What is the largest prime number in the world. What is the largest and simplest number?

American mathematicians have calculated the largest prime number (remember that such numbers are only divisible by one and themselves).

The research was carried out as part of the Great Internet Mersenne Prime Search (GIMPS) project, aimed specifically at finding new prime numbers. This is an online project in which mathematicians from various scientific centers. They record and check prime numbers using special software.

It would seem that finding a prime number is not so difficult, but this is the case if we are talking about, say, the number 7 or 19. But with more in large numbers everything is much more complicated: for example, only by trial and error can one understand that the number 11319033 is not simple, because it can be divided into 213 and 53141. That is why complex computing systems are used for searches.

The discovery of the new numbers champion was made on December 26, 2017 by Jonathan Pace. The 51-year-old electrical engineer has been hunting for record-breaking prime numbers for 14 years.

The largest prime number he discovered was named M77232917. It can be written as 2 77232917 -1 (read: two to the power of 77232917 minus one). This number is almost a million digits larger than its record-breaking predecessor.

Illustration "News.Science".

In addition, this is the anniversary, fiftieth, number from the group of Mersenne numbers. These are extremely rare prime numbers of the form M n =2 n -1, where n is natural number. The group was named after the French mathematician Marin Mersenne, who studied these numbers more than 350 years ago.

By the way, members of this “closed club” play important role in number theory, cryptography and generation pseudorandom numbers. It is believed that there are an infinite number of Mersenne primes, but this has yet to be proven.

Researchers note that confirmation of the “simplicity” of the large number took six days of continuous calculations. To prove that there were no errors in the initial discovery process, M77232917 was independently verified by four different programs. Moreover, each inspection took from 34 to 82 hours.

For his discovery, Jonathan Pace will receive three thousand US dollars (171 thousand rubles at the exchange rate as of January 10, 2018).

By the way, anyone can calculate the next number champion by downloading a free program from the GIMPS website.

Let us remind you that many Mersenne numbers are thanks to GIMPS specialists. As a rule, they become the most large numbers in the history of mathematics.

One of the main goals of the project is still to find a prime number with a hundred million digits, for which the Electronic Frontier Foundation is offering a reward of 150 thousand US dollars. But, in essence, what is money when it comes to the magic of numbers?

“The largest prime number” is a project of journalist Kirill Ivanov and the duo electronic musicians « Christmas decorations"(Alexander Zaitsev and Ilya Baramia), created in St. Petersburg. It all started with viscous ambient music, accompanied by Kirill reciting strange, painfully childish poems. The debut album was released on the Snegiri label in 2007, whose general producer, Oleg Nesterov, considered it one of the first signs of the birth of the “new urban poetry” genre. The disc received a lot of praise from journalists who took it to the department of alternative hip-hop. GQ magazine eventually awarded Kirill Ivanov the title of “Musician of the Year,” placing him on the group cover behind Valentin Yudashkin.

Kirill Ivanov was born on August 26, 1984 in Leningrad, in one of the residential areas of which he spent his childhood. He studied Latin and Ancient Greek at school, but preferred chemistry to them and entered the medical faculty of St. Petersburg State University. After finishing his studies, Kirill realized that he was not going to stay in medicine (“I thought I would be a doctor, but the medical bureaucratic machine made me terribly nervous”) and left the institute, concentrating on work - he sold newspapers, worked as a loader, but eventually found himself in journalism. “And at first I took on everything - I wrote for some corporate publications, I came up with “letters from readers” for money for a women’s glossy magazine, to which no one wanted to send letters of their own free will. For two years he worked as a correspondent and music columnist for TimeOut-Petersburg.” WITH in printed words Kirill said goodbye when he was called to television to work as a reporter on Ilya Stogov’s “Week in the City” program.

While still at the institute, Ivanov began to study music, joining the group “Acoustics of Children's Speech”: “We only had two concerts, both ended in triumph - we were kicked off the stage. For any musician, it seems to me, this is a great success. Then the group fell apart - we couldn’t decide what exactly we needed to play and how. And I, somehow by accident, came up with my own group, which consisted and still consists of one person. In general, it was important to me that this was a group, because “project” sounds somehow strange.”

