The largest in value. The largest number in the world
home Answering such a difficult question, what is it, the most big number in the world, first it should be noted that today there are 2 accepted ways of naming numbers - English and American. According to the English system, the suffixes -billion or -million are added to each large number in order, resulting in the numbers million, billion, trillion, trillion, and so on. If we proceed from the American system, then according to it, the suffix -million must be added to each large number, resulting in the formation of the numbers trillion, quadrillion and large ones. It should also be noted here that the English number system is more common in modern world
, and the numbers in it are quite sufficient for the normal functioning of all systems of our world.
Of course, the answer to the question about the largest number from a logical point of view cannot be unambiguous, because if you just add one to each subsequent digit, you get a new larger number, therefore, this process has no limit. However, oddly enough, there is still the largest number in the world and it is listed in the Guinness Book of Records.
Graham's number is the largest number in the world – 0322234872396701848518 64390591045756272 62464195387.
It is this number that is recognized in the world as the largest in the Book of Records, but it is very difficult to explain what it is and how large it is. In a general sense, these are triplets multiplied together, resulting in a number that is 64 orders of magnitude higher than the point of understanding of each person. As a result, we can only give the final 50 digits of Graham's number 
this number does not, however, it is sometimes used in mathematics to express infinity. 
This number was also invented by mathematician Edward Kasner and his nephew Milton Sirotta. In a general sense, it represents a number to the tenth power of a googol. Answering the question of many inquisitive people, how many zeros are in the Googleplex, it is worth noting that in the classical version there is no way to represent this number, even if you cover all the paper on the planet with classical zeros.
Skewes number 
Another contender for the title of largest number is the Skewes number, proven by John Littwood in 1914. According to the evidence given, this number is approximately 8.185 10370.
Moser number 
This method of naming very large numbers was invented by Hugo Steinhaus, who proposed denoting them by polygons. As a result of three mathematical operations performed, the number 2 is born in a megagon (a polygon with mega sides).
As you can already notice, great amount mathematicians have made efforts to find it - the largest number in the world. The extent to which these attempts were successful, of course, is not for us to judge, however, it must be noted that the real applicability of such numbers is doubtful, because they are not even amenable to human understanding. In addition, there will always be a number that will be greater if you perform a very simple mathematical operation +1.
Back in the fourth grade, I was interested in the question: “What are numbers greater than a billion called? 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, searching has accelerated significantly. Now I present all the information I found so that others can answer the question: “What are the names of large and very big numbers?".
A little history
Southern and eastern Slavic peoples Alphabetical numbering was used to record numbers. Moreover, for the Russians, not all letters played the role of numbers, but only those that are in the Greek alphabet. A special “title” icon was placed above the letter indicating the number. At the same time, the numerical values of the letters increased in the same order as the letters in the Greek alphabet (the order of the letters of the Slavic alphabet was slightly 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 numbers. For example, until the 15th century, the number "twenty" was written as "two tens" (two tens), but was then shortened for faster pronunciation. Until the 15th century, the number "forty" was denoted by the word "fourty", and in the 15th-16th centuries this word was replaced by the word "forty", which originally meant a bag in which 40 squirrel or sable skins were placed. There are two options about the origin of the word “thousand”: from the old name “thick hundred” or from a modification of the Latin word centum - “hundred”.
The name “million” first appeared in Italy in 1500 and was formed by adding an augmentative suffix to the number “mille” - a thousand (i.e., it meant “big thousand”), it penetrated into the Russian language later, and before that the same meaning in in Russian it was designated 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 magnifying 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 rich people had $1,000,000,000. In the ancient (18th century) “Arithmetic” of Magnitsky, a table of the names of numbers is given, brought to the “quadrillion” (10^24, according to the system through 6 digits). Perelman Ya.I. in the book "Entertaining Arithmetic" the names of large numbers of that time are given, slightly different from today's: septillion (10^42), octalion (10^48), nonalion (10^54), decalion (10^60), endecalion (10^ 66), dodecalion (10^72) and it is written that “there are no further names.”
Principles for constructing names and a list of large numbers
All names of large numbers are constructed in a fairly simple way: 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 thousand (mille) and the augmentative suffix -million. There are two main types of names for large numbers in the world:
system 3x+3 (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 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 billion, which is also called billion).
