Is there a last number. Big numbers have big names

As a child, I was tormented by the question of what is the largest number, and I plagued almost everyone with this stupid question. Having learned the number one million, I asked if there was a number greater than a million. Billion? And more than a billion? Trillion? And more than a trillion? Finally, someone smart was found who explained to me that the question is stupid, since it is enough just to add one to the largest number, and it turns out that it has never been the largest, since there are even larger numbers.

And now, after many years, I decided to ask another question, namely: What is the largest number that has its own name? Fortunately, now there is an Internet and you can puzzle them with patient search engines that will not call my questions idiotic ;-). Actually, this is what I did, and here's what I found out as a result.

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

The American system is built quite simply. All titles big numbers are constructed as follows: at the beginning there is a Latin ordinal number, and at the end a 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 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 trilliard 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 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 "myriads" is widely used, which means not a certain number at all, but an innumerable, uncountable number of things. It is believed that the word myriad (English myriad) came to European languages from ancient Egypt.

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 search engine named after him. Google. Note that "Google" is trademark, and googol is a number.

In the famous Buddhist treatise Jaina Sutra, dating back to 100 BC, there is a number asankhiya(from Chinese asentzi- incalculable), equal to 10 140. It is believed that this number is equal to the number of cosmic cycles required 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 10 100. 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 primes. It means e to the extent e to the extent e to the power of 79, that is, e e e 79. Later, Riele (te Riele, H. J. J. "On the Sign of the Difference P(x)-Li(x)." Math. Comput. 48 , 323-328, 1987) reduced the Skewes number to e e 27/4 , which is approximately equal to 8.185 10 370 . 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, the Avogadro number, etc.

But it should be noted that there is a second Skewes number, which in mathematics is denoted as Sk 2 , which is even larger than the first Skewes number (Sk 1). Skuse's second number, was introduced by J. Skuse in the same article to denote the number up to which the Riemann hypothesis is valid. Sk 2 is equal to 10 10 10 10 3 , that is 10 10 10 1000 .

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 named a number Mega, and the number is 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:

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 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 number(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 a 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:

AT general view 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 G 63 began to be called 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. And, here, that the Graham number is greater than the Moser number.

P.S. In order to bring great benefit to all mankind and become famous for centuries, I decided to invent and name the largest number myself. This number will be called stasplex and it is equal to the number G 100 . Memorize it, and when your children ask what is the largest number in the world, tell them that this number is called stasplex.

Update (4.09.2003): Thanks everyone for the comments. It turned out that when writing the text, I made several mistakes. I'll try to fix it now.

1. I made several mistakes at once, just mentioning Avogadro's number. First, several people pointed out to me that 6.022 10 23 is actually the most natural number. And secondly, there is an opinion, and it seems to me true, that Avogadro's number is not a number at all in the proper, mathematical sense of the word, since it depends on the system of units. Now it is expressed in "mol -1", but if it is expressed, for example, in moles or something else, then it will be expressed in a completely different figure, but it will not stop being Avogadro's number at all.
2. 10 000 - darkness
   100,000 - legion
   1,000,000 - leodre
   10,000,000 - Raven or Raven
   100 000 000 - deck
   Interestingly, the ancient Slavs also loved large numbers, they knew how to count up to a billion. Moreover, they called such an account a “small account”. In some manuscripts, the authors also considered " great score", reaching the number 10 50. About numbers greater than 10 50 it was said: "And more than this the human mind can understand." The names used in the "small account" were transferred to the "great account", but with a different meaning. So, darkness meant no longer 10,000, but a million, legion - darkness of topics (million millions); leodr - legion of legions (10 to 24 degrees), then it was said - ten leodres, one hundred leodres, ..., and, finally, one hundred thousand legions leodrov (10 to 47); the leodr of leodrov (10 to 48) was called the raven and, finally, the deck (10 to 49).
3. The topic of national names of numbers can be expanded if we recall the forgotten by me Japanese system the names of numbers, which is very different from the English and American systems (I will not draw hieroglyphs, if anyone is interested, then they are):
   100-ichi
   10 1 - jyuu
   10 2 - hyaku
   103-sen
   104 - man
   108-oku
   10 12 - chou
   10 16 - kei
   10 20 - gai
   10 24 - jyo
   10 28 - jyou
   10 32 - kou
   10 36-kan
   10 40 - sei
   1044 - sai
   1048 - goku
   10 52 - gougasya
   10 56 - asougi
   10 60 - nayuta
   1064 - fukashigi
   10 68 - murioutaisuu
4. Regarding the numbers of Hugo Steinhaus (in Russia, for some reason, his name was translated as Hugo Steinhaus). botev assures that the idea of ​​writing super-large numbers in the form of numbers in circles does not belong to Steinhouse, but to Daniil Kharms, who, long before him, published this idea in the article "Raising the Number". I also want to thank Evgeny Sklyarevsky, the author of the most interesting site on entertaining mathematics on the Russian-language Internet - Arbuza, for the information that Steinhouse came up with not only the numbers mega and megiston, but also proposed another number mezzanine, which is (in his notation) "circled 3".
5. Now for the number myriad or myrioi. As for the origin of this number, there are different opinions. 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 ball with a diameter of a myriad of Earth diameters) no more than 10 63 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 10 67 (only a myriad of times more). The names of the numbers Archimedes suggested are as follows:
   1 myriad = 10 4 .
   1 di-myriad = myriad myriad = 10 8 .
   1 tri-myriad = di-myriad di-myriad = 10 16 .
   1 tetra-myriad = three-myriad three-myriad = 10 32 .
   etc.