Work on the album of the new “group” took Kirill about two years. He quickly decided on how and what to do: “When I came up with SBPC, I had the idea that the music would have no drums or beats at all. That is, so that the rhythm is set by the melody. And the recitative was supposed to “rip up” this fabric of music. I wanted to make music that was both hip-hop and electronic, so that the music had both fragility and some kind of inner power. Well, besides, there had to be some kind of detachment in this music. It’s as if she’s playing somewhere in the next room and you have to strain to hear her.”

NAME

Let's refresh our memory of the school mathematics course: any number that is divisible only by one and itself is called prime. That is, 3 is a prime number (it can only be divided by 3 and 1), but 4, which is also divisible by 2, is not. Prime numbers infinitely many, and, naturally, at every moment of time there is a certain limit, the largest prime number discovered by mathematicians.

Kirill: “It’s clear that he doesn’t actually exist. But there is the largest prime number, known to mankind. And I was very interested in this internal contradiction: on the one hand, this is a huge number, it’s hard to even imagine, on the other hand, it is still simple, despite the prohibitive number of characters, it is divisible only by itself and by one. I realized that this is what I need. Something very big, something that is difficult to understand, and at the same time extremely simple and clear - this is mathematics. By and large, all the most important experiences and sensations are exactly like this: powerful, complex, and at the same time simple, instantly recognizable, cannot be confused with anything.”

Science does not stand still and constantly names a new prime number, which is the largest - this also attracted Ivanov, who decided that he had new group there will be a dynamically changing name. After all, “The Biggest Prime Number” is a spelling adopted for the convenience of others, and at the time of the album’s release the group’s name was: “2³²⁵⁸²⁶⁵⁷−1.” This is exactly the number that was discovered on September 4, 2006 by American mathematicians Curtis Cooper and Stephen Boone; and before that, Kirill’s group was called “2³°⁴°²⁴⁵⁷−1”. Thus, the name of the group will constantly change - approximately every six months.

Kirill Ivanov was introduced to “Christmas Tree Toys” by Mikhail, MC of the “2H COMPANY” project. Mikhail Fenichev, Mikhail Ilyin and Kirill worked together in a music store and independently pursued their own creative work.

Alexander Zaitsev (“Christmas Tree Toys”): “I more than a year I listened to this album at different stages. Misha Fenichev brought me CDs and said: our friend recorded them, listen. I listened, told Misha about my impressions, and a few months later he brought new version. I really liked that Kirill assembles his music from random noises, that it is devoid of the slightest hint of fashion and relevance, all this was done for himself, with love, and I wanted to preserve this feeling from his music as much as possible.”

Kirill: “At some point, Sasha called me and said that he had listened to the record and liked it. After that, “Toys” began to call me to perform with them - I started playing live.”

Based on the results of the joint concert activities Ilya and Sasha from YOI decided to help Kirill bring the album to fruition - it turned out that the strange, fleeting music makes a lasting impression on the audience. Ivanov really liked to confuse the audience: “I perform, the crowd stands silently, no one disperses, and no one claps. Some true effect was produced - the audience did not really understand how to react to all this, they had never encountered anything like this before.” Having been nervous for the sake of decency at the first performances (“Every week I broadcast to a much larger audience on TV, but before the concert it was scary”), Kirill, who increasingly performed as part of the “2H COMPANY”, decided to go real check in battle and went with friends to the “Invasion 2006” festival. An unexpected triumph awaited him there: “We arrived and saw a gigantic crowd, which in one impulse was singing along to Konstantin Kinchev’s hit “We are Orthodox”! At that moment, I realized that we had arrived exactly where we needed to go. No one was particularly expecting us here; no one, of course, came to the “Invasion” specifically to look at us - that would be nonsense. And we arrived. It was probably ours best concert: first – “Toys”, then – “2H COMPANY” with me. The listeners were extremely surprised. We achieved a strange effect - the people who came to listen to the song “We are Orthodox” did not drive us off the stage. Some even shouted the choruses.”