Below is a general list of numbers used in Russia:
| Number | Name | Latin numeral | Magnifying attachment SI | Diminishing prefix SI | Practical significance |
| 10 1 | ten | deca- | deci- | Number of fingers on 2 hands | |
| 10 2 | one 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- | Estimated Population of India |
| 10 12 | trillion | tres (III) | tera- | pico- | 1/13 of Russia's gross domestic product in rubles for 2003 |
| 10 15 | quadrillion | quattor (IV) | peta- | femto- | 1/30 of the length of a parsec in meters |
| 10 18 | quintillion | quinque (V) | exa- | atto- | 1/18th of the number of grains from the legendary award to the inventor of chess |
| 10 21 | sextillion | sex (VI) | zetta- | ceto- | 1/6 of the mass of planet Earth in tons |
| 10 24 | septillion | septem (VII) | yotta- | yocto- | Number of molecules in 37.2 liters of air |
| 10 27 | octillion | octo (VIII) | nah- | sieve- | Half of Jupiter's mass in kilograms |
| 10 30 | quintillion | novem (IX) | dea- | threado- | 1/5 of all microorganisms on the planet |
| 10 33 | decillion | decem (X) | una- | revolution | Half the mass of the Sun in grams |
The pronunciation of the numbers that follow often differs.
| Number | Name | Latin numeral | Practical significance |
| 10 36 | andecillion | undecim (XI) | |
| 10 39 | duodecillion | duodecim (XII) | |
| 10 42 | thredecillion | 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 | septemvigintillion | ||
| 10 87 | octovigintillion | ||
| 10 90 | novemvigintillion | ||
| 10 93 | trigintillion | triginta (XXX) | |
| 10 96 | antigintillion |
- ...
- 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 - quinquagintillion (quinquaginta, L)
- 10 183 - sexagintillion (sexaginta, LX)
- 10,213 - septuagintillion (septuaginta, LXX)
- 10,243 - octogintillion (octoginta, LXXX)
- 10,273 - nonagintillion (nonaginta, XC)
- 10 303 - centillion (Centum, C)
- 10 306 - ancentillion or centunillion
- 10 309 - duocentillion or centullion
- 10 312 - trecentillion or centtrillion
- 10 315 - quattorcentillion or centquadrillion
- 10 402 - tretrigyntacentillion or centretrigyntillion
The numbers follow:
Some literary references:
- Perelman Ya.I. "Fun arithmetic." - M.: Triada-Litera, 1994, pp. 134-140
- Vygodsky M.Ya. "Handbook of Elementary Mathematics". - St. Petersburg, 1994, pp. 64-65
- "Encyclopedia of Knowledge". - comp. IN AND. Korotkevich. - St. Petersburg: Sova, 2006, p. 257
- “Interesting about physics and mathematics.” - Quantum Library. issue 50. - M.: Nauka, 1988, p. 50
Place zeros after any number or multiply with tens raised to an arbitrary power. It won't seem enough. It will seem like a lot. But the bare records are still not very impressive. The piling up of zeros in the humanities causes 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 another one... And the number will come out even larger.
And yet, are there words in Russian or any other language to denote very large numbers? Those that are more than a million, a billion, a trillion, a billion? And in general, how much is a billion?
It turns out that there are two systems for naming numbers. But not Arab, Egyptian, or any other ancient civilizations, but American and English.
In the American system numbers are called like this: take the Latin numeral + - illion (suffix). This gives the numbers:
Trillion - 1,000,000,000,000 (12 zeros)
Quadrillion - 1,000,000,000,000,000 (15 zeros)
Quintillion - 1 followed by 18 zeros
Sextillion - 1 and 21 zeros
Septillion - 1 and 24 zeros
octillion - 1 followed by 27 zeros
Nonillion - 1 and 30 zeros
Decillion - 1 and 33 zeros
The formula is simple: 3 x+3 (x is a Latin numeral)
In theory, there should also be the numbers anilion (unus in Latin - one) and duolion (duo - two), but, in my opinion, such names are not used at all.
English number 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 - illiard. I mean:
Trillion - 1 and 21 zeros (in the American system - sextillion!)
Trillion - 1 and 24 zeros (in the American system - septillion)
Quadrillion - 1 and 27 zeros
Quadrillion - 1 and 30 zeros
Quintillion - 1 and 33 zeros
Quinilliard - 1 and 36 zeros
Sextillion - 1 and 39 zeros
Sextillion - 1 and 42 zeros
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 us not be afraid!
In Russia, the American system of naming numbers has been adopted. We borrowed the name of the number “billion” from the English system - 1,000,000,000 = 10 9
Where is the “cherished” billion? - But a billion is a billion! American style. And even though we use American system, and “billion” was taken from English.