If there are comments -

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 designating 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 his honor that the famous search system) - one followed by 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

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

Interesting will be the fact that this system used not only in America and Canada, but also in Russia. In addition, it also has its own scientific name: the naming system for numbers with 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 stands for 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. 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." Numeric value its - unit with 140 zeros - 10 140. 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. over this project long time an American scientist from Missouri worked, 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 today works in this direction great amount scientists around the world.

Simple Conclusions

So what is the biggest number today? On the this 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.

A child today asked: "What is the name of the largest number in the world?" The question is interesting. I got into the Internet and on the first line of Yandex I found a detailed article in LiveJournal. Everything is detailed there. It turns out that there are two systems for naming numbers: English and American. And, for example, a quadrillion according to the English and American systems are completely different numbers! The largest non-composite number is Million = 10 to the power of 3003.
As a result, the son came to a completely reasonable input that one can count indefinitely.

Original taken from ctac The largest number in the world

As a child, I was tormented by the question of what kind of
the biggest number, and I've been harassing this stupid
a question for almost everyone. Knowing the number
million, I asked if there is a number greater
million. Billion? And more than a billion? Trillion?
And more than a trillion? Finally found someone smart
who explained to me that the question is stupid, because
enough to add to
to a large number one, and it turns out that it
has never been the biggest since there exist
the number is even greater.

And now, after many years, I decided to ask myself another
question, namely: what is the most
a large number that has its own
title? Fortunately, now there is an Internet and puzzle
they can be patient search engines that do not
will call my questions idiotic ;-).
Actually, this is what I did, and this is the result
found out.

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

The American system is built quite
simply. All 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).
This is how numbers come out - trillion, quadrillion,
quintillion, sextillion, septillion, octillion,
nonillion and decillion. American system
used in USA, Canada, France and Russia.
Find out the number of zeros in a number written by
American system, you can use a simple formula
3 x+3 (where x is a Latin numeral).

English naming system most
widespread in the world. It is used, for example, in
Great Britain and Spain, as well as in most
former English and Spanish colonies. Titles
numbers in this system are built like this: like this: to
add a suffix to the Latin numeral
-million, the next number (1000 times greater)
built on the same principle
Latin numeral, but the suffix is ​​-billion.
That is, after a trillion in the English system
goes a trillion, and only then a quadrillion, for
followed by a quadrillion, and so on. So
thus, a quadrillion in English and
American systems are completely different
numbers! Find the number of zeros in a number
written in the English system and
ending with the suffix -million, you can
formula 6 x+3 (where x is a Latin numeral) and
by the formula 6 x+6 for numbers ending in
-billion.

Transferred from the English system to the Russian language
only the number billion (10 9), which is still
it would be more correct to call it what it is called
Americans - by a billion, since we have adopted
It's the American system. But who do we have
the country is doing something according to the rules! ;-) By the way,
sometimes in Russian they use the word
trillion (you can see for yourself,
running a search in Google or Yandex) and means it, judging by
everything, 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,
those. numbers that have their own
names without any Latin prefixes. Such
there are several numbers, but more about them I
I'll tell you a little later.

Let's go back to writing with the help of Latin
numerals. It would seem that they can
write numbers to infinity, but this is not
quite so. Now I will explain why. Let's see for
beginning as the numbers from 1 to 10 33 are called:

And so, now the question arises, what next. What
there for a decillion? In principle, it is possible, of course,
by combining prefixes to generate such
monsters like: andecillion, duodecillion,
tredecillion, quattordecillion, quindecillion,
sexdecillion, septemdecillion, octodecillion and
novemdecillion, but these will already be composite
names, but we were interested in
own number names. Therefore own
names according to this system, in addition to those indicated above, there are also
you can only get three
- vigintillion (from lat. viginti —
twenty), centillion (from lat. percent- one hundred) and
million (from lat. mille- one thousand). More
thousands of proper names for numbers among the Romans
was not available (all numbers over a thousand they had
composite). For example, a million (1,000,000) Romans
called centena milia, i.e. "ten hundred
thousand". And now, in fact, the table:

Thus, according to a similar system of numbers
greater than 10 3003 , which would have
get your own, non-compound name
impossible! However, more numbers
million are known - these are the very
off-system numbers. Finally, let's talk about them.