The next experiment was the participation of “SBPC” in the acclaimed collection “Wild Christmas Tree Toys”. It was then that the general public first heard Kirill’s voice on the tracks “Snoopy” and “White”, which were also included in his debut album, but in a modified form. According to Alexander Zaitsev, these tracks turned out to be extremely important for understanding further work with Ivanov: “We wanted the record to be solid and electronic, and therefore we wrote our own music for Kirill’s lyrics. It was in the process of writing it that I realized how important the connection between Kirill’s texts and his own music, and at that moment it became approximately clear how to record his own album." Kirill took part in the recording of the second album “2H COMPANY”, called “The Art of AK-47 Care”, and “YO” concentrated on his record.

Kirill recorded the main part of the material himself, following the advice of “YOI”.

Alexander Zaitsev: “I understood that this is quite difficult music to perceive, which needs some intervention in order to sound properly full force. That’s why I offered to help him record the album.” Gradually, all instrumental tracks were dropped from the album, and the remaining compositions were shortened by half. There are not so many differences between Ivanov’s final version and what came out after straightening Sasha and Ilya, as Kirill explains: “Toys,” in general, did not change anything. They helped me with some technical things - they just understand it all better. They mixed the record. And one more thing - the track “Big and Small” - we recorded together.
They added some effects to some tracks, but these are rather technical changes. At the same time, Sasha and Ilya helped me a lot ideologically. We talked to them quite a bit about the music itself."

“Igrushki” wanted to get away from their traditional sound and did not add an obvious beat to the “SBPC” tracks, trying to make the sound warmer with the help of Soviet synthesizers RITM-2 and POLIVOX. Zaitsev says this about the structure that he was afraid to break: “The main charm of the music of this album is that it was made in a completely non-digital way: all the music consists of street noise recorded on a tape recorder, snatches of speech, samples of old recorded records, melodies sung by or played at children's musical instruments and old analog synthesizers... There is nothing modern in it, it, like the lyrics, consists of memories.” Indeed, according to Kirill’s plan, everything was already in place: “It sounds ridiculous, but somehow unexpectedly I come up with a certain melody - even if it has two notes. And after a very short time I already know exactly how it should sound. Down to every micronoise. I write everything down pretty quickly too. Despite the fact that my music sounds very unnecessary, lax, as if I would swap a couple of noises and nothing would change - for me it is very clearly organized.”

Of course, the album cannot be reduced to “music of memories” alone, because there are also texts that emerge quite suddenly and disappear just as quickly (Ivanov is very proud of this structure of tracks), pronounced at great speed, but at the same time devoid of unnecessary words and constructions . Kirill: “Usually I have some phrase spinning in my head that I heard somewhere or came up with myself. It seems to me that there is something important hidden in this phrase, it somehow resonates with me. Usually it has several meanings at once. And at some point, a critical mass of such phrases and thoughts accumulates, and I write the text very quickly - in about 15 minutes. But it is fundamentally important that these are not poems. I don’t perceive these texts that way and never call them that; without music they have no value for me.”

These texts contain as many memories as the music, if not more - according to Alexander Zaitsev, these are stories about what we have almost forgotten, but can still try to remember. He compares Ivanov's work with Proust; but Galya Chikis, another participant in the “Wild Christmas Tree Toys” project, called the album “new songs for new children.” Indeed, in the texts of “SBHR” images and intonations appear that are understandable to several generations at once - SpongeBob, Snoopy, chewing gum, going to the zoo for a birthday. This is what modern lullabies could sound like (if only moms and dads could learn them). However, Zaitsev considers the text “Dinosaur” to be one of the toughest among what “Toys” had the opportunity to work with, and Kirill himself, weakly agreeing with the “childishness”, clarifies: “Rather, these are stories about the reflection of an adult, about his memories of childhood and not only. They talk without strain about the fact that everyone is on their own, that everyone is unhappy and is always left alone with something completely unfamiliar and very big, frighteningly big. Everyone experiences exactly the same feeling in childhood - simply because of the difference in size: you are small, everyone else is big. But with adults it’s the same.”

Mathematicians have named the largest prime number ever determined. 17,425,170 - this is exactly how many digits are contained in the largest prime number recently discovered by American mathematicians.

A prime number is a natural number that is divisible only by itself and one without a remainder. So, the longest prime number has 17,425,170 digits. This number replaces the prime number discovered in 2008, which had only 12,978,189 digits.

