There is no such number. Despite the fact that as you move along the number axis, prime numbers are less and less common, they will still occur until infinity.
Proving this is pretty easy. Recall that a prime number is divisible only by itself and by one, and is not divisible by any other numbers. This is equivalent to the fact that a prime number is not divisible by any other prime number less than itself (why this is so becomes clear if we recall that any natural composite number can be decomposed into a product of primes). Suppose that we have found the largest prime number N. We multiply all prime numbers from 1 to N and add 1 to the resulting product. We get the number M, which will be greater than N, and which will also be prime, because when divided by any prime number less than will give a remainder of 1. Therefore, our original assumption is wrong, and there is no largest prime number.
That is, the name of the SBPCH group is such an oxymoron, a joke for those who understand. In conclusion, I will add that the search for large prime numbers is a kind of competitive sport among supercomputers :)
Great question, it also became interesting, and here is what I found on the Tape (forgive me):
US mathematician Curtis Cooper received the largest known this moment prime numbers - the so-called 48th Mersenne number. The discovery is reported on the site of the distributed computing project GIMPS (Great Internet Mersenne Prime Search), in which the number was discovered.
Its entry in the decimal number system consists of 17,425,170 characters. For comparison, the length of the previous record holder was 12,978,189 characters. A prime number is a number that is only divisible by itself and one.
It took 39 days for a personal computer at the University of Central Missouri, where Cooper works, to test whether the new number was prime. Independent verification was carried out by three researchers at once on different machines, including a 32-core server provided by Novartis.
For Curtis Cooper new record became the third - previously, he managed to detect the largest prime numbers in 2005 and 2006. In 2008, UCLA mathematicians broke Cooper's record by discovering the aforementioned prime number, which has 12,978,189 digits.
For the previous discovery, the GIMPS project received a $100,000 EFF prize for discovering the first prime number with more than 10 million characters. The project divided the money received into small bonuses to encourage the next discoveries - for example, Cooper with the 48th Mersenne claims 3 thousand dollars.
Mersenne primes are primes of the form 2p - 1, where p is also a prime. For the new number, this figure is 57 885 161. These numbers have gained popularity due to the fact that it is convenient to apply the Lucas-Lehmer criterion of simplicity to them. So far, the infinity of the set of Mersenne primes has not been proved.
So SBHR is oh-hoo, which is understandable.
If I understood the question correctly, then you do not need the SBP, but the largest and simplest - that is, the simplest to understand.
You can give an example of the Gramm number (Although rather "Graham", but my brain itself substitutes the second "m" there): It is (relatively) easy to understand, so I'll try:
33=27. That is 33=.
33=333, i.e. 3 to the power of 27.
And yes, the number of "exponentiation" is shown not by the number of arrows, but by the number after them. This number is the height of the degrees and is called the "Tower".
It's clear?
Let's take it as the truth, which is clear. Move on. If two arrows indicated the height of this tower, then three arrows work according to the following principle:
33=333=3(333). 327. Well, how?
It's hard to imagine, but not really to understand, is it?
This is just the beginning, so let's move on.
We figured out the three arrows. Let's move on to four. Here already, as you might guess, "The tower sits on the tower, and drives the tower" The quote is not mine.
33=3(33)=3(327)=333...<327>...3. This number, by the way, is called the number g1.
By the way, if you want a little specifics, then this is a tower of triples from Earth to Mars.
But that's not the worst. The fact is that (sit down) there is a number g2, in which (guess what?) g1 arrows. Introduced? Me neither.
But there is also g3, in which, respectively, g2 arrows.
And g4.
And g5.
And g6.
We got to the heart of the Gramm number. Gramm's number is g64. Just.
And my advice to you: Do not under any circumstances try to imagine even g2, it is not far from madness.
Respect if you mastered this boring article.
