What is the name of the largest number in the world. What are big numbers called?

Countless different numbers surround us every day. Surely many people at least once wondered what number is considered the largest. You can simply tell a child that this is a million, but adults are well aware that other numbers follow a million. For example, one has only to add one to the number every time, and it will become more and more - this happens ad infinitum. But if you disassemble the numbers that have names, you can find out what the largest number in the world is called.

The appearance of the names of numbers: what methods are used?

To date, there are 2 systems according to which names are given to numbers - American and English. The first is quite simple, and the second is the most common around the world. The American one allows you to give names to large numbers like this: first, the ordinal number in Latin is indicated, and then the suffix “million” is added (the exception here is a million, meaning a thousand). This system is used by Americans, French, Canadians, and it is also used in our country.

English is widely used in England and Spain. According to it, the numbers are named as follows: the numeral in Latin is “plus” with the suffix “million”, and the next (a thousand times greater) number is “plus” “billion”. For example, a trillion comes first, followed by a trillion, a quadrillion follows a quadrillion, and so on.

So, the same number in different systems can mean different things, for example, an American billion in the English system is called a billion.

Off-system numbers

In addition to numbers that are written according to known systems (given above), there are also off-system ones. They have their own names, which do not include Latin prefixes.

You can start their consideration with a number called a myriad. It is defined as one hundred hundreds (10000). But for its intended purpose, this word is not used, but is used as an indication of an innumerable multitude. Even Dahl's dictionary will kindly provide a definition of such a number.

Next after the myriad is the googol, denoting 10 to the power of 100. For the first time this name was used in 1938 by an American mathematician E. Kasner, who noted that his nephew came up with this name.

Google (search engine) got its name in honor of Google. Then 1 with a googol of zeros (1010100) is a googolplex - Kasner also came up with such a name.

Even larger than the googolplex is the Skewes number (e to the power of e to the power of e79), proposed by Skuse when proving the Riemann conjecture on prime numbers (1933). There is another Skewes number, but it is used when the Rimmann hypothesis is unfair. It is rather difficult to say which of them is greater, especially when it comes to large degrees. However, this number, despite its "enormity", cannot be considered the most-most of all those that have their own names.

And the leader among the largest numbers in the world is the Graham number (G64). It was he who was used for the first time to conduct proofs in the field of mathematical science (1977).

When it comes to such a number, you need to know that you cannot do without a special 64-level system created by Knuth - the reason for this is the connection of the number G with bichromatic hypercubes. Knuth invented the superdegree, and in order to make it convenient to record it, he suggested using the up arrows. So we learned what the largest number in the world is called. It is worth noting that this number G got into the pages of the famous Book of Records.

Sooner or later, everyone is tormented by the question, what is the largest number. A child's question can be answered in a million. What's next? Trillion. And even further? In fact, the answer to the question of what are the largest numbers is simple. It is simply worth adding one to the largest number, as it will no longer be the largest. This procedure can be continued indefinitely. Those. it turns out there is no largest number in the world? Is it infinity?

But if you ask yourself: what is the largest number that exists, and what is its own name? Now we all know...

There are two systems for naming numbers - American and English.

The American system is built quite simply. All the names of large numbers are built like this: at the beginning there is a Latin ordinal number, and at the end the suffix -million is added to it. The exception is the name "million" which is the name of the number one thousand (lat. mille) and the magnifying suffix -million (see table). So the numbers are obtained - trillion, quadrillion, quintillion, sextillion, septillion, octillion, nonillion and decillion. The American system is used in the USA, Canada, France and Russia. You can find out the number of zeros in a number written in the American system using the simple formula 3 x + 3 (where x is a Latin numeral).

The English naming system is the most common in the world. It is used, for example, in Great Britain and Spain, as well as in most of the former English and Spanish colonies. The names of numbers in this system are built like this: like this: a suffix -million is added to the Latin numeral, the next number (1000 times larger) is built according to the principle - the same Latin numeral, but the suffix is ​​-billion. That is, after a trillion in the English system comes a trillion, and only then a quadrillion, followed by a quadrillion, and so on. Thus, a quadrillion according to the English and American systems are completely different numbers! You can find out the number of zeros in a number written in the English system and ending with the suffix -million using the formula 6 x + 3 (where x is a Latin numeral) and using the formula 6 x + 6 for numbers ending in -billion.

