The largest number that has a name. What is the name of the largest number in the world

Date: 06.11.2021

Back in the fourth grade, I was interested in the question: "What are the names of numbers over a billion? And why?" Since then, I have been looking for all the information on this issue for a long time and collecting it bit by bit. But with the advent of Internet access, searches have accelerated significantly. Now I present all the information I have found so that others can also answer the question: "What are the names of large and very large numbers?"

A bit of history

The southern and eastern Slavic peoples used alphabetical numbering to write numbers. Moreover, among the Russians, not all letters played the role of numbers, but only those that are in the Greek alphabet. A special "titlo" icon was placed above the letter denoting the number. At the same time, the numerical values of the letters increased in the same order in which the letters in the Greek alphabet followed (the order of the letters in the Slavic alphabet was somewhat different).

In Russia, Slavic numbering was preserved until the end of the 17th century. Under Peter I, the so-called "Arabic numbering" prevailed, which we still use today.

There were also changes in the names of the numbers. For example, until the 15th century, the number "twenty" was designated as "two ten" (two tens), but then it was shortened for a faster pronunciation. Until the 15th century, the number "forty" was denoted by the word "fourty", and in the 15th-16th centuries this word was supplanted by the word "forty", which originally meant a sack containing 40 squirrel or sable skins. There are two variants of the origin of the word "thousand": from the old name "thick one hundred" or from a modification of the Latin word centum - "one hundred".

The name "million" first appeared in Italy in 1500 and was formed by adding a magnifying suffix to the number "millet" - a thousand (that is, it meant "a large thousand"), it penetrated into the Russian language later, and before that the same meaning in in Russian it was denoted by the number "leodr". The word "billion" came into use only since the Franco-Prussian war (1871), when the French had to pay Germany an indemnity of 5,000,000,000 francs. Like “million,” the word “billion” comes from the root “thousand” with the addition of an Italian augmentation suffix. In Germany and America for some time the word "billion" meant the number 100,000,000; this explains that the word billionaire was used in America before any of the wealthy had $ 1,000,000,000. In the old (XVIII century) "Arithmetic" of Magnitsky, a table of the names of numbers is given, brought to "quadrillion" (10 ^ 24, according to the system after 6 digits). Perelman Ya.I. in the book "Entertaining arithmetic" the names of large numbers of that time are given, somewhat different from those of today: septillion (10 ^ 42), octalion (10 ^ 48), nonalion (10 ^ 54), decallion (10 ^ 60), endecalion (10 ^ 66), dodecalion (10 ^ 72) and it is written that "there are no further names".

Naming Principles and List of Large Numbers
All the names of large numbers are constructed in a rather simple way: 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 (mille) and the augmentation suffix-million. There are two main types of names for large numbers in the world:
3x + 3 system (where x is a Latin ordinal number) - this system is used in Russia, France, USA, Canada, Italy, Turkey, Brazil, Greece
and the 6x system (where x is a Latin ordinal number) - this system is the most common in the world (for example: Spain, Germany, Hungary, Portugal, Poland, Czech Republic, Sweden, Denmark, Finland). In it, the missing intermediate 6x + 3 end with the suffix -billion (from it we borrowed a billion, which is also called a billion).

The general list of numbers used in Russia is presented below:

Number	Name	Latin numeral	Increasing prefix SI	Reducing prefix SI	Practical value
10 1	ten		deca	deci-	Number of fingers on 2 hands
10 2	hundred		hecto-	centi-	About half the number of all states on Earth
10 3	thousand		kilo	Milli-	Approximate number of days in 3 years
10 6	million	unus (I)	mega-	micro-	5 times the number of drops in a 10 liter bucket of water
10 9	billion (billion)	duo (II)	giga-	nano-	Approximate population of India
10 12	trillion	tres (III)	tera-	pico	1/13 of the gross domestic product of Russia in rubles for 2003
10 15	quadrillion	quattor (IV)	peta-	femto-	1/30 parsec length in meters
10 18	quintillion	quinque (V)	ex-	atto-	1/18 of the number of grains from the legendary chess inventor award
10 21	sextillion	sex (VI)	zetta-	chain	1/6 the mass of planet Earth in tons
10 24	septillion	septem (VII)	yotta-	yokto-	The number of molecules in 37.2 liters of air
10 27	octillion	octo (VIII)	no-	sieve-	Half the mass of Jupiter in kilograms
10 30	quintillion	novem (IX)	de-	thread-	1/5 of all microorganisms on the planet
10 33	decillion	decem (X)	una-	roaring	Half the mass of the Sun in grams

The pronunciation of the numbers below is often different.

