## List of numbers |

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The definition of what is classed as a number is rather diffuse and based on historical distinctions. For example the pair of numbers (3,4) is commonly regarded as a number when it is in the form of a complex number (3+4i), but not when it is in the form of a vector (3,4). This list will also be categorised with the standard convention of

This list focuses on numbers as *not* a list of *designate* numbers. The distinction is drawn between the *number* five, an *numeral* five, the

- natural numbers
- classes of natural numbers
- integers
- rational numbers
- irrational numbers
- real numbers
- hypercomplex numbers
- transfinite numbers
- numbers representing physical quantities
- numbers without specific values
- named numbers
- see also
- notes
- further reading
- external links

The natural numbers are a subset of the integers and are of historical and pedagogical value as they can be used for *six* (6) coins on the table") and *third* (3rd) largest city in the country"). In common language, words used for counting are "

The inclusion of

Natural numbers may be used as

Natural numbers may have properties specific to the individual number or may be part of a set (such as prime numbers) of numbers with a particular property.

List of mathematically significant natural numbers

1 , the multiplicative identity. Also the only natural number (not including 0) that isn't prime or composite.2 , the base of thebinary number system, used in almost all modern computers and information systems. Also notable as the only evenprime number .3 , 2^{2}-1, the firstMersenne number . It is the first odd prime, and it is also the 2 bit integer maximum value.4 , the firstcomposite number 6 , the first of the series ofperfect numbers , whose proper factors sum to the number itself.9 , the firstodd number that iscomposite 11 , the fifth prime and first palindromic multi-digit number17 , the sum of the first 4 prime numbers, and the only prime which is the sum of 4 consecutive primes.24 , allDirichlet characters mod *n*arereal if and only if*n*is a divisor of 24.25 , the firstcentered square number besides 1 that is also a square number27 , thecube of 3, the value of , where isKnuth's up-arrow notation .28 , the secondperfect number .30 , the smallestsphenic number .32 , the smallest nontrivialfifth power .36 , the smallest number which isperfect power but notprime power .72 , the smallestAchilles number .255 , 2^{8}− 1, aMersenne number and the smallestperfect totient number that is neither a power of three nor thrice a prime; it is also the largest number that can be represented using an8-bit unsignedinteger 341 , the smallest base 2Fermat pseudoprime .496 , the thirdperfect number .1729 , theHardy–Ramanujan number , also known as the secondtaxicab number ; that is, the smallest positive integer that can be written as the sum of two positive cubes in two different ways.^{[1]}8128 , the fourth perfect number.142857 , the smallestbase 10 cyclic number .9814072356 , the largestperfect power that contains no repeated digits in base ten.

Along with their mathematical properties, many integers have

List of integers notable for their cultural meanings.

3 , significant inChristianity as theTrinity . Also considered significant inHinduism (Trimurti ,Tridevi ). Holds significance in a number of ancient mythologies.4 , considered an "unlucky number" in modern China, Japan and Korea due to its audible similarity to the word "Death."5 , number of fingers or toes for almost all amphibians, reptiles and mammals7 , considered a"lucky" number in Western cultures.8 , considered a"lucky" number in Chinese culture.9 , a significant number inNorse Mythology .^{[citation needed]}12 , thenumber base for some ancient counting systems and the basis for some modern measuring systems. Known as adozen .13 , considered an"unlucky" number in Western superstition. Also known as a "Baker's Dozen".15 , the number of players on arugby union team. It is also the first point received intennis .16 , the base of the hexadecimal number system which is utilized within many programming languages.18 , age of majority in most countries in the world.^{[citation needed]}19 , the length of one side of aGo board.21 , the legaldrinking age in theUnited States .22 , the namesake ofcatch-22 , a paradoxical condition in which there is no escape due to mutually conflicting or dependent conditions.23 , number ofchromosomes in a humanhaploid . Other human cells have 23 pairs of chromosomes.26 , the number ofEnglish letters , bijective base 26 is used in thecolumns ofMicrosoft Excel .42 , the "answer to the ultimate question of life, the universe, and everything" in the popular 1979 science fiction work.The Hitchhiker's Guide to the Galaxy 69 , used as slang to refer to a sexual act.86 , a slang term that is used in the American popular culture as a transitive verb to mean throw out or get rid of.^{[2]}108 , considered sacred by theDharmic Religions . Approximately equal to the ratio of the distance from Earth to Sun and diameter of the Sun.420 , a code-term that refers to the consumption ofcannabis .616 , the true value of "Number of the Beast".^{[citation needed]}666 , theNumber of the Beast from the Book of Revelation.786 , regarded as sacred in the MuslimAbjad numerology .5040 , mentioned byPlato in theas one of the most important numbers for the city.Laws

List of integers notable for their use in units, measurements and scales.

10 , the number of digits in thedecimal number system.14 , the number of days in afortnight .16 , the number of digits in thehexadecimal number system.24 , number ofhours in aday 25 , the number of cents in aquarter .31 , the number of days most months of the year have.60 , thenumber base for some ancient counting systems, such as theBabylonians' , and the basis for many modern measuring systems.365 , the number of days in the common year.

List of integers notable in computing

8 , the number ofbits in abyte 256 , The number of possible combinations within8 bits , or abyte .1024 , the number of bytes in akibibyte . It's also the number of bits in akibibit .65535 , 2^{16}− 1, the maximum value of a16-bit unsigned integer.65536 , 2^{16}, the number of possible16-bit combinations.65537 , 2^{16}+ 1, the most popular RSA public key prime exponent in most SSL/TLS certificates on the Web/Internet.16777216 , 2^{24}, or 16^{6}; the hexadecimal "million" (0x1000000), and the total number of possible color combinations in 24/32-bitTrue Color computer graphics.2147483647 , 2^{31}− 1, the maximum value of a32-bit signed integer usingtwo's complement representation.9223372036854775807 , 2^{63}− 1, the maximum value of a64-bit signed integer usingtwo's complement representation.

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