Only the number billion (10 9) passed from the English system into the Russian language, which, nevertheless, would be more correct to call it the way the Americans call it - a billion, since we have adopted the American system. But who in our country does something according to the rules! 😉 By the way, sometimes the word trillion is also used in Russian (you can see for yourself by running a search in Google or Yandex) and it means, apparently, 1000 trillion, i.e. quadrillion.

In addition to numbers written using Latin prefixes in the American or English system, the so-called off-system numbers are also known, i.e. numbers that have their own names without any Latin prefixes. There are several such numbers, but I will talk about them in more detail a little later.

Let's go back to writing using Latin numerals. It would seem that they can write numbers to infinity, but this is not entirely true. Now I will explain why. First, let's see how the numbers from 1 to 10 33 are called:

And so, now the question arises, what next. What is a decillion? In principle, it is possible, of course, by combining prefixes to generate such monsters as: andecillion, duodecillion, tredecillion, quattordecillion, quindecillion, sexdecillion, septemdecillion, octodecillion and novemdecillion, but these will already be compound names, and we were interested in our own names numbers. Therefore, according to this system, in addition to the above, you can still get only three proper names - vigintillion (from lat. viginti- twenty), centillion (from lat. percent- one hundred) and a million (from lat. mille- one thousand). The Romans did not have more than a thousand proper names for numbers (all numbers over a thousand were composite). For example, a million (1,000,000) Romans called centena milia i.e. ten hundred thousand. And now, actually, the table:

Thus, according to a similar system, numbers greater than 10 3003, which would have its own, non-compound name, cannot be obtained! But nevertheless, numbers greater than a million are known - these are the same off-system numbers. Finally, let's talk about them.

The smallest such number is a myriad (it is even in Dahl's dictionary), which means a hundred hundreds, that is, 10,000. True, this word is outdated and practically not used, but it is curious that the word "myriad" is widely used, which does not mean a certain number at all, but an uncountable, uncountable set of something. It is believed that the word myriad (English myriad) came to European languages ​​from ancient Egypt.

There are different opinions about the origin of this number. Some believe that it originated in Egypt, while others believe that it was born only in Ancient Greece. Be that as it may, in fact, the myriad gained fame precisely thanks to the Greeks. Myriad was the name for 10,000, and there were no names for numbers over ten thousand. However, in the note "Psammit" (i.e., the calculus of sand), Archimedes showed how one can systematically build and name arbitrarily large numbers. In particular, placing 10,000 (myriad) grains of sand in a poppy seed, he finds that in the Universe (a sphere with a diameter of a myriad of Earth diameters) no more than 1063 grains of sand would fit (in our notation). It is curious that modern calculations of the number of atoms in the visible universe lead to the number 1067 (only a myriad times more). The names of the numbers Archimedes suggested are as follows:
1 myriad = 104.
1 di-myriad = myriad myriad = 108.
1 tri-myriad = di-myriad di-myriad = 1016.
1 tetra-myriad = three-myriad three-myriad = 1032.
etc.

Googol (from the English googol) is the number ten to the hundredth power, that is, one with one hundred zeros. The "googol" was first written about in 1938 in the article "New Names in Mathematics" in the January issue of the journal Scripta Mathematica by the American mathematician Edward Kasner. According to him, his nine-year-old nephew Milton Sirotta suggested calling a large number "googol". This number became well-known thanks to the Google search engine named after him. Note that "Google" is a trademark and googol is a number.

Edward Kasner.

On the Internet, you can often find mention that Google is the largest number in the world, but this is not so ...

In the well-known Buddhist treatise Jaina Sutra, dating back to 100 BC, the number Asankheya (from the Chinese. asentzi- incalculable), equal to 10 140. It is believed that this number is equal to the number of cosmic cycles necessary to gain nirvana.

Googolplex (English) googolplex) - a number also invented by Kasner with his nephew and meaning one with a googol of zeros, that is, 10 10100. Here is how Kasner himself describes this "discovery":

Words of wisdom are spoken by children at least as often as by scientists. The name "googol" was invented by a child (Dr. Kasner"s nine-year-old nephew) who was asked to think up a name for a very big number, namely, 1 with a hundred zeros after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. a googol, but is still finite, as the inventor of the name was quick to point out.

Mathematics and the Imagination(1940) by Kasner and James R. Newman.