Number	Name	Latin numeral	Practical value
10 36	andecillion	undecim (XI)
10 39	duodecillion	duodecim (XII)
10 42	tredecillion	tredecim (XIII)	1/100 of the number of air molecules on Earth
10 45	quattordecillion	quattuordecim (XIV)
10 48	quindecillion	quindecim (XV)
10 51	sexdecillion	sedecim (XVI)
10 54	septemdecillion	septendecim (XVII)
10 57	octodecillion		So many elementary particles in the sun
10 60	novemdecillion
10 63	vigintillion	viginti (XX)
10 66	anvigintillion	unus et viginti (XXI)
10 69	duovigintillion	duo et viginti (XXII)
10 72	trevigintillion	tres et viginti (XXIII)
10 75	quattorvigintillion
10 78	quinvigintillion
10 81	sexvigintillion		So many elementary particles in the universe
10 84	septemwigintillion
10 87	octovigintillion
10 90	novemvigintillion
10 93	trigintillion	triginta (XXX)
10 96	antrigintillion

10 100 - googol (the number was invented by the 9-year-old nephew of the American mathematician Edward Kasner)

10 123 - quadragintillion (quadraginta, XL)

10 153 - quinquaginta, L

10,183 - sexaginta (LX)

10 213 - septuagintillion (septuaginta, LXX)

10 243 - octogintillion (octoginta, LXXX)

10 273 - nonagintillion (nonaginta, XC)

10,303 - centillion (Centum, C)

Further names can be obtained either by direct or reverse order of Latin numerals (as it is correct, it is not known):

10 306 - antcentillion or centunillion

10 309 - duocentillion or centduollion

10 312 - trecentillion or centtrillion

10 315 - quattorcentillion or centquadrillion

10 402 - tretrigintacentillion or centtretrigintillion

I believe that the second spelling option will be the most correct, since it is more consistent with the construction of numerals in Latin and avoids ambiguities (for example, in the number trecentillion, which, according to the first spelling, is 10 903 and 10 312).
Numbers further:
Some literary references:

Perelman Ya.I. "Entertaining arithmetic". - M .: Triada-Litera, 1994, pp. 134-140

Vygodsky M. Ya. "Handbook of Elementary Mathematics". - S-Pb., 1994, pp. 64-65

"Encyclopedia of Knowledge". - comp. IN AND. Korotkevich. - St. Petersburg: Owl, 2006, p. 257

"Interesting about physics and mathematics." - Library Kvant. no. 50. - M .: Nauka, 1988, p. 50

Many people are interested in questions about how large numbers are called and which number is the largest in the world. We will deal with these interesting questions in this article.

History

The southern and eastern Slavic peoples used alphabetical numbering to write numbers, and only those letters that are in the Greek alphabet. A special “titlo” icon was placed above the letter that denoted the number. The numerical values of the letters increased in the same order in which the letters followed in the Greek alphabet (in the Slavic alphabet, the order of the letters was slightly different). In Russia, Slavic numbering was preserved until the end of the 17th century, and under Peter I they switched to “Arabic numbering”, which we still use today.

The names of the numbers have changed too. So, until the 15th century, the number “twenty” was designated as “two ten” (two dozen), and then it was reduced for a faster pronunciation. Until the 15th century, the number 40 was called “fourty”, then it was supplanted by the word “forty”, originally denoting a bag containing 40 squirrel or sable skins. The name “million” appeared in Italy in 1500. It was formed by adding a magnifying suffix to the number millet (thousand). Later, this name came to the Russian language.