"The largest prime number" - a project of journalist Kirill Ivanov and a duo of electronic musicians " Christmas decorations"(Alexander Zaitsev and Ilya Baramia), created in St. Petersburg. It all started with a viscous ambient, accompanied by which Kirill recited strange painfully childish poems. The debut album was released on the Snegiri label in 2007, general producer which, Oleg Nesterov, considered him one of the first signs of the birth of the genre "new urban poetry". The disc received many accolades from journalists who put it through the alternative hip-hop department. GQ magazine eventually gave 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 sleeping 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. Finishing his studies, Kirill realized that he was not going to stay in medicine (“I thought I would be a doctor, but the medical bureaucracy made me terribly nervous”) and left the institute, concentrating on work - he sold newspapers, worked as a loader, but eventually found himself in journalism. “Moreover, at first I took on everything in a row - I wrote to some corporate publications, I came up with “readers' letters” for money for a women's gloss, 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 printed word when he was called to television - to work as a reporter in Ilya Stogov's program "A Week in the Big City".
Even at the institute, Ivanov began to study music, joining the Acoustics of Children's Speech group: “We had only two concerts, both ended in triumph - we were kicked out of the stage. For any musician, I think this is a great success. Then the band fell apart - we could not decide what exactly we should play and how. And I, somehow by chance, came up with my own group, which consisted and to this day consists of one person. In general, it was important for me that this was a group, because the “project” sounds somehow strange.
Work on the album of the new "group" took Kirill about two years. With how and what to do, he quickly decided: “When I came up with“ SBPCH ”, I had an idea that there were no drums in the music at all, a beat. That is, for the rhythm to be set by the melody. And the recitative was supposed to “rip open” this fabric of music. I wanted to make music different from hip-hop and electronic at the same time, so that the music would have both fragility and some kind of inner power at the same time. Well, besides, there had to be some detachment in this music. It’s like she’s playing somewhere in the next room and you have to strain to hear her.”
TITLE
Let's refresh our memory school course Mathematics: A prime number is any number that is only divisible by 1 and itself. That is, 3 is a prime number (it can only be divided by 3 and 1), and 4, which is also divisible by 2, is not. There are infinitely many prime numbers, and, naturally, at every moment of time there is a certain limit, the largest prime number discovered by mathematicians.
Cyril: “It is clear that he, in fact, does not exist. But there is the largest prime number, known to mankind. And I was very interested in it. internal contradiction: on the one hand, this is a huge number, it is even difficult to imagine it, on the other hand, it is still simple, despite the prohibitive number of characters, it is divisible only by itself and by one. I understand - this is what you need. Something very large, something that is difficult to understand, and at the same time extremely simple and clear - this is mathematics. By by and large, all the most important experiences and sensations are exactly like this: powerful, complex, and at the same time simple, instantly recognizable, you can’t confuse it with anything. ”
Science does not stand still and constantly calls out every new prime number, which is the largest - this also attracted Ivanov, who decided that his 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 release of the album, the group is called: “2³²⁵⁸²⁶⁵⁷−1”. It was this number that was discovered on September 4, 2006 by American mathematicians Curtis Cooper and Stephen Boon; and before that, Kirill's group was called "2³°⁴°²⁴⁵⁷−1". Thus, the name of the group will constantly change - about once every six months.
Mikhail Ivanov, the MC of the 2H COMPANY project, introduced Kirill Ivanov to "Christmas Toys". Mikhail Fenichev, Mikhail Ilyin and Kirill worked together in a music store and independently engaged in their own creativity.
Alexander Zaitsev (“Christmas Toys”): “I have been listening to this album for more than a year at different stages. Misha Fenichev brought me discs and said: here is our friend who recorded it, listen. I listened, told Misha about my impressions, and after a few months he brought new version. I really liked that Kirill collects 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.
Cyril: “At some point, Sasha called me and said that he had listened to the record and he liked it. After that, "Toys" began to call me to perform with them - I started playing live.
As a result of the joint concert activity Ilya and Sasha from "YoI" decided to help Kirill bring the album to perfection - it turned out that the strange fleeting music makes an indelible impression on the audience. Ivanov really liked to confuse the audience: “I speak, the crowd stands silently, no one disperses, and no one claps. There was some kind of right effect - the audience did not really understand how to react to all this, they had not come across something like this before. Nervous for decency at the first performances (“I broadcast every week to a much larger audience on TV, but it was scary before the concert”), Kirill, who increasingly performed as part of 2H COMPANY, decided to undergo a real test of combat 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 unison, sang along to Konstantin Kinchev’s hit “We are Orthodox”! At that moment, I realized that we had come to the right place. No one was especially expecting us here, no one, of course, came to the "Invasion" specifically to look at us - that would be nonsense. And we have arrived. It 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 yelled the refrains.”