Even more than a googolplex number, Skewes' number was proposed by Skewes in 1933 (Skewes. J. London Math. soc. 8, 277-283, 1933.) in proving the Riemann conjecture concerning prime numbers. It means e to the extent e to the extent e to the power of 79, i.e. eee79. Later, Riele (te Riele, H. J. J. "On the Sign of the Difference P(x)-Li(x)." Math. Comput. 48, 323-328, 1987) reduced Skuse's number to ee27/4, which is approximately equal to 8.185 10370. It is clear that since the value of the Skewes number depends on the number e, then it is not an integer, so we will not consider it, otherwise we would have to recall other non-natural numbers - the number pi, the number e, etc.

But it should be noted that there is a second Skewes number, which in mathematics is denoted as Sk2, which is even larger than the first Skewes number (Sk1). The second Skuse number was introduced by J. Skuse in the same article to denote a number for which the Riemann hypothesis is not valid. Sk2 is 101010103, which is 1010101000 .

As you understand, the more degrees there are, the more difficult it is to understand which of the numbers is greater. For example, looking at the Skewes numbers, without special calculations, it is almost impossible to understand which of these two numbers is larger. Thus, for superlarge numbers, it becomes inconvenient to use powers. Moreover, you can come up with such numbers (and they have already been invented) when the degrees of degrees simply do not fit on the page. Yes, what a page! They won't even fit into a book the size of the entire universe! In this case, the question arises how to write them down. The problem, as you understand, is solvable, and mathematicians have developed several principles for writing such numbers. True, every mathematician who asked this problem came up with his own way of writing, which led to the existence of several, unrelated, ways to write numbers - these are the notations of Knuth, Conway, Steinhouse, etc.

Consider the notation of Hugo Stenhaus (H. Steinhaus. Mathematical Snapshots, 3rd edn. 1983), which is quite simple. Steinhouse suggested writing large numbers inside geometric shapes - a triangle, a square and a circle:

Steinhouse came up with two new super-large numbers. He called the number - Mega, and the number - Megiston.

The mathematician Leo Moser refined Stenhouse's notation, which was limited by the fact that if it was necessary to write numbers much larger than a megiston, difficulties and inconveniences arose, since many circles had to be drawn one inside the other. Moser suggested drawing not circles after squares, but pentagons, then hexagons, and so on. He also proposed a formal notation for these polygons, so that numbers could be written without drawing complex patterns. Moser notation looks like this:

• • n[k+1] = "n in n k-gons" = n[k]n.

Thus, according to Moser's notation, Steinhouse's mega is written as 2, and megiston as 10. In addition, Leo Moser suggested calling a polygon with the number of sides equal to mega - megagon. And he proposed the number "2 in Megagon", that is, 2. This number became known as the Moser's number, or simply as a moser.

But the moser is not the largest number. The largest number ever used in a mathematical proof is the limiting value known as Graham's number, first used in 1977 in the proof of one estimate in Ramsey theory. It is associated with bichromatic hypercubes and cannot be expressed without the special 64-level system of special mathematical symbols introduced by Knuth in 1976.

Unfortunately, the number written in the Knuth notation cannot be translated into the Moser notation. Therefore, this system will also have to be explained. In principle, there is nothing complicated in it either. Donald Knuth (yes, yes, this is the same Knuth who wrote The Art of Programming and created the TeX editor) came up with the concept of superpower, which he proposed to write with arrows pointing up:

In general, it looks like this:

I think that everything is clear, so let's get back to Graham's number. Graham proposed the so-called G-numbers:

The number G63 became known as the Graham number (it is often denoted simply as G). This number is the largest known number in the world and is even listed in the Guinness Book of Records.

So there are numbers bigger than Graham's number? There is, of course, the Graham number + 1 for starters. As for the significant number… well, there are some fiendishly difficult areas of mathematics (particularly the field known as combinatorics) and computer science where numbers even larger than the Graham number occur. But we have almost reached the limit of what can be rationally and clearly explained.

sources http://ctac.livejournal.com/23807.html
http://www.uznayvse.ru/interesting-facts/samoe-bolshoe-chislo.html
http://www.vokrugsveta.ru/quiz/310/

https://masterok.livejournal.com/4481720.html

The world of science is simply amazing with its knowledge. However, even the most brilliant person in the world will not be able to comprehend them all. But you need to strive for it. That is why in this article I want to figure out what it is, the largest number.

About systems

First of all, it must be said that there are two systems for naming numbers in the world: American and English. Depending on this, the same number can be called differently, although they have the same meaning. And at the very beginning it is necessary to deal with these nuances in order to avoid uncertainty and confusion.