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

googol(from English googol) is the number ten in
hundredth power, that is, one followed by one hundred zeros. O
"googole" was first written in 1938 in an article
"New Names in Mathematics" in the January issue of the magazine
Scripta Mathematica American mathematician Edward Kasner
(Edward Kasner). According to him, call "googol"
a large number offered his nine year old
nephew of Milton Sirotta.
This number became well-known thanks to
named after him, a search engine Google. note that
"Google" is a trademark, and googol is a number.

In the famous Buddhist treatise Jaina Sutras,
related to 100 BC, there is a number asankhiya
(from Chinese asentzi- incalculable), equal to 10 140.
It is believed that this number is equal to the number
cosmic cycles necessary for gaining
nirvana.

Googolplex(English) googolplex) - number also
invented by Kasner with his nephew and
meaning one with a googol of zeros, i.e. 10 10 100 .
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. At the same time that he suggested "googol" he gave a
name for a still larger number: "Googolplex." A googolplex is much larger than 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 is a number
Skewes "number" was proposed by Skewes in 1933
year (Skewes. J. London Math. soc. 8 , 277-283, 1933.) at
hypothesis proof
Riemann concerning prime numbers. It
means e to the extent e to the extent e in
powers of 79, i.e. e e e 79 . 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 e e 27/4 ,
which is approximately equal to 8.185 10 370 . understandable
the point is that since the value of the Skewes number depends on
numbers e, then it is not an integer, so
we will not consider it, otherwise we would have to
recall other non-natural numbers - number
pi, e, Avogadro's number, etc.

But it should be noted that there is a second number
Skewes, which in mathematics is denoted as Sk 2,
which is even greater than the first Skewes number (Sk 1).
Skuse's second number, was introduced by J.
Skewes in the same article to denote a number, up to
which the Riemann hypothesis is valid. Sk 2
equals 10 10 10 10 3 , i.e. 10 10 10 1000
.

As you understand, the more in the number of degrees,
the more difficult it is to understand which of the numbers is larger.
For example, looking at the Skewes numbers, without
special calculations are almost impossible
figure out which of the two numbers is greater. So
Thus, for superlarge numbers, use
degrees becomes uncomfortable. Moreover, it is possible
come up with such numbers (and they have already been invented) when
degrees of degrees just don't fit on the page.
Yes, what a page! They won't fit, even in a book,
the size of the entire universe! In this case, rise
The question is how to write them down. Trouble how are you
understand is decidable, and mathematicians have developed
several principles for writing such numbers.
True, every mathematician who asked this
problem came up with his own way of recording that
led to the existence of several, unrelated
with each other, the ways to write numbers are
notations by Knuth, Conway, Steinhouse, etc.

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

Steinhouse came up with two new extra-large
numbers. He named a number Mega, and the number is Megiston.

Mathematician Leo Moser finalized the notation
Stenhouse, which was limited to what if
it was necessary to write down the numbers much more
megiston, there were difficulties and inconveniences, so
how I had to draw many circles one
inside another. Moser suggested after squares
draw not circles, but pentagons, then
hexagons and so on. He also suggested
formal notation for these polygons,
to be able to write numbers without drawing
complex drawings. Moser notation looks like this:

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

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

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

In general, it looks like this:

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

The number G 63 began to be called number
Graham(it is often denoted simply as G).
This number is the largest known in
world number and even listed in the "Book of Records
Guinness. "Ah, that Graham's number is greater than the number
Moser.

P.S. To be of great benefit
to all mankind and be glorified through the ages, I
I decided to come up with and name the biggest
number. This number will be called stasplex and
it is equal to the number G 100 . Remember it and when
your children will ask what is the biggest
world number, tell them what this number is called stasplex.

Countless various numbers surrounds 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 Skuses number (e to the power of e to the power of e79), proposed by Skuse when proving the Riemann conjecture about prime numbers(1933). There is another Skewes number, but it is used when the Rimmann hypothesis is unfair. Which of them is more difficult to say, especially when it comes to to a large extent. 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 evidence in the field mathematical science(1977).

When we are talking about 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.