In the old (XVIII century) "Arithmetic" by Magnitsky, a table of the names of numbers is given, brought to "quadrillion" (10 ^ 24, according to the system after 6 digits). Perelman Ya.I. in the book "Entertaining arithmetic" the names of large numbers of that time are given, somewhat different from those of today: septillion (10 ^ 42), octalion (10 ^ 48), nonalion (10 ^ 54), decallion (10 ^ 60), endecalion (10 ^ 66), dodecalion (10 ^ 72) and it is written that "there are no further names."

Methods for constructing names of large numbers

There are 2 main ways of naming large numbers:

American system which is used in the USA, Russia, France, Canada, Italy, Turkey, Greece, Brazil. The names of large numbers are built quite simply: first comes the Latin ordinal number, and the suffix “-million” is added to it at the end. Exceptions are the number “million”, which is the name of the number thousand (mille) and the augmentation suffix “-million”. The number of zeros in a number written in the American system can be found by the formula: 3x + 3, where x is a Latin ordinal
English system most widespread in the world, it is used in Germany, Spain, Hungary, Poland, Czech Republic, Denmark, Sweden, Finland, Portugal. The names of numbers according to this system are built as follows: the suffix “-million” is added to the Latin numeral, the next number (1000 times larger) is the same Latin numeral, but the suffix “-billion” is added. The number of zeros in the number, which is written in the English system and ends with the suffix “-million”, can be found by the formula: 6x + 3, where x is a Latin ordinal number. The number of zeros in numbers ending with the suffix “-billion” can be found by the formula: 6x + 6, where x is a Latin ordinal number.

Only the word billion passed from the English system to the Russian language, which is nevertheless more correct to call it as the Americans call it - billion (since the American system of naming numbers is used in Russian).

In addition to numbers that are written in the American or English system using Latin prefixes, off-system numbers are known that have their own names without Latin prefixes.

Proper names of large numbers

Number		Latin numeral	Name	Practical value
10 1	10		ten	Number of fingers on 2 hands
10 2	100		hundred	About half the number of all states on Earth
10 3	1000		thousand	Approximate number of days in 3 years
10 6	1000 000	unus (I)	million	5 times the number of drops per 10 liter. bucket of water
10 9	1000 000 000	duo (II)	billion (billion)	Approximate population of India
10 12	1000 000 000 000	tres (III)	trillion
10 15	1000 000 000 000 000	quattor (IV)	quadrillion	1/30 parsec length in meters
10 18		quinque (V)	quintillion	1/18 of the number of grains from the legendary chess inventor award
10 21		sex (VI)	sextillion	1/6 the mass of planet Earth in tons
10 24		septem (VII)	septillion	The number of molecules in 37.2 liters of air
10 27		octo (VIII)	octillion	Half the mass of Jupiter in kilograms
10 30		novem (IX)	quintillion	1/5 of all microorganisms on the planet
10 33		decem (X)	decillion	Half the mass of the Sun in grams

Vigintillion (from Lat.viginti - twenty) - 10 63
Centillion (from Lat.centum - one hundred) - 10 303
Million (from Latin mille - thousand) - 10 3003

For numbers over a thousand, the Romans did not have their own names (all the names of numbers were further compound).

Compound names for large numbers

In addition to proper names, for numbers greater than 10 33, compound names can be obtained by combining prefixes.

Compound names for large numbers

Number	Latin numeral	Name	Practical value
10 36	undecim (XI)	andecillion
10 39	duodecim (XII)	duodecillion
10 42	tredecim (XIII)	tredecillion	1/100 of the number of air molecules on Earth
10 45	quattuordecim (XIV)	quattordecillion
10 48	quindecim (XV)	quindecillion
10 51	sedecim (XVI)	sexdecillion
10 54	septendecim (XVII)	septemdecillion
10 57		octodecillion	So many elementary particles in the sun
10 60		novemdecillion
10 63	viginti (XX)	vigintillion
10 66	unus et viginti (XXI)	anvigintillion
10 69	duo et viginti (XXII)	duovigintillion
10 72	tres et viginti (XXIII)	trevigintillion
10 75		quattorvigintillion
10 78		quinvigintillion
10 81		sexvigintillion	So many elementary particles in the universe
10 84		septemwigintillion
10 87		octovigintillion
10 90		novemvigintillion
10 93	triginta (XXX)	trigintillion
10 96		antrigintillion