American system

It will be interesting that this system is used not only in America and Canada, but also in Russia. In addition, it has its own scientific name: the system of naming numbers with a short scale. How are large numbers called in this system? Well, the secret is pretty simple. At the very beginning, there will be a Latin ordinal number, after which the well-known suffix “-million” will simply be added. The following fact will be interesting: in translation from Latin, the number "million" can be translated as "thousands". The following numbers belong to the American system: a trillion is 10 12, a quintillion is 10 18, an octillion is 10 27, etc. It will also be easy to figure out how many zeros are written in the number. To do this, you need to know a simple formula: 3 * x + 3 (where "x" in the formula is a Latin numeral).

English system

However, despite the simplicity of the American system, the English system is still more common in the world, which is a system for naming numbers with a long scale. Since 1948, it has been used in countries such as France, Great Britain, Spain, as well as in countries - former colonies of England and Spain. The construction of numbers here is also quite simple: the suffix “-million” is added to the Latin designation. Further, if the number is 1000 times larger, the suffix "-billion" is already added. How can you find out the number of zeros hidden in a number?

1. If the number ends in "-million", you will need the formula 6 * x + 3 ("x" is a Latin numeral).
2. If the number ends in "-billion", you will need the formula 6 * x + 6 (where "x", again, is a Latin numeral).

Examples

At this stage, for example, we can consider how the same numbers will be called, but on a different scale.

You can easily see that the same name in different systems means different numbers. Like a trillion. Therefore, considering the number, you still need to first find out according to which system it is written.

Off-system numbers

It is worth mentioning that, in addition to system numbers, there are also off-system numbers. Maybe among them the largest number was lost? It's worth looking into this.

1. Google. This number is ten to the hundredth power, that is, one followed by one hundred zeros (10,100). This number was first mentioned back in 1938 by scientist Edward Kasner. A very interesting fact: the global search engine "Google" is named after a rather large number at that time - Google. And the name came up with Kasner's young nephew.
2. Asankhiya. This is a very interesting name, which is translated from Sanskrit as "innumerable." Its numerical value is one with 140 zeros - 10140. The following fact will be interesting: this was known to people as early as 100 BC. e., as evidenced by the entry in the Jaina Sutra, a famous Buddhist treatise. This number was considered special, because it was believed that the same number of cosmic cycles are needed to reach nirvana. Also at that time, this number was considered the largest.
3. Googolplex. This number was invented by the same Edward Kasner and his aforementioned nephew. Its numerical designation is ten to the tenth power, which, in turn, consists of the hundredth power (that is, ten to the googolplex power). The scientist also said that in this way you can get as large a number as you want: googoltetraplex, googolhexaplex, googoloctaplex, googoldekaplex, etc.
4. Graham's number is G. This is the largest number recognized as such in the recent 1980 by the Guinness Book of Records. It is significantly larger than the googolplex and its derivatives. And scientists did say that the whole Universe is not able to contain the entire decimal notation of Graham's number.
5. Moser number, Skewes number. These numbers are also considered one of the largest and they are most often used in solving various hypotheses and theorems. And since these numbers cannot be written down by generally accepted laws, each scientist does it in his own way.

Latest developments

However, it is still worth saying that there is no limit to perfection. And many scientists believed and still believe that the largest number has not yet been found. And, of course, the honor to do this will fall to them. An American scientist from Missouri worked on this project for a long time, his work was crowned with success. On January 25, 2012, he found the new largest number in the world, which consists of seventeen million digits (which is the 49th Mersenne number). Note: until that time, the largest number was the one found by the computer in 2008, it had 12 thousand digits and looked like this: 2 43112609 - 1.

Not the first time

It is worth saying that this has been confirmed by scientific researchers. This number went through three levels of verification by three scientists on different computers, which took a whopping 39 days. However, these are not the first achievements in such a search for an American scientist. Previously, he had already opened the largest numbers. This happened in 2005 and 2006. In 2008, the computer interrupted Curtis Cooper's streak of victories, but in 2012 he regained the palm and the well-deserved title of discoverer.

About the system

How does it all happen, how do scientists find the biggest numbers? So, today most of the work for them is done by a computer. In this case, Cooper used distributed computing. What does it mean? These calculations are carried out by programs installed on the computers of Internet users who have voluntarily decided to take part in the study. As part of this project, 14 Mersenne numbers were identified, named after the French mathematician (these are prime numbers that are divisible only by themselves and by one). In the form of a formula, it looks like this: M n = 2 n - 1 ("n" in this formula is a natural number).