The new number was discovered by mathematicians from the University of Central Missouri, USA. The calculations took place as part of the Great Internet Mersenne Prime Search (GIMPS) project, which is a large-scale volunteer computing project related to the search for Mersenne prime numbers. The system itself represents a specially designed software, which runs on thousands of computers. When the largest prime number is found, a thorough check is carried out to confirm that the number is prime. A computer with an Intel i7 processor, for example, took four and a half days to test, so it really was not an easy task.

The previous largest prime number also could not be published in a regular publication; for comparison, a standard note on the “Details Worlds” has several thousand characters. Ten thousand is already a big article, a million characters will be in a book, and a billion, accordingly, will be a small library of a thousand volumes. When printed in close font, the largest prime number will take up a large bookcase, so it is unlikely that anyone will decide to transfer paper to it. You can write it to a file or use an elegant notation: the record holder is exactly 257885161 - 1.

Numbers of the form 2N-1 are also called Mersenne numbers after the French researcher Marin Mersenne, who first described them in the first half of the 17th century. Such numbers are used in software pseudorandom number generators - hence the interest in them not only among theorists, but also among practitioners. Large prime numbers are also of interest to cryptography experts, so the Electronic Frontier Foundation has even approved awards of $50,000, $100,000, $150,000, and $250,000 for calculating prime numbers with a million, ten million, one hundred million, and a billion digits, respectively.

Complex Simplicity

The number of prime numbers is infinite and this is easy to prove: let’s take all the prime numbers that have already been calculated, multiply them together and add one. When we divide by any factor, by definition we get a remainder of one, so this number is not divisible by any of the previous prime numbers. And, moreover, it cannot be divided into anything else other than itself: the only problem is that calculating such numbers from a certain point is too difficult even with the help of supercomputers.

And the Mersenne numbers 2N-1 differ in that they are much easier to calculate and, in addition, there is a special test that allows you to quickly (compared to searching through all the simple factors) prove their simplicity; Mersenne numbers have long been the largest prime numbers... but so far no one can say whether the largest Mersenne prime number exists; Today, out of the entire set of such numbers, only 48 Mersenne primes are known.

Look full version the largest number can be found at www.isthe.com/chongo/tech/math/digit/m57 885161/huge-prime-c.html

Publisher: Snegiri
Release date: May 2007
Number of tracks: 9
Catalog number: CIS 032-2

The duo “Yolochnye Igrushki” continues its journey into the world of new, impetuous poets - following the second album “2H COMPANY” the debut album of the group “The Biggest Simple Number” is released, which is awaited with interest by everyone who has sunk into the soul stories about little skiers and the unfortunate a bird in an airplane turbine from the collection “Wild Christmas Tree Toys.” These are both terribly adult and childishly spontaneous stories, uninvented and embellished, but evoking a pleasant feeling of finding something long forgotten. Touching musical minimalism, strange manner speaking - “SBHR” is somewhere in the middle between melodic recitation and alternative hip-hop, between blank verse and diaries, between high-speed delivery of information and a gentle lullaby before bed.

MATHEMATICIAN

Kirill Ivanov, aka “The Biggest Prime Number,” was born on August 26, 1984 in Leningrad, in one of the residential areas of which he spent his childhood. He studied Latin and Ancient Greek at school, but preferred chemistry to them and entered the medical faculty of St. Petersburg State University. After finishing his studies, Kirill realized that he was not going to stay in medicine (“I thought I would be a doctor, but the medical bureaucratic machine made me terribly nervous”) and left the institute, concentrating on work - he sold newspapers, worked as a loader, but eventually found himself in journalism. “And at first I took on everything - I wrote for some corporate publications, I came up with “letters from readers” for money for a women’s glossy magazine, to which no one wanted to send letters of their own free will. For two years he worked as a correspondent and music columnist for TimeOut-Petersburg.” Kirill said goodbye to the written word when he was called to television to work as a reporter in Ilya Stogov’s program “A Week in the City.”

NAME

Let's refresh our memory of the school mathematics course: any number that is divisible only by one and itself is called prime. That is, 3 is a prime number (it can only be divided by 3 and 1), but 4, which is also divisible by 2, is not. There are an infinite number of prime numbers, and, naturally, at every moment of time there is a certain limit, the largest prime number discovered by mathematicians.