The next experiment was the participation of "SBPC" in the sensational collection "Wild Christmas 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 texts. It was in 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 it own album". Kirill took part in the recording of the second album "2H COMPANY", called "The Art of Caring for the AK-47", and "YoI" concentrated on his record.
Kirill recorded the main part of the material himself, guided by the advice of "YoI".
Alexander Zaitsev: “I understood that this is a rather difficult music to perceive, which needs some intervention in order to sound in full force. That's why I offered to help him record the album." Gradually, all instrumental tracks fell out of the album, and the rest of the compositions were shortened by half. There are not so many differences between the final version of Ivanov and what came out after the straightening of Sasha and Ilya, as Kirill explains: “Toys”, in general, did not change anything. They helped me with some technical things - they just understand all this better. They put the record down. And one more thing - the track "Big and Small" - we recorded together.
In some tracks they added some effects, but rather, these are technical changes. At the same time, Sasha and Ilya helped me a lot ideologically. We talked quite a lot with them about the music itself."
"Toys" wanted to get away from their traditional sound and did not add an obvious beat to the tracks of "SBPC", trying to make the sound warmer with the help of Soviet synthesizers RITM-2 and POLIVOKS. Zaitsev says this about the structure that he was afraid to break: “The main charm of the music of this album is that it is made in an absolutely non-digital way: all the music consists of street noise recorded on a voice recorder, snippets of speech, from samples of old sawed-down records, from melodies sung or played on children's musical instruments and old analog synthesizers… It has nothing of the present, it, like the lyrics, consists of memories.” Indeed, according to Cyril's plan, everything was already in place: “It sounds ridiculous, but somehow unexpectedly I come up with a certain melody - even if it contains two notes. And after a very a short time I already know exactly how it should sound. Down to every micronoise. I write everything down pretty fast too. Despite the fact that my music sounds very optional, sloppy, as if I would change a couple of noises in places and nothing will change - for me it is very clearly organized.
Of course, the album is not reduced to the “music of memories” alone, because there are also texts that emerge quite suddenly and disappear just as quickly (Ivanov is very proud of such a structure of the tracks), pronounced at great speed, but at the same time devoid of unnecessary words and constructions . Cyril: “Usually, I have some phrase that I heard somewhere or came up with myself. It seems to me that there is something important 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 15 minutes. But it is fundamentally important that these are not poems. I don’t perceive these lyrics that way and never call them that, without music they have no value for me.”
There are just as many memories in these texts as in music, if not more - according to Alexander Zaitsev, these are stories about what we have almost forgotten, but we 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 how modern lullabies could sound (if moms and dads managed to memorize them). However, Zaitsev considers the text “Dinosaur” to be one of the toughest among those that “Toys” had a chance to work with, and Kirill himself, languidly agreeing with “childishness”, clarifies: “Rather, these are stories about the reflection of an adult, about his memories of childhood and not only. Without anguish, they talk about the fact that everyone is on his own, that everyone is unhappy and always remains 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 it's the same for adults."
Publisher: Snegiri
Release date: May 2007
Number of tracks: 9
Catalog number: CIS 032-2
The duet "Christmas Toys" continues its journey into the world of new, impetuous poets - after 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 of stories about little skiers and the unfortunate a bird in an airplane turbine from the collection "Wild Christmas Toys". These are both terribly adult and childishly direct stories, uninvented and embellished, but evoking a pleasant feeling of finding something long forgotten. Touching musical minimalism, a strange way of speaking - "SBHR" is somewhere in the middle between melodic declamation and alternative hip-hop, between blank verse and diaries, between high-speed delivery of information and a gentle lullaby at bedtime.
MATHEMATICIAN
Kirill Ivanov, aka "The Biggest Prime Number", was born on August 26, 1984 in Leningrad, in one of the sleeping 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. Finishing his studies, Kirill realized that he was not going to stay in medicine (“I thought I would be a doctor, but the medical bureaucracy made me terribly nervous”) and left the institute, concentrating on work - he sold newspapers, worked as a loader, but eventually found himself in journalism. “Moreover, at first I took on everything in a row - I wrote to some corporate publications, I came up with “readers' letters” for money for a women's gloss, 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 printed word when he was called to television - to work as a reporter in Ilya Stogov's program "A Week in the Big City".