About bonuses

A logical question may arise: what makes scientists work in this direction? So, this, of course, is the excitement and desire to be a pioneer. However, even here there are bonuses: Curtis Cooper received a cash prize of $3,000 for his brainchild. But that's not all. The Electronic Frontier Special Fund (abbreviation: EFF) encourages such searches and promises to immediately award cash prizes of $150,000 and $250,000 to those who submit 100 million and a billion prime numbers for consideration. So there is no doubt that a huge number of scientists around the world are working in this direction today.

Simple Conclusions

So what is the biggest number today? At the moment, it was found by an American scientist from the University of Missouri, Curtis Cooper, which can be written as follows: 2 57885161 - 1. Moreover, it is also the 48th number of the French mathematician Mersenne. But it is worth saying that there can be no end to these searches. And it is not surprising if, after a certain time, scientists will provide us with the next newly found largest number in the world for consideration. There is no doubt that this will happen in the very near future.

Put zeros after any number or multiply with tens raised to an arbitrarily large power. It won't seem like much. It will seem like a lot. But naked recordings, after all, are not too impressive. The heaping zeros in the humanities cause not so much surprise as a slight yawn. In any case, to any largest number in the world that you can imagine, you can always add one more ... And the number will come out even more.

And yet, are there words in Russian or any other language for denoting very large numbers? Those that are more than a million, billion, trillion, billion? And in general, a billion is how much?

It turns out that there are two systems for naming numbers. But not Arabic, Egyptian, or any other ancient civilizations, but American and English.

In the American system numbers are called like this: the Latin numeral is taken + - million (suffix). Thus, the numbers are obtained:

Trillion - 1,000,000,000,000 (12 zeros)

Quadrillion - 1,000,000,000,000,000 (15 zeros)

Quintillion - 1 and 18 zeros

Sextillion - 1 and 21 zero

Septillion - 1 and 24 zero

octillion - 1 followed by 27 zeros

Nonillion - 1 and 30 zeros

Decillion - 1 and 33 zero

The formula is simple: 3 x + 3 (x is a Latin numeral)

In theory, there should also be numbers anilion (unus in Latin - one) and duolion (duo - two), but, in my opinion, such names are not used at all.

English naming system more widespread.

Here, too, the Latin numeral is taken and the suffix -million is added to it. However, the name of the next number, which is 1,000 times greater than the previous one, is formed using the same Latin number and the suffix - billion. I mean:

Trillion - 1 and 21 zero (in the American system - sextillion!)

Trillion - 1 and 24 zeros (in the American system - septillion)

Quadrillion - 1 and 27 zeros

Quadribillion - 1 followed by 30 zeros

Quintillion - 1 and 33 zero

Quinilliard - 1 followed by 36 zeros

Sextillion - 1 followed by 39 zeros

Sextillion - 1 and 42 zero

The formulas for counting the number of zeros are:

For numbers ending in - illion - 6 x+3

For numbers ending in - billion - 6 x+6

As you can see, confusion is possible. But let's not be afraid!

In Russia, the American system for naming numbers has been adopted. From the English system, we borrowed the name of the number "billion" - 1,000,000,000 \u003d 10 9

And where is the "cherished" billion? - Why, a billion is a billion! American style. And although we use the American system, we took the "billion" from the English one.

Using the Latin names of numbers and the American system, let's call the numbers:

- vigintillion- 1 and 63 zeros

- centillion- 1 and 303 zeros

- Million- one and 3003 zeros! Oh-hoo...

But this, it turns out, is not all. There are also off-system numbers.

And the first one is probably myriad- one hundred hundreds = 10,000

googol(it is in honor of him that the famous search engine is named) - one and one hundred zeros

In one of the Buddhist treatises, a number is named asankhiya- one and one hundred and forty zeros!

Number name googolplex(like Google) was invented by the English mathematician Edward Kasner and his nine-year-old nephew - unit c - dear mother! - googol zeros!!!

But that's not all...

The mathematician Skewes named the Skewes number after himself. It means e to the extent e to the extent e to the power of 79, i.e. e e e 79

And then a big problem arose. You can think of names for numbers. But how to write them down? The number of degrees of degrees of degrees is already such that it simply does not fit on the page! :)

And then some mathematicians began to write numbers in geometric shapes. And the first, they say, such a method of recording was invented by the outstanding writer and thinker Daniil Ivanovich Kharms.

And yet, what is the BIGGEST NUMBER IN THE WORLD? - It is called STASPLEX and is equal to G 100,

where G is the Graham number, the largest number ever used in mathematical proofs.