10 123 - quadragintillion
10 153 - quinquagintillion
10 183 - sexagintillion
10 213 - septuagintillion
10 243 - octogintillion
10 273 - nonagintillion
10,303 - centillion

Further names can be obtained by direct or reverse order of Latin numerals (as it is not known correctly):

10 306 - antcentillion or centunillion
10 309 - duocentillion or centduollion
10 312 - trecentillion or centtrillion
10 315 - quattorcentillion or centquadrillion
10 402 - tretrigintacentillion or centtretrigintillion

The second spelling is more consistent with the construction of numbers in Latin and avoids ambiguities (for example, in the number trecentillion, which, according to the first spelling, is 10 903 and 10 312).

10 603 - ducentillion
10 903 - trecentillion
10 1203 - quadringentillion
10 1503 - quingentillion
10 1803 - Sescentillion
10 2103 - septingentillion
10 2403 - octingentillion
10 2703 - nongentillion
10 3003 - million
10 6003 - duomillion
10 9003 - tremillion
10 15003 - quinquemillion
10 308760 -ion
10 3000003 - Million
10 6000003 - duomiliamilillion

Myriad- 10 000. The name is outdated and practically not used. However, the word “myriads” is widely used, which does not mean a certain number, but an innumerable, uncountable set of something.

Googol ( English . googol) — 10 100. This number was first written by the American mathematician Edward Kasner in 1938 in the journal Scripta Mathematica in the article “New Names in Mathematics”. According to him, his 9-year-old nephew Milton Sirotta suggested the name so. This number became common knowledge thanks to the Google search engine named after him.

Asankheya(from Chinese asenci - uncountable) - 10 1 4 0. This number is found in the famous Buddhist treatise Jaina Sutra (100 BC). It is believed that this number is equal to the number of cosmic cycles required to attain nirvana.

Googolplex ( English . Googolplex) — 10 ^ 10 ^ 100. This number was also invented by Edward Kasner and his nephew, it means one with a googol of zeros.

Skuse's number (Skewes' number, Sk 1) means e to the e to the e to the 79th power, that is, e ^ e ^ e ^ 79. This number was proposed by Skewes in 1933 (Skewes. J. London Math. Soc. 8, 277-283, 1933.) in the proof of the Riemann conjecture concerning prime numbers. Later, Riel (te Riele, HJJ "On the Sign of the Difference P (x) -Li (x)." Math. Comput. 48, 323-328, 1987) reduced the Skuse number to e ^ e ^ 27/4, which is approximately 8.185 10 ^ 370. However, this number is not an integer, so it is not included in the table of large numbers.

Skewes' second number (Sk2) is equal to 10 ^ 10 ^ 10 ^ 10 ^ 3, that is, 10 ^ 10 ^ 10 ^ 1000. This number was introduced by J. Skuse in the same article to denote the number up to which the Riemann hypothesis is valid.

For very large numbers, it is inconvenient to use powers, so there are several ways to write numbers - notation by Knuth, Conway, Steinhouse, etc.

Hugo Steinhouse proposed to write large numbers inside geometric shapes (triangle, square and circle).

The mathematician Leo Moser refined Steinhouse's notation by suggesting that after the squares, draw pentagons instead of circles, then hexagons, etc. Moser also proposed a formal notation for these polygons so that numbers could be written down without drawing complex drawings.

Steinhouse came up with two new super-large numbers: Mega and Megiston. In Moser's notation, they are written as follows: Mega – 2, Megiston- 10. Leo Moser also proposed to call a polygon with the number of sides equal to mega - megagon, and also proposed the number “2 in Megagon” - 2. The last number is known as Moser's number or just like Moser.

There are numbers greater than Moser. The largest number used in mathematical proof is number Graham(Graham's number). It was first used in 1977 to prove one estimate in Ramsey's theory. This number is associated with bichromatic hypercubes and cannot be expressed without a special 64-level system of special mathematical symbols introduced by Knuth in 1976. Donald Knuth (who wrote The Art of Programming and created the TeX editor) came up with the concept of superdegree, which he proposed to write down with arrows pointing up:

In general

Graham suggested G-numbers:

The G 63 number is called the Graham number, often denoted simply G. This number is the largest known number in the world and is listed in the Guinness Book of Records.