Kirill: “It’s clear that he doesn’t actually exist. But there is the largest prime number known to mankind. And I was very interested in this internal contradiction: on the one hand, this is a huge number, it’s hard to even imagine, on the other hand, it is still simple, despite the prohibitive number of signs, it is divisible only by itself and by one. I realized that this is what I need. Something very big, something that is difficult to understand, and at the same time extremely simple and clear - this is mathematics. By and large, all the most important experiences and sensations are exactly like this: powerful, complex, and at the same time simple, instantly recognizable, cannot be confused with anything.”

Science does not stand still and constantly names a new prime number, which is the largest - this also attracted Ivanov, who decided that his new group would have a dynamically changing name. After all, “The Biggest Prime Number” is a spelling adopted for the convenience of others, and at the time of the album’s release the group’s name was: “232582657?1”. This is exactly the number that was discovered on September 4, 2006 by American mathematicians Curtis Cooper and Stephen Boone; and before that, Kirill’s group was called “230402457?1”. Thus, the name of the group will constantly change - approximately every six months.

MEETING

Alexander Zaitsev (“Christmas Tree Toys”): “I listened to this album at different stages for more than a year. Misha Fenichev brought me CDs and said: our friend recorded them, listen. I listened, told Misha about my impressions, and a few months later he brought a new version. I really liked that Kirill assembles his music from random noises, that it is devoid of the slightest hint of fashion and relevance, all this was done for himself, with love, and I wanted to preserve this feeling from his music as much as possible.”

Kirill: “At some point, Sasha called me and said that he had listened to the record and liked it. After that, “Toys” began to call me to perform with them - I started playing live.”

Based on the results of their joint concert activities, Ilya and Sasha from YOI decided to help Kirill bring the album to fruition - it turned out that the strange, fleeting music makes a lasting impression on the audience. Ivanov really liked to confuse the audience: “I perform, the crowd stands silently, no one disperses, and no one claps. Some true effect was produced - the audience did not really understand how to react to all this, they had never encountered anything like this before.” Having been nervous for the sake of decency at the first performances (“Every week I broadcast to a much larger audience on TV, but before the concert I was scared”), Kirill, who increasingly performed as part of the 2H COMPANY, decided to undergo a real test in battle and went with his friends to the festival "Invasion 2006". An unexpected triumph awaited him there: “We arrived and saw a gigantic crowd, which in one impulse was singing along to Konstantin Kinchev’s hit “We are Orthodox”! At that moment, I realized that we had arrived exactly where we needed to go. No one was particularly expecting us here; no one, of course, came to the “Invasion” specifically to look at us - that would be nonsense. And we arrived. This was probably our best concert: first – “Toys”, then – “2H COMPANY” with me. The listeners were extremely surprised. We achieved a strange effect - the people who came to listen to the song “We are Orthodox” did not drive us off the stage. Some even shouted the choruses.”

The next experiment was the participation of “SBPC” in the acclaimed collection “Wild Christmas Tree Toys”. It was then that the general public first heard Kirill’s voice on the tracks “Snoopy” and “White”, which were also included in his debut album, but in a modified form. According to Alexander Zaitsev, these tracks turned out to be extremely important for understanding further work with Ivanov: “We wanted the record to be solid and electronic, and therefore we wrote our own music for Kirill’s lyrics. It was during the process of writing it that I realized how important the connection between Kirill’s lyrics and his own music is, and at that moment it became approximately clear how to record his own album.” Kirill took part in the recording of the second album “2H COMPANY”, called “The Art of AK-47 Care”, and “YO” concentrated on his record.

ALBUM

Kirill recorded the main part of the material himself, following the advice of “YOI”.

Alexander Zaitsev: “I understood that this is quite difficult music to perceive, which needs some intervention in order to sound at full strength. That’s why I offered to help him record the album.” Gradually, all instrumental tracks were dropped from the album, and the remaining compositions were shortened by half. There are not so many differences between Ivanov’s final version and what came out after straightening Sasha and Ilya, as Kirill explains: “Toys,” in general, did not change anything. They helped me with some technical things - they just understand it all better. They mixed the record. And one more thing - the track “Big and Small” - we recorded together.
They added some effects to some tracks, but these are rather technical changes. At the same time, Sasha and Ilya helped me a lot ideologically. We talked to them quite a bit about the music itself."