This number - stasplex - was invented by a wonderful person, our compatriot Stas Kozlovsky, to LJ to which I address you :) - ctac

There are numbers that are so incredibly, incredibly large that it would take the entire universe to even write them down. But here's what's really maddening... some of these incomprehensibly large numbers are extremely important to understanding the world.

When I say "the largest number in the universe," I really mean the largest meaningful number, the maximum possible number that is useful in some way. There are many contenders for this title, but I warn you right away: there is indeed a risk that trying to understand all this will blow your mind. And besides, with too much math, you get little fun.

Googol and googolplex

Edward Kasner

We could start with two, very likely the biggest numbers you've ever heard of, and these are indeed the two biggest numbers that have generally accepted definitions in the English language. (There is a fairly precise nomenclature used for numbers as large as you would like, but these two numbers are not currently found in dictionaries.) Google, since it became world famous (albeit with errors, note. in fact it is googol) in the form of Google, was born in 1920 as a way to get children interested in big numbers.

To that end, Edward Kasner (pictured) took his two nephews, Milton and Edwin Sirott, on a New Jersey Palisades tour. He invited them to come up with any ideas, and then the nine-year-old Milton suggested “googol”. Where he got this word from is unknown, but Kasner decided that or a number in which one hundred zeros follow the one will henceforth be called a googol.

But young Milton didn't stop there, he came up with an even bigger number, the googolplex. It's a number, according to Milton, that has a 1 first and then as many zeros as you can write before you get tired. While the idea is fascinating, Kasner felt a more formal definition was needed. As he explained in his 1940 book Mathematics and the Imagination, Milton's definition leaves open the perilous possibility that the occasional buffoon might become a superior mathematician to Albert Einstein simply because he has more stamina.

So Kasner decided that the googolplex would be , or 1, followed by a googol of zeros. Otherwise, and in a notation similar to that with which we will deal with other numbers, we will say that the googolplex is . To show how fascinating this is, Carl Sagan once remarked that it was physically impossible to write down all the zeros of a googolplex because there simply wasn't enough room in the universe. If the entire volume of the observable universe is filled with fine dust particles approximately 1.5 microns in size, then the number of different ways in which these particles can be arranged will be approximately equal to one googolplex.

Linguistically speaking, googol and googolplex are probably the two largest significant numbers (at least in English), but, as we will now establish, there are infinitely many ways to define “significance”.

Real world

If we talk about the largest significant number, there is a reasonable argument that this really means that you need to find the largest number with a value that actually exists in the world. We can start with the current human population, which is currently around 6920 million. World GDP in 2010 was estimated to be around $61,960 billion, but both numbers are small compared to the roughly 100 trillion cells that make up the human body. Of course, none of these numbers can compare with the total number of particles in the universe, which is usually considered to be about , and this number is so large that our language does not have a word for it.

We can play around with measurement systems a bit, making the numbers bigger and bigger. Thus, the mass of the Sun in tons will be less than in pounds. A great way to do this is to use the Planck units, which are the smallest possible measures for which the laws of physics still hold. For example, the age of the universe in Planck time is about . If we go back to the first Planck time unit after the Big Bang, we see that the density of the Universe was then . We're getting more and more, but we haven't even reached a googol yet.

The largest number with any real application in the world - or, in this case, real application in the worlds - probably , is one of the latest estimates of the number of universes in the multiverse. This number is so large that the human brain will literally be unable to perceive all these different universes, since the brain is only capable of roughly configurations. In fact, this number is probably the largest number with any practical meaning, if you do not take into account the idea of ​​the multiverse as a whole. However, there are still much larger numbers lurking there. But in order to find them, we must go into the realm of pure mathematics, and there is no better place to start than prime numbers.

Mersenne primes

Part of the difficulty is coming up with a good definition of what a “meaningful” number is. One way is to think in terms of primes and composites. A prime number, as you probably remember from school mathematics, is any natural number (not equal to one) that is divisible only by itself. So, and are prime numbers, and and are composite numbers. This means that any composite number can eventually be represented by its prime divisors. In a sense, the number is more important than, say, because there is no way to express it in terms of the product of smaller numbers.

Obviously we can go a little further. , for example, is actually just , which means that in a hypothetical world where our knowledge of numbers is limited to , a mathematician can still express . But the next number is already prime, which means that the only way to express it is to directly know about its existence. This means that the largest known prime numbers play an important role, but, say, a googol - which is ultimately just a collection of numbers and , multiplied together - actually does not. And since prime numbers are mostly random, there is no known way to predict that an incredibly large number will actually be prime. To this day, discovering new prime numbers is a difficult task.