Using the Latin names of numbers and the American system, we name the numbers:
- vigintillion- 1 and 63 zeros
- centillion- 1 and 303 zeros
- million- one and 3003 zeros! Oh-ho-ho...
But this, it turns out, is not all. There are also non-system numbers.
And the first of them is probably myriad- one hundred hundreds = 10,000
Google(it is in his honor that the famous search system) - one and one hundred zeros
In one of the Buddhist treatises the number is named asankheya- one and one hundred and forty zeros!
Number name googolplex(like Google) came up with English mathematician Edward Kasner and his nine-year-old nephew - one with - dear mother! - googol zeros!!!
But that's not all...
The mathematician Skuse named the Skuse number after himself. It means e to a degree e to a degree e to the power of 79, that is e e e 79
And then a big difficulty arose. You can come up with names for numbers. But how to write them down? The number of degrees of degrees of degrees is already such that it simply cannot be removed onto the page! :)
And then some mathematicians began to write numbers in geometric shapes. And they say that the first to come up with this method of recording was the outstanding writer and thinker Daniil Ivanovich Kharms.
And yet, what is the BIGGEST NUMBER IN THE WORLD? - It’s called STASPLEX and is equal to G 100,
where G is Graham's number, the largest number ever used in mathematical proof.
This number - stasplex - was invented wonderful person, our compatriot Stas Kozlovsky, LJ to which I am directing you :) - ctac
10 to the 3003rd power
Disputes about which one is the most big number in the world are ongoing. Different calculus systems offer different variants and people don’t know what to believe, and which figure to consider as the largest.
This question has interested scientists since the times of the Roman Empire. The biggest problem lies in the definition of what a “number” is and what a “digit” is. At one time, people for a long time considered the largest number to be a decillion, that is, 10 to the 33rd power. But, after scientists began to actively study American and English metric systems, it was discovered that the largest number in the world is 10 to the 3003rd power - a million. Men in Everyday life They believe that the largest figure is a trillion. Moreover, this is quite formal, since after a trillion, names are simply not given, because the counting begins to be too complex. However, purely theoretically, the number of zeros can be added indefinitely. Therefore, it is almost impossible to imagine even purely visually a trillion and what follows it.
In Roman numerals
On the other hand, the definition of “number” as understood by mathematicians is a little different. A number means a sign that is universally accepted and is used to indicate a quantity expressed in a numerical equivalent. The second concept of “number” means the expression of quantitative characteristics in a convenient form through the use of numbers. It follows from this that numbers are made up of digits. It is also important that the number has symbolic properties. They are conditioned, recognizable, unchangeable. Numbers also have sign properties, but they follow from the fact that numbers consist of digits. From this we can conclude that a trillion is not a number at all, but a number. Then what is the largest number in the world if it is not a trillion, which is a number?
The important thing is that numbers are used as components of numbers, but not only that. A number, however, is the same number if we are talking about some things, counting them from zero to nine. This system of features applies not only to the familiar Arabic numerals, but also to Roman I, V, X, L, C, D, M. These are Roman numerals. On the other hand, V I I I is a Roman numeral. In Arabic calculus it corresponds to the number eight.
In Arabic numerals
Thus, it turns out that counting units from zero to nine are considered numbers, and everything else is numbers. Hence the conclusion that the largest number in the world is nine. 9 is a sign, and a number is a simple quantitative abstraction. A trillion is a number, and not a number at all, and therefore cannot be the largest number in the world. A trillion can be called the largest number in the world, and that is purely nominally, since numbers can be counted ad infinitum. The number of digits is strictly limited - from 0 to 9.
It should also be remembered that the numerals and numbers of different numerals do not coincide, as we saw from the examples with Arabic and Roman numerals and numerals. This happens because numbers and numbers are simple concepts that are invented by man himself. Therefore, a number in one number system can easily be a number in another and vice versa.
Thus, the largest number is innumerable, because it can continue to be added indefinitely from digits. As for the numbers themselves, in the generally accepted system, 9 is considered the largest number.
Sometimes people who are not involved in mathematics wonder: what is the largest number? On the one hand, the answer is obvious - infinity. Bores will even clarify that “plus infinity” or “+∞” is used by mathematicians. But this answer will not convince the most corrosive, especially since it is not natural number, but a mathematical abstraction. But having understood the issue well, they can discover a very interesting problem.
Indeed, there is no size limit in this case, but there is a limit to human imagination. Each number has a name: ten, one hundred, billion, sextillion, and so on. But where does people's imagination end?
Not to be confused with a trademark of Google Corporation, although they have a common origin. This number is written as 10100, that is, one followed by a hundred zeros. It is difficult to imagine, but it was actively used in mathematics.