“Igrushki” wanted to get away from their traditional sound and did not add an obvious beat to the “SBPC” tracks, trying to make the sound warmer with the help of Soviet synthesizers RITM-2 and POLIVOX. Zaitsev says this about the structure that he was afraid to break: “The main charm of the music of this album is that it was made in a completely non-digital way: all the music consists of street noise recorded on a tape recorder, snatches of speech, samples of old recorded records, melodies sung by or played on children’s musical instruments and old analog synthesizers... There is nothing modern in it, it, like the lyrics, consists of memories.” Indeed, according to Kirill’s plan, everything was already in place: “It sounds ridiculous, but somehow unexpectedly I come up with a certain melody - even if it has two notes. And after a very short time I already know exactly how it should sound. Down to every micronoise. I write everything down pretty quickly too. Despite the fact that my music sounds very unnecessary, lax, as if I would swap a couple of noises and nothing would change - for me it is very clearly organized.”

Kirill Ivanov about the album tracks:

1. Little people
“As a child, I really liked the story about a boy who had a favorite model of a ship and was sure that little people lived inside. He thought about them all the time and finally could not stand it and broke the ship. There were no people inside. I was always sure that they just left - that’s what the text says. I remember when I was little, my grandmother and I often discussed that the boy should put a small rug soaked in ink before going on deck. Then the little men, who, of course, only came out at night, would have left traces. And this is also a text about what you shouldn’t wonder about.”

2. White
“When I was studying medicine, I constantly went on duty at the hospital just for the sake of practice, often assisting in large operations. And then one day we operated under local anesthesia on a young drunkard who had just fallen from a fifth-floor window. At some point, he jumped up from the operating table and tried to run away. Naked, covered in blood, with unsutured wounds, he ran around the building, and I followed him. Eventually the guards came and calmed him down. Then I thought that even if you actively fight back from life, everything will still end in something very similar. This guy simply stood out from the background of people who lay meekly with all these IVs and catheters in the wards.”

3. Dinosaur
“I really was never particularly interested in dinosaurs. But there is always some feeling of unhappiness from them. A huge misfortune - the scaly giants suddenly disappeared and disappeared, as if they had never existed. This is a song about some, roughly speaking, “difficulties in translation.” About why one person loves another, but they cannot be together. It’s not even clear why.”

4. Chewing gums, angry bears and Fedya
“I just wanted to write a lullaby. This is a conversation between a father and son. Parents, after all, often, persuading a child to fall asleep (also a strange practice - how can you say: “go to sleep quickly!”), promise that as soon as he wakes up, something amazing awaits him.”

5. Snoopy
“I never had any kind of Snoopy cult, but I certainly knew about it. I always liked his detachment. He is, of course, someone's dog, but, in general, he is on his own. He thinks about something of his own all the time. But the main thing is that he always goes with his friend. For a very long time I had a dream to have not just a friend, but someone who would “do not spill the water.” This song is about this feeling of kinship, some kind of community.”

6. Ikea
“The text of this song was written by my friend, film critic Vasily Stepanov. The phrase “please don’t dance!” I somehow composed it myself and still didn’t know how to use it. And then music was written that you can’t dance to anyway. All together this sounds, it seems to me, truly depressing. That's what I wanted."

7. Birthday and animals
“I wanted to write a text about the zoo, but nothing interesting came out. In addition, there are zoos in both St. Petersburg and Moscow, but - for different reasons - they are equally dull. I also wanted to write a text that would real story- with a beginning and an end. I probably came up with the chorus only two years later.”

8. Big and small
“I really wanted to write a song about the war. I often sing the song " Dark night"to different children, like a lullaby. And I, of course, didn’t count on it and now I don’t think I wrote something similar - it’s impossible.”

9. Istanbul
“On December 31, 2005, I found myself completely alone in Istanbul, meeting New Year without friends, in some nightclub among hundreds of Turks. Then I crossed a huge bridge on foot, which, it seems, no one walks at all, not on New Year’s, but even on ordinary days - the bridge between Europe and Asia. And indeed there was a ferry and a little girl - one might say, the only one with whom I spoke during my entire stay in Istanbul.”