/physics-mathematics/mathematics/largest-known-prime-number-spanning-41-million-digits-discovered-by-amateur-mathematician-using-free-software
https://www.popularmechanics.com/science/math/a62695223/biggest-prime-number/
https://www.popsci.com/science/largest-prime-number/
https://www.smithsonianmag.com/smart-news/amateur-mathematician-discovers-the-largest-known-prime-number-with-more-than-41-million-digits-180985321/
https://www.newscientist.com/article/2452686-amateur-sleuth-finds-largest-known-prime-number-with-41-million-digits/
https://www.sciencefocus.com/news/new-prime-number
https://sherwood.news/culture/new-largest-prime-number-discovered-by-former-nvidia-software-engineer/
https://www.tomshardware.com/tech-industry/former-nvidia-engineer-discovers-41-million-digit-prime-largest-prime-number-known-to-man-was-uncovered-and-verified-with-the-help-of-gpus
https://www.washingtonpost.com/science/2024/10/23/nvidia-prime-mersenne-gpu-cloud/
https://gizmodo.com/nvidia-computer-finds-largest-known-prime-blows-past-record-by-16-million-digits-2000514948
https://fermatslibrary.com/p/6883b84b
https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test
https://en.wikipedia.org/wiki/Great_Internet_Mersenne_Prime_Search
https://en.wikipedia.org/wiki/Probable_prime
https://en.wikipedia.org/wiki/Largest_known_prime_number
I'm geeking out right now – a new #MersennePrime may have been discovered for the first time in six years!! :MOULE_Shock:
#Math #Mathematics #GIMPS #PrimeNumbers #Prime #PrimeNumber #Maths
Сорок мегабайт простоты
Привет, Хабр! Наконец-то я могу опубликовать статью, написание которой оттягивал, кажется, целую пятилетку. Ну, знаете, "можешь не писать - не пиши", да и повода особого не было... Но теперь повод появился - да ещё какой! - в свете которого не схватить перо было бы сущим престулением. Без лишних предисловий - найдено 52-ое известное простое число Мерсенна! Какое-какое число?
https://habr.com/ru/articles/850458/
#gimps #prime_numbers #mersenne_prime #136279841
The largest #PrimeNumber (so far) was discovered five years ago today!
It’s a #MersennePrime discovered by a computer used by Patrick Laroche, an IT professional from Florida, who used the #prime-finding software Prime95 to stress-test his builds. It’s part of something called #GIMPS (Great Internet Mersenne Prime Search) that anyone can participate in and maybe discover the next largest Mersenne prime!
![Excerpt from the linked article, reading:
“GIMPS Discovers Largest Known Prime Number: 2 [raised to the power of] 82,589,933-1
BLOWING ROCK, NC, December 21, 2018 -- The Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 2 [raised to the power of] 82,589,933-1, having 24,862,048 digits. A computer volunteered by Patrick Laroche made the find on December 7, 2018. Patrick is one of thousands of volunteers using free GIMPS software available at www.mersenne.org/download/.
The new prime number, also known as M82589933, is calculated by multiplying together 82,589,933 twos, and then subtracting one. It is more than one and a half million digits larger than the previous record prime number, in a special class of extremely rare prime numbers known as Mersenne primes. It is only the 51st known Mersenne prime ever discovered, each increasingly more difficult to find. Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. GIMPS, founded in 1996, has discovered the last 17 Mersenne primes. Volunteers download a free program to search for these primes, with a cash award offered to anyone lucky enough to find a new prime. Prof. Chris Caldwell maintains an authoritative web site on the largest known primes, and has an excellent history of Mersenne primes.”](https://files.mastodon.social/cache/media_attachments/files/111/538/942/510/743/188/original/6428bdfbbec2db64.jpeg)
Considering how often the system did freeze after the #RAM upgrade from #DDR4 2133 to 3200 this was deserved.
Hope all future double checks turn out to be correct after UEFI update and reset.
It is remarkable that the equation | x^2 | = 2 has no rational solution. But it has a solution in special finite fields. I think the old Pythagorean would like the result.
#MathDay #BasicResearch #gimps #ChatGPT #OESI (41/n)
Here is the way I found this sequence independent from the handbook. Order the numbers in the Galois field G(p) symmetrically to zero. One half is denoted as positive numbers, the other as negative. If a is a positive number in this field, then the equation
| x^2 | = a has always a solution if p is a Safe prime.
Details can be found in my essay, will be published if time permits it.
#MathDay #BasicResearch #gimps #ChatGPT #OESI (40/n)
p is prime and 2p+1 is also prime. I just learned from the "The Handbook of Integer Sequences" ( https://oeis.org ) these are Sophie Germain primes or Safe primes if p and (p-1)/2 are prime numbers.
#MathDay #BasicResearch #gimps #ChatGPT #OESI (39/n)
After a nearly two year break, my PC is back at number crunching for the Great Internet Mersenne Prime Search: https://www.mersenne.org/why_join/.
Concerning the added cost of electricity, it's a good trade-off between not using my heating, ever.