Countless different numbers surround us every day. Surely many people wondered at least once 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, it is only necessary to add one to the number each time, and it will become more and more - this happens ad infinitum. But if you take apart the numbers that have names, you can find out what the largest number in the world is called.

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

Today there are 2 systems according to which numbers are given names - American and English. The first is fairly straightforward, while the second is the most common around the world. American allows you to give names to large numbers like this: first, the ordinal number in Latin is indicated, and then the suffix "illion" is added (the exception here is a million, meaning a thousand). This system is used by the 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 "illion", and the next (a thousand times larger) number is "plus" "illiard". For example, first comes a trillion, followed by a trillion, followed by a quadrillion, and so on.

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

Off-system numbers

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

You can start considering them 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 the innumerable. Even Dahl's dictionary will kindly provide a definition of such a number.

The next after the myriad is googol, denoting 10 to the power of 100. This name was first used in 1938 - by a mathematician from America E. Kasner, who noted that this name was invented by his nephew.

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

Even larger in comparison with the googolplex is the Skuse number (e to the e to the power of e79), proposed by Skuse in the proof of the Rimmann conjecture on primes (1933). There is another Skuse number, but it is applied when the Rimmann hypothesis is not valid. It is rather difficult to say which of them is more, 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 carry out 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 Knut - the reason for this is the connection of the number G with bichromatic hypercubes. The whip invented a superdegree, and in order to make it convenient to make her notes, he suggested using the up arrows. So we learned the name of the largest number in the world. It is worth noting that this G number got on the pages of the famous Book of Records.

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 this. 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 number naming systems 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, you need to deal with these particular 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 also has its own scientific name: the short-scale naming system for numbers. What are large numbers called in this system? So, 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 turn out to be interesting: in translation from the Latin language, the number “million” can be translated as “thousand”. 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 not be difficult 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 widespread 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 that were 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 added. How can you find out the number of zeros hidden in the number?

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

Examples of

At this stage, as an example, you 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. For example, a trillion. Therefore, considering a 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 the system numbers, there are also non-systemic numbers. Perhaps the largest number was lost among them? It's worth looking into this.

Googol. 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 the scientist Edward Kasner. A very interesting fact: the world search engine "Google" is named after a rather large number at that time - googol. And the name was invented by Kasner's young nephew.
Asankheya. This is a very interesting name, which is translated from Sanskrit as "innumerable". Its numerical value is one with 140 zeros - 10 140. The following fact will be interesting: it 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 is needed to reach nirvana. Also at that time this number was considered the largest.
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, googletaplex, googoldecaplex, etc.
Graham's number - G. This is the largest number recognized as such in the near 1980 by the Guinness Book of Records. It is significantly larger than googolplex and its derivatives. And scientists did say that the entire Universe is not able to contain the entire decimal notation of Graham's number.
Moser's number, Skuse's number. These numbers are also considered one of the largest and they are most often used when solving various hypotheses and theorems. And since these numbers cannot be written down by all 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, they will be honored to do this. An American scientist from Missouri worked on this project for a long time, his works were crowned with success. On January 25, 2012, he found the new largest number in the world, which is seventeen million digits (which is the 49th Mersenne number). Note: until that time, the largest number was found by a computer in 2008, it consisted of 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 passed 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. He had previously opened the largest numbers. This happened in 2005 and 2006. In 2008, the computer interrupted a series of victories by Curtis Cooper, but in 2012 he regained the palm and the well-deserved title of discoverer.

About the system

How does this all happen, how do scientists find the largest numbers? So, today the computer does most of the work for them. In this case, Cooper used distributed computing. What does it mean? These calculations are carried out by programs installed on computers of Internet users who voluntarily decided to take part in the study. Within the framework of this project, 14 Mersenne numbers were determined, 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 passion and desire to be a pioneer. However, there are also bonuses here: for his brainchild, Curtis Cooper received a cash prize of $ 3,000. But that's not all. The Electronic Frontiers Foundation (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 billion prime numbers. So there is no doubt that a huge number of scientists around the world are working in this direction today.