The mathematicians of ancient Greece had a concept of prime numbers at least as early as 500 BC, and 2000 years later people still only knew what prime numbers were up to about 750. Euclid's thinkers saw the possibility of simplification, but until the Renaissance mathematicians couldn't really use it in practice. These numbers are known as Mersenne numbers and are named after the 17th century French scientist Marina Mersenne. The idea is quite simple: a Mersenne number is any number of the form . So, for example, and this number is prime, the same is true for .

Mersenne primes are much faster and easier to determine than any other kind of prime, and computers have been hard at work finding them for the past six decades. Until 1952, the largest known prime number was a number—a number with digits. In the same year, it was calculated on a computer that the number is prime, and this number consists of digits, which makes it already much larger than a googol.

Computers have been on the hunt ever since, and the th Mersenne number is currently the largest prime number known to mankind. Discovered in 2008, it is a number with almost millions of digits. This is the largest known number that cannot be expressed in terms of any smaller numbers, and if you want to help find an even larger Mersenne number, you (and your computer) can always join the search at http://www.mersenne. org/.

Skewes number

Stanley Skuse

Let's go back to prime numbers. As I said before, they behave fundamentally wrong, which means that there is no way to predict what the next prime number will be. Mathematicians have been forced to turn to some rather fantastic measurements in order to come up with some way to predict future primes, even in some nebulous way. The most successful of these attempts is probably the prime number function, invented in the late 18th century by the legendary mathematician Carl Friedrich Gauss.

I'll spare you the more complicated math - anyway, we still have a lot to come - but the essence of the function is this: for any integer, it is possible to estimate how many primes there are less than . For example, if , the function predicts that there should be prime numbers, if - prime numbers less than , and if , then there are smaller numbers that are prime.

The arrangement of primes is indeed irregular, and is only an approximation of the actual number of primes. In fact, we know that there are primes less than , primes less than , and primes less than . It's a great estimate, to be sure, but it's always just an estimate... and more specifically, an estimate from above.

In all known cases up to , the function that finds the number of primes slightly exaggerates the actual number of primes less than . Mathematicians once thought that this would always be the case, ad infinitum, and that this certainly applies to some unimaginably huge numbers, but in 1914 John Edensor Littlewood proved that for some unknown, unimaginably huge number, this function will begin to produce fewer primes, and then it will switch between overestimation and underestimation an infinite number of times.

The hunt was for the starting point of the races, and that's where Stanley Skuse appeared (see photo). In 1933, he proved that the upper limit, when a function that approximates the number of primes for the first time gives a smaller value, is the number. It is difficult to truly understand, even in the most abstract sense, what this number really is, and from this point of view it was the largest number ever used in a serious mathematical proof. Since then, mathematicians have been able to reduce the upper bound to a relatively small number, but the original number has remained known as the Skewes number.

So, how big is the number that makes even the mighty googolplex dwarf? In The Penguin Dictionary of Curious and Interesting Numbers, David Wells describes one way in which the mathematician Hardy was able to make sense of the size of the Skewes number:

"Hardy thought it was 'the largest number ever to serve any particular purpose in mathematics' and suggested that if chess were played with all the particles of the universe as pieces, one move would consist of swapping two particles, and the game would stop when the same position was repeated a third time, then the number of all possible games would be equal to about the number of Skuse''.

One last thing before moving on: we talked about the smaller of the two Skewes numbers. There is another Skewes number, which the mathematician found in 1955. The first number is derived on the grounds that the so-called Riemann Hypothesis is true - a particularly difficult hypothesis in mathematics that remains unproven, very useful when it comes to prime numbers. However, if the Riemann Hypothesis is false, Skewes found that the jump start point increases to .

The problem of magnitude

Before we get to a number that makes even Skewes' number look tiny, we need to talk a little about scale because otherwise we have no way of estimating where we're going to go. Let's take a number first - it's a tiny number, so small that people can actually have an intuitive understanding of what it means. There are very few numbers that fit this description, since numbers greater than six cease to be separate numbers and become "several", "many", etc.

Now let's take , i.e. . Although we can't really intuitively, as we did for the number , figure out what , imagine what it is, it's very easy. So far everything is going well. But what happens if we go to ? This is equal to , or . We are very far from being able to imagine this value, like any other very large one - we are losing the ability to comprehend individual parts somewhere around a million. (Admittedly, it would take an insanely long time to actually count to a million of anything, but the point is that we are still able to perceive that number.)