Even at the institute, Ivanov began to study music, joining the Acoustics of Children's Speech group: “We had only two concerts, both ended in triumph - we were kicked out of the stage. For any musician, I think this is a great success. Then the band fell apart - we could not decide what exactly we should play and how. And I, somehow by chance, came up with my own group, which consisted and to this day consists of one person. In general, it was important for me that this was a group, because the “project” sounds somehow strange.
Work on the album of the new "group" took Kirill about two years. With how and what to do, he quickly decided: “When I came up with“ SBPCH ”, I had an idea that there were no drums in the music at all, a beat. That is, for the rhythm to be set by the melody. And the recitative was supposed to “rip open” this fabric of music. I wanted to make music different from hip-hop and electronic at the same time, so that the music would have both fragility and some kind of inner power at the same time. Well, besides, there had to be some detachment in this music. It’s like she’s playing somewhere in the next room and you have to strain to hear her.”
TITLE
Let's refresh our memory of a school mathematics course: a prime number is any number that is divisible only by one and itself. That is, 3 is a prime number (it can only be divided by 3 and 1), and 4, which is also divisible by 2, is not. There are infinitely many prime numbers, and, naturally, at every moment of time there is a certain limit, the largest prime number discovered by mathematicians.
Cyril: “It is clear that he, in fact, does not 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 is even difficult to imagine it, on the other hand, it is still simple, despite the prohibitive number of characters, it is divisible only by itself and by one. I understand - this is what you need. Something very large, 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, you can’t confuse it with anything. ”
Science does not stand still and constantly names all the 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 Simple Number” is a spelling adopted for the convenience of others, and at the time of the release of the album, the group is called like this: “232582657?1”. It was this number that was discovered on September 4, 2006 by American mathematicians Curtis Cooper and Stephen Boon; and before that, Cyril's group was called "230402457? 1". Thus, the name of the group will constantly change - about once every six months.
MEETING
Mikhail Ivanov, the MC of the 2H COMPANY project, introduced Kirill Ivanov to "Christmas Toys". Mikhail Fenichev, Mikhail Ilyin and Kirill worked together in a music store and independently engaged in their own creativity.
Alexander Zaitsev (“Christmas Toys”): “I have been listening to this album for more than a year at different stages. Misha Fenichev brought me discs and said: here is our friend who recorded it, listen. I listened, told Misha about my impressions, and after a few months he brought a new version. I really liked that Kirill collects 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.
Cyril: “At some point, Sasha called me and said that he had listened to the record and he liked it. After that, "Toys" began to call me to perform with them - I started playing live.
As a result of the joint concert activity, Ilya and Sasha from "YoI" decided to help Kirill bring the album to his mind - it turned out that the strange fleeting music makes an indelible impression on the audience. Ivanov really liked to confuse the audience: “I speak, the crowd stands silently, no one disperses, and no one claps. There was some kind of right effect - the audience did not really understand how to react to all this, they had not come across something like this before. Nervous for decency at the first performances (“I broadcast every week to a much larger audience on TV, but it was scary before the concert”), Kirill, who increasingly performed as part of 2H COMPANY, decided to undergo a real test of combat 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 unison, sang along to Konstantin Kinchev's hit “We are Orthodox”! At that moment, I realized that we had come to the right place. No one was especially expecting us here, no one, of course, came to the "Invasion" specifically to look at us - that would be nonsense. And we have arrived. It 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 yelled the refrains.”
The next experiment was the participation of "SBPC" in the sensational collection "Wild Christmas 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 texts. It was in 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 Caring for the AK-47", and "YoI" concentrated on his record.
ALBUM
Kirill recorded the main part of the material himself, guided by the advice of "YoI".
Alexander Zaitsev: “I understood that this is a rather difficult music to perceive, which needs some intervention in order to sound in full force. That's why I offered to help him record the album." Gradually, all instrumental tracks fell out of the album, and the rest of the compositions were shortened by half. There are not so many differences between the final version of Ivanov and what came out after the straightening of Sasha and Ilya, as Kirill explains: “Toys”, in general, did not change anything. They helped me with some technical things - they just understand all this better. They put the record down. And one more thing - the track "Big and Small" - we recorded together.