Simple conclusions

So what's 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 this search. And it is not surprising if, after a certain time, scientists will submit to us for consideration the next newly found largest number in the world. There is no doubt that this will happen as soon as possible.

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

And now, many years later, I decided to ask another question, namely: what is the largest number that has its own name? Fortunately, now there is an Internet and they can be puzzled by patient search engines that will not call my questions idiotic ;-). Actually, this is what I did, and this is what I found out as a result.

Number	Latin name	Russian prefix
1	unus	an-
2	duo	duo-
3	tres	three-
4	quattuor	quadri-
5	quinque	quinti-
6	sex	sex-
7	septem	septi-
8	octo	oct-
9	novem	non-
10	decem	deci-

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

The American system is pretty simple. All the names of large numbers are constructed as follows: at the beginning there is a Latin ordinal number, and at the end the suffix-million is added to it. An exception is the name "million" which is the name of the number one thousand (lat. mille) and the increasing suffix-million (see table). This is how 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: so: the 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, there is a trillion, and only then a quadrillion, followed by a quadrillion, etc. Thus, a quadrillion in 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 by the formula 6 x + 3 (where x is a Latin numeral) and by the formula 6 x + 6 for numbers ending in -billion.

Only the number billion (10 9) passed from the English system to the Russian language, which would still be more correct to call it as the Americans call it - a billion, since it is the American system that has been adopted in our country. 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 according to the American or English system, 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. Let me explain why. Let's see for a start how the numbers from 1 to 10 33 are called:

Name	Number
Unit	10 0
Ten	10 1
Hundred	10 2
Thousand	10 3
Million	10 6
Billion	10 9
Trillion	10 12
Quadrillion	10 15
Quintillion	10 18
Sextillion	10 21
Septillion	10 24
Octillion	10 27
Quintillion	10 30
Decillion	10 33

And so, now the question arises, what's next. What's behind the decillion? In principle, of course, 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, but we were interested in 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. centum- one hundred) and a million (from lat. mille- thousand). The Romans did not have more than a thousand of their own names for numbers (all numbers over a thousand were composite). For example, the Romans called a million (1,000,000) decies centena milia, that is, "ten hundred thousand". And now, in fact, the table:

Thus, according to such a system, the number is greater than 10 3003, which would have its own, non-compound name, it is impossible to get! But nevertheless, numbers more than a million million are known - these are the very off-system numbers. Let's finally tell you about them.

Name	Number
Myriad	10 4
Googol	10 100
Asankheya	10 140
Googolplex	10 10 100
Second Skewes number	10 10 10 1000
Mega	2 (in Moser notation)
Megiston	10 (in Moser notation)
Moser	2 (in Moser notation)
Graham's number	G 63 (in Graham notation)
Stasplex	G 100 (in Graham notation)

The smallest such number is myriad(it is even in Dahl's dictionary), which means a hundred hundred, that is, 10,000. This word, however, is outdated and is 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 things. It is believed that the word myriad came into 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. Googol was first written about in 1938 in the article "New Names in Mathematics" in the January issue of 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 a trademark and googol is a number.

In the famous Buddhist treatise of the Jaina Sutra, dating back to 100 BC, there is a number asankheya(from whale. asenci- uncountable) equal to 10 140. It is believed that this number is equal to the number of cosmic cycles required to attain nirvana.

Googolplex(eng. googolplex) is a number also invented by Kasner with his nephew and means one with a googol of zeros, that is, 10 10 100. This 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.

An even larger number than the googolplex, the 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 79th power, that is, e e e 79. Later, Riele (te Riele, H. J. J. "On the Sign of the Difference NS(x) -Li (x). " Math. Comput. 48 , 323-328, 1987) reduced the Skewes number to e e 27/4, which is approximately 8.185 10 370. It is clear that since the value of Skuse's 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 - pi, e, Avogadro's number, etc.