However, although we cannot imagine, we are at least able to understand in general terms what 7600 billion is, perhaps by comparing it to something like US GDP. We have gone from intuition to representation to mere understanding, but at least we still have some gap in our understanding of what a number is. This is about to change as we move one more rung up the ladder.

To do this, we need to switch to the notation introduced by Donald Knuth, known as arrow notation. These notations can be written as . When we then go to , the number we get will be . This is equal to where the total of triplets is. We have now vastly and truly surpassed all the other numbers already mentioned. After all, even the largest of them had only three or four members in the index series. For example, even the Super Skewes number is "only" - even with the fact that both the base and the exponents are much larger than , it is still absolutely nothing compared to the size of the number tower with billions of members.

Obviously, there is no way to comprehend such huge numbers... and yet, the process by which they are created can still be understood. We could not understand the real number given by the tower of powers, which is a billion triples, but we can basically imagine such a tower with many members, and a really decent supercomputer will be able to store such towers in memory, even if it cannot calculate their real values .

It's getting more and more abstract, but it's only going to get worse. You might think that a tower of powers whose exponent length is (moreover, in a previous version of this post I made exactly that mistake), but it's just . In other words, imagine that you were able to calculate the exact value of a power tower of triples, which consists of elements, and then you took this value and created a new tower with as many in it as ... which gives .

Repeat this process with each successive number ( note starting from the right) until you do this once, and then finally you get . This is a number that is simply incredibly large, but at least the steps to get it seem to be clear if everything is done very slowly. We can no longer understand numbers or imagine the procedure by which they are obtained, but at least we can understand the basic algorithm, only in a sufficiently long time.

Now let's prepare the mind to actually blow it up.

Graham's (Graham's) number

Ronald Graham

This is how you get Graham's number, which ranks in the Guinness Book of World Records as the largest number ever used in a mathematical proof. It is absolutely impossible to imagine how big it is, and it is just as difficult to explain exactly what it is. Basically, Graham's number comes into play when dealing with hypercubes, which are theoretical geometric shapes with more than three dimensions. The mathematician Ronald Graham (see photo) wanted to find out what was the smallest number of dimensions that would keep certain properties of a hypercube stable. (Sorry for this vague explanation, but I'm sure we all need at least two math degrees to make it more accurate.)

In any case, the Graham number is an upper estimate of this minimum number of dimensions. So how big is this upper bound? Let's get back to a number so large that we can understand the algorithm for obtaining it rather vaguely. Now, instead of just jumping up one more level to , we'll count the number that has arrows between the first and last triples. Now we are far beyond even the slightest understanding of what this number is or even of what needs to be done to calculate it.

Now repeat this process times ( note at each next step, we write the number of arrows equal to the number obtained at the previous step).

This, ladies and gentlemen, is Graham's number, which is about an order of magnitude above the point of human understanding. It is a number that is so much more than any number you can imagine - it is far more than any infinity you could ever hope to imagine - it simply defies even the most abstract description.

But here's the weird thing. Since Graham's number is basically just triplets multiplied together, we know some of its properties without actually calculating it. We can't represent Graham's number in any notation we're familiar with, even if we used the entire universe to write it down, but I can give you the last twelve digits of Graham's number right now: . And that's not all: we know at least the last digits of Graham's number.

Of course, it's worth remembering that this number is only an upper bound in Graham's original problem. It is possible that the actual number of measurements required to fulfill the desired property is much, much less. In fact, since the 1980s, it has been believed by most experts in the field that there are actually only six dimensions - a number so small that we can understand it on an intuitive level. The lower bound has since been increased to , but there is still a very good chance that the solution to Graham's problem does not lie near a number as large as Graham's.

To infinity

So there are numbers bigger than Graham's number? There are, of course, for starters there is the Graham number. As for the significant number... well, there are some fiendishly difficult areas of mathematics (in particular, the area known as combinatorics) and computer science, in which there are numbers even larger than Graham's number. But we have almost reached the limit of what I can hope can ever reasonably explain. For those who are reckless enough to go even further, additional reading is offered at your own risk.

Well, now an amazing quote that is attributed to Douglas Ray ( note To be honest, it sounds pretty funny:

“I see clumps of vague numbers lurking out there in the dark, behind the little spot of light that the mind candle gives. They whisper to each other; talking about who knows what. Perhaps they do not like us very much for capturing their little brothers with our minds. Or maybe they just lead an unambiguous numerical way of life, out there, beyond our understanding.''