In some tracks they added some effects, but rather, these are technical changes. At the same time, Sasha and Ilya helped me a lot ideologically. We talked quite a lot with them about the music itself."
"Toys" wanted to get away from their traditional sound and did not add an obvious beat to the tracks of "SBPC", trying to make the sound warmer with the help of Soviet synthesizers RITM-2 and POLIVOKS. Zaitsev says this about the structure that he was afraid to break: “The main charm of the music of this album is that it is made in an absolutely non-digital way: all the music consists of street noise recorded on a voice recorder, snippets of speech, from samples of old sawed-down records, from melodies sung or played on children's musical instruments and old analog synthesizers... There is nothing of the present in it, it, like the lyrics, consists of memories. Indeed, according to Cyril's plan, everything was already in place: “It sounds ridiculous, but somehow unexpectedly I come up with a certain melody - even if it contains 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 fast too. Despite the fact that my music sounds very optional, sloppy, as if I would change a couple of noises in places and nothing will change - for me it is very clearly organized.
Of course, the album is not reduced to the “music of memories” alone, because there are also texts that emerge quite suddenly and disappear just as quickly (Ivanov is very proud of such a structure of the tracks), pronounced at great speed, but at the same time devoid of unnecessary words and constructions . Cyril: “Usually, I have some phrase that I heard somewhere or came up with myself. It seems to me that there is something important 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 15 minutes. But it is fundamentally important that these are not poems. I don’t perceive these lyrics that way and never call them that, without music they have no value for me.”
There are just as many memories in these texts as in music, if not more - according to Alexander Zaitsev, these are stories about what we have almost forgotten, but we 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 how modern lullabies could sound (if moms and dads managed to memorize them). However, Zaitsev considers the text “Dinosaur” to be one of the toughest among those that “Toys” had a chance to work with, and Kirill himself, languidly agreeing with “childishness”, clarifies: “Rather, these are stories about the reflection of an adult, about his memories of childhood and not only. Without anguish, they talk about the fact that everyone is on his own, that everyone is unhappy and always remains 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 it's the same for adults."
Kirill Ivanov about the tracks of the album:
1. Little people
“As a child, I really liked the story about a boy who had a favorite ship model and he was sure that little people lived inside. He thought about them all the time and in the end could not stand it and broke the ship. There were no people inside. I was always sure that they just left - about this and the text. I remember when I was little, my grandmother and I often discussed that the boy should have put a small rug soaked in ink before going on deck. Then the little men, who, of course, went out only at night, would have left traces. And it’s also a text about what you shouldn’t ask.”
2. White
“When I studied medicine, I constantly went on duty at the hospital just for the sake of practice, often assisted in major operations. And then one day we operated under local anesthesia on a young drunkard who had just fallen out of a fifth-floor window. At some point, he jumped up from the operating table and tried to run away. Naked, covered in blood, with unsewn 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 fight back so actively from life, everything will still end up with something very similar. This guy just really stood out against the background of people who meekly lay with all these droppers and catheters in the wards.
3. Dinosaur
“I've never really been particularly interested in dinosaurs. But from them there is always some feeling of unhappiness. A huge misfortune - the scaly giants suddenly took and disappeared, as if they were not there. After all, this is a song about some, roughly speaking, “translation difficulties”. About why one person loves another, but they cannot be together. It's not even clear why."
4. Chewing gum, angry bears and Fedya
“I just wanted to write a lullaby. This is a conversation between father and son. After all, parents often, persuading a child to fall asleep (also a strange practice - how can you say: “sleep soon!”), 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've always liked his detachment. He, of course, someone's dog, but, in general, on his own. Thinking about something all the time. But the main thing is that he always walks with his friend. For a very long time I had a dream to have not just a friend, but one that "does not spill 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 once wrote it myself and did not know how to use it. And then the music was written, under which you can’t dance anyway. All together it sounds, it seems to me, really dreary. That's what I wanted."
7. Birthday and animals
“I wanted to write a text about the zoo, but nothing interesting happened. In addition, there are zoos in both St. Petersburg and Moscow, but different reasons- equally dull. I also wanted to write a text in which there would be real story- beginning and end. I came up with the chorus, probably, 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, of course, I didn’t count and now I don’t think that I wrote something similar - it’s impossible.”