But it should be noted that there is a second Skuse number, which in mathematics is denoted as Sk 2, which is even greater than the first Skuse number (Sk 1). Second Skewes 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 there are in the number of degrees, the more difficult it is to understand which of the numbers is greater. For example, looking at the Skuse numbers, without special calculations, it is almost impossible to understand which of these two numbers is greater. Thus, it becomes inconvenient to use powers for very large numbers. Moreover, you can think of 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 will not fit, even in 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 wondered about 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 Steinhaus (H. Steinhaus. Mathematical Snapshots, 3rd edn. 1983), which is pretty simple. Stein House proposed to write large numbers inside geometric shapes - a triangle, a square and a circle:

Steinhaus came up with two new super-large numbers. He called the 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 required to write numbers much larger than a megiston, difficulties and inconveniences arose, since many circles had to be drawn inside one another. Moser suggested drawing not circles, but pentagons after the squares, then hexagons, and so on. He also proposed a formal notation for these polygons so that numbers could be written down without drawing complex drawings. Moser's notation looks like this:

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

But Moser is not the largest number either. The largest number ever used in mathematical proof is a limiting value known as Graham's number(Graham "s number), first used in 1977 to prove one estimate in Ramsey's 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 Knuth's notation cannot be translated into the Moser system. Therefore, we will have to explain this system as well. In principle, there is nothing complicated about it either. Donald Knuth (yes, yes, this is the same Knuth who wrote "The Art of Programming" and created the TeX editor) invented the concept of superdegree, which he proposed to write down with arrows pointing up:

In general, it looks like this:

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

The number G 63 became known as Graham number(it is often denoted simply as G). This number is the largest known number in the world and is even included in the Guinness Book of Records. Ah, here's that Graham's number is greater than Moser's.

P.S. In order to bring great benefit to all mankind and become famous for centuries, I decided to come up with 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 I made several mistakes while writing the text. I'll try to fix it now.

I made several mistakes at once by simply mentioning Avogadro's number. Firstly, several people pointed out to me that in fact 6.022 · 10 23 is the most natural number. And secondly, there is an opinion, and it seems to me correct, that Avogadro's number is not at all a number in the proper, mathematical sense of the word, since it depends on the system of units. Now it is expressed in "mole -1", but if you express it, for example, in moles or something else, it will be expressed in a completely different number, but this will not stop being Avogadro's number at all.
10,000 - darkness
100,000 - legion
1,000,000 - leodr
10,000,000 - a raven or a lie
100,000,000 - deck
Interestingly, the ancient Slavs also loved large numbers and knew how to count up to a billion. Moreover, they called such an account "small account". In some manuscripts, the authors also considered the "great score", reaching the number of 10 50. About numbers more than 10 50 it was said: "And the human mind cannot understand more than this." The names used in "small count" were carried over to "great count", but with a different meaning. So, darkness meant no longer 10,000, but a million, a legion meant darkness for those (a million million); leodr - legion of legions (10 to 24 degrees), then it was said - ten leodr, one hundred leodr, ..., and, finally, one hundred thousand leodr legion (10 to 47); leodr leodr (10 in 48) was called a raven and, finally, a deck (10 in 49).
The topic of national names for numbers can be expanded if we recall the forgotten Japanese system of naming numbers, which is very different from the English and American systems (I will not draw hieroglyphs, if someone is interested, they are):
10 0 - ichi
10 1 - jyuu
10 2 - hyaku
10 3 - sen
10 4 - man
10 8 - 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
10 44 - sai
10 48 - goku
10 52 - gougasya
10 56 - asougi
10 60 - nayuta
10 64 - fukashigi
10 68 - muryoutaisuu
Concerning 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 belongs not to Steinhaus, but to Daniil Kharms, who published this idea for nothing 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 - Watermelon, for the information that Steinhaus came up with not only the mega and megiston numbers, but also suggested another number mezzon, equal (in its notation) to "3 in a circle".
Now about the number myriad or myrioi. 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 reality, but the myriad gained fame thanks to the Greeks. Myriad was the name for 10,000, but there were no names for numbers over ten thousand. However, in the note "Psammit" (ie the calculus of sand), Archimedes showed how one can systematically construct 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's 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 10 67 (just a myriad of times more). Archimedes suggested the following names for numbers:
1 myriad = 10 4.
1 d-myriad = myriad of myriads = 10 8.
1 three-myriad = di-myriad of di-myriads = 10 16.
1 tetra-myriad = three-myriad three-myriad = 10 32.
etc.

If there are any comments -