It's funny that it was invented by a child - the nephew of the mathematician Edward Kasner. In 1938, my uncle entertained his younger relatives with discussions about very large numbers. To the child’s indignation, it turned out that such a wonderful number had no name, and he gave his own version. Later, my uncle inserted it into one of his books, and the term stuck.
Theoretically, a googol is a natural number, because it can be used for counting. But it’s unlikely that anyone will have the patience to count to the end. Therefore, only theoretically.
And as for the name Google, then a common mistake has crept in. The first investor and one of the co-founders was in a hurry when he wrote out the check and missed the letter “O”, but in order to cash it, the company had to be registered with this particular spelling.
Googolplex
This number is a derivative of googol, but is significantly larger than it. The prefix “plex” means raising ten to a power equal to the base number, so guloplex is 10 to the power of 10 to the power of 100 or 101000.
The resulting number exceeds the number of particles in the observable Universe, which is estimated to be about 1080 degrees. But this did not stop scientists from increasing the number by simply adding the prefix “plex” to it: googolplexplex, googolplexplexplex and so on. And for particularly perverted mathematicians, they invented a variant of magnification without the endless repetition of the prefix “plex” - they simply put Greek numbers in front of it: tetra (four), penta (five) and so on, up to deca (ten). The last option sounds like a googoldecaplex and means a tenfold cumulative repetition of the procedure of raising the number 10 to the power of its base. The main thing is not to imagine the result. You still won’t be able to realize it, but it’s easy to get mentally injured.
48th Mersen number
Main characters: Cooper, his computer and a new prime number
Relatively recently, about a year ago, we managed to discover the next, 48th Mersen number. On this moment it is the largest prime number in the world. Let us recall that prime numbers- these are those that are divisible without a remainder only by one and by themselves. The simplest examples are 3, 5, 7, 11, 13, 17 and so on. The problem is that the further into the wilds, the less common such numbers are. But the more valuable is the discovery of each next one. For example, a new prime number consists of 17,425,170 digits, if represented in the form familiar to us decimal system Reckoning. The previous one had about 12 million characters.
It was discovered by the American mathematician Curtis Cooper, who delighted the mathematical community with a similar record for the third time. It took 39 days of running his personal computer just to check his result and prove that this number was indeed prime.
This is what the Graham number looks like in Knuth arrow notation. It’s difficult to say how to decipher this without having a complete higher education in theoretical mathematics. It is also impossible to write it down in our usual decimal form: the observable Universe is simply not able to accommodate it. Building one degree at a time, as is the case with googolplexes, is also not a solution.
Good formula, just unclear
So why do we need this seemingly useless number? Firstly, for the curious, it was placed in the Guinness Book of Records, and this is already a lot. Secondly, it was used to solve a problem included in the Ramsey problem, which is also unclear, but sounds serious. Thirdly, this number is recognized as the largest ever used in mathematics, and not in comic proofs or intellectual games, but to solve a very specific mathematical problem.
Attention! The following information is dangerous for your mental health! By reading it, you accept responsibility for all consequences!
For those who want to test their mind and meditate on the Graham number, we can try to explain it (but only try).
Imagine 33. It's pretty easy - it turns out 3*3*3=27. What if we now raise three to this number? The result is 3 3 to the 3rd power, or 3 27. In decimal notation, this is equal to 7,625,597,484,987. A lot, but for now it can be realized.
In Knuth's arrow notation, this number can be displayed somewhat more simply - 33. But if you add only one arrow, it becomes more complicated: 33, which means 33 to the power of 33 or in power notation. If we expand to decimal notation, we get 7,625,597,484,987 7,625,597,484,987. Are you still able to follow your thoughts?
Next stage: 33= 33 33 . That is, you need to calculate this wild number from the previous action and raise it to the same power.
And 33 is only the first of 64 terms of Graham's number. To get the second one, you need to calculate the result of this mind-blowing formula and substitute the corresponding number of arrows into diagram 3(...)3. And so on, another 63 times.
I wonder if anyone other than him and a dozen other supermathematicians will be able to get to at least the middle of the sequence without going crazy?
Did you understand something? We are not. But what a thrill!
Why do we need the largest numbers? This is difficult for the average person to understand and comprehend. But with their help, a few specialists are able to introduce new technological toys to ordinary people: phones, computers, tablets. Ordinary people are also unable to understand how they work, but they are happy to use them for their entertainment. And everyone is happy: ordinary people get their toys, “supernerds” have the opportunity to continue playing their mind games.