9. Istanbul
“On December 31, 2005, I found myself completely alone in Istanbul, met New Year without friends, in some nightclub among hundreds of Turks. Then he crossed a huge bridge on foot, which, it seems, no one walks at all, not only on New Year's Day, but even on ordinary days - a 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.
American mathematicians have calculated the largest prime number (recall that such numbers are only divisible by one and themselves).
The study was carried out as part of the Great Internet Mersenne Prime Search (GIMPS) project, aimed precisely at finding new primes. This is an online project in which mathematicians from various scientific centers. They fix and check prime numbers using special software.
It would seem that a prime number is not so difficult to find, but this is the case if we are talking about, say, the number 7 or 19. But with more large numbers everything is much more complicated: for example, only by trial and error can one understand that the number 11319033 is not prime, because it can be divided by 213 and 53141. That is why complex computing systems are used for searches.
The discovery of the new number champion was made on December 26, 2017 by Jonathan Pace. The 51-year-old electrical engineer has been on the hunt for record high primes 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 more than its record-breaking predecessor, by almost a million digits.
Illustration "News. Science".
In addition, this is an anniversary, fiftieth, number from the Mersenne group of 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 over 350 years ago.
By the way, the members of this " closed club"play important role in number theory, cryptography and pseudo-random number generation. It is believed that there are an infinite number of Mersenne primes, but this has yet to be proven.
The researchers note that confirmation of the "simplicity" of the a large number took six days of continuous computing. To prove the absence of errors in the initial discovery process, the number M77232917 was checked independently by four various programs. Moreover, each check took from 34 to 82 hours.
For his discovery, Jonathan Pace will receive three thousand US dollars (171 thousand rubles at the rate of 01/10/2018).
By the way, anyone can calculate the next number champion by downloading a free program from the GIMPS website.
Recall that many Mersenne numbers are due to GIMPS specialists. As a rule, they become the most big 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 US Electronic Frontier Foundation is offering a $150,000 reward. But, in essence, what is money when it comes to the magic of numbers?
Mathematicians have named the largest prime number that has ever been determined. 17,425,170 - this is how many digits are contained in the largest prime number discovered recently by American mathematicians.
A prime number is a natural number that is only divisible by itself and one without a remainder. So, in the longest prime number, they counted 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 were carried out as part of the Great Internet Mersenne Prime Search (GIMPS), which is a large-scale voluntary computing project related to the search for Mersenne primes. The system itself is a specially designed software that runs on thousands of computers. When the largest prime number is found, a thorough check is made to confirm that the number is prime. A computer with an Intel i7 processor, for example, was tested for four and a half days, so it really was not an easy task.
The past largest prime number also could not be published in the regular edition; for comparison, a standard note on the "Details of the Worlds" has several thousand characters. Ten thousand is already a large article, a million characters will be in a book, and a billion, respectively, will be a small library of a thousand volumes. When printing in small type, the largest prime number will occupy a large bookcase, so it is unlikely that anyone will decide to transfer paper to this. You can write it to a file or use the 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 described them for the first time in the first half of the 17th century. Such numbers are used in software pseudo-random number generators - hence the interest in them not only for theoreticians, but also for practitioners. Large primes are also of interest to cryptographers, which is why the Electronic Frontier Foundation has even approved $50,000, 100,000, 150,000, and 250,000 awards for computing prime numbers with a million, ten million, one hundred million, and a billion digits, respectively.
Sophisticated simplicity
The number of prime numbers is infinite and it is easy to prove: let's take all the prime numbers already counted, multiply them together and add one. When divided 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 divisible by anything other than itself: the only problem is that it is too difficult to calculate such numbers from a certain point on, even with the help of supercomputers.
And Mersenne numbers 2N-1 differ in that they are noticeably easier to calculate and, in addition, there is a special test that allows you to quickly (compared to enumeration of all prime factors) prove their simplicity; Mersenne numbers have long since become the largest primes... but so far no one can say whether there is a largest Mersenne prime; of the entire set of such numbers, only 48 Mersenne primes are known today.
Look full version the largest number is available at www.isthe.com/chongo/tech/math/digit/m57 885161/huge-prime-c.html
