List of numbers

This is adynamic listand may never be able to satisfy particular standards for completeness. You can help byadding missing itemswithreliable sources.

This is a list of notablenumbersand articles about notable numbers. The list does not contain all numbers in existence as most of thenumber setsare infinite. Numbers may be included in the list based on their mathematical, historical or cultural notability, but all numbers have qualities that could arguably make them notable. Even the smallest "uninteresting" number is paradoxically interesting for that very property. This is known as theinteresting number paradox.

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 acomplex number(3+4i), but not when it is in the form of avector(3,4). This list will also be categorized with the standard convention oftypes of numbers.

This list focuses on numbers asmathematical objectsand isnota list ofnumerals,which are linguistic devices: nouns, adjectives, or adverbs thatdesignatenumbers. The distinction is drawn between thenumberfive (anabstract objectequal to 2+3), and thenumeralfive (thenounreferring to the number).

Natural numbers

Main article:Natural number

Natural numbers are a subset of the integers and are of historical and pedagogical value as they can be used forcountingand often have ethno-cultural significance (see below). Beyond this, natural numbers are widely used as a building block for other number systems including theintegers,rational numbersandreal numbers.Natural numbers are those used forcounting(as in "there aresix(6) coins on the table ") andordering(as in "this is thethird(3rd) largest city in the country "). In common language, words used for counting are"cardinal numbers"and words used for ordering are"ordinal numbers".Defined by thePeano axioms,the natural numbers form an infinitely large set. Often referred to as "the naturals", the natural numbers are usually symbolised by a boldfaceN(orblackboard bold$\mathbb {\mathbb {N} }$,UnicodeU+2115ℕDOUBLE-STRUCK CAPITAL N).

The inclusion of0in the set of natural numbers is ambiguous and subject to individual definitions. Inset theoryandcomputer science,0 is typically considered a natural number. Innumber theory,it usually is not. The ambiguity can be solved with the terms "non-negative integers", which includes 0, and "positive integers", which does not.

Natural numbers may be used ascardinal numbers,which may go byvarious names.Natural numbers may also be used asordinal numbers.

Mathematical significance

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 is not prime or composite.
• 2,the base of thebinary numbersystem, used in almost all modern computers and information systems. Also the only natural even number to also be prime.
• 3,2²-1, the firstMersenne primeand firstFermat number.It is the first odd prime, and it is also the 2 bit integer maximum value.
• 4,the firstcomposite number.
• 5,the sum of the first two primes and only prime which is the sum of 2 consecutive primes. The ratio of the length from the side to a diagonal of a regular pentagon is thegolden ratio.
• 6,the first of the series ofperfect numbers,whose proper factors sum to the number itself.
• 9,the firstoddnumber that iscomposite.
• 11,the fifth prime and first palindromic multi-digit number in base 10.
• 12,the firstsublime number.
• 17,the sum of the first 4 prime numbers, and the only prime which is the sum of 4 consecutive primes.
• 24,allDirichlet charactersmodnarerealif and only ifnis a divisor of 24.
• 25,the firstcentered square numberbesides 1 that is also a square number.
• 27,thecubeof 3, the value of 3³.
• 28,the secondperfect number.
• 30,the smallestsphenic number.
• 32,the smallest nontrivialfifth power.
• 36,the smallest number which is aperfect powerbut not aprime power.
• 70,the smallestweird number.
• 72,the smallestAchilles number.
• 108,the secondAchilles number.
• 255,2⁸− 1, the smallestperfect totient numberthat is neither a power of three nor thrice a prime; it is also the largest number that can be represented using an8-bitunsignedinteger.
• 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.
• 8128,the fourth perfect number.
• 142857,the smallestbase 10cyclic number.
• 9814072356,the largestperfect powerthat contains no repeated digits in base ten.

Cultural or practical significance

Along with their mathematical properties, many integers haveculturalsignificanceor are also notable for their use in computing and measurement. As mathematical properties (such as divisibility) can confer practical utility, there may be interplay and connections between the cultural or practical significance of an integer and its mathematical properties.

List of integers notable for their cultural meanings

• 3,significant inChristianityas theTrinity.Also considered significant inHinduism(Trimurti,Tridevi). Holds significance in a number of ancient mythologies.
• 4,considered an"unlucky" numberin modern China, Japan and Korea due to its audible similarity to the word "death" in their respective languages.
• 7,the number of days in a week, and considered a "lucky" number in Western cultures.
• 8,considered a"lucky" number in Chinese culturedue to its aural similarity to the Chinese term for prosperity.
• 12,a common grouping known as adozenand the number of months in a year, of constellations of theZodiacandastrological signsand ofApostlesofJesus.
• 13,considered an"unlucky" numberin Western superstition. Also known as a "Baker's dozen".
• 17,consideredill-fatedin Italy and other countries of Greek and Latin origins.
• 18,considered a "lucky" number due to it being the value for theHebrew word for lifeinJewish numerology.
• 40,considered a significant number inTengrismand Turkish folklore. Multiple customs, such as those relating to how many days one must visit someone after a death in the family, include the number forty.
• 42,the "answer to the ultimate question of life, the universe, and everything" in the popular 1979 science fiction workThe Hitchhiker's Guide to the Galaxy.
• 69,a slang term for reciprocaloral sex.
• 86,a slang term that is used in the American popular culture as a transitive verb to mean throw out or get rid of.
• 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.
• 666,thenumber of the beastfrom theBook of Revelation.
• 786,regarded as sacred in the MuslimAbjad numerology.
• 5040,mentioned byPlatoin theLawsas one of the most important numbers for the city.

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

• 10,the number of digits in thedecimalnumber system.
• 12,thenumber basefor measuring time in many civilizations.
• 14,the number of days in afortnight.
• 16,the number of digits in thehexadecimalnumber system.
• 24,number ofhoursin aday.
• 31,the number of days most months of the year have.
• 60,thenumber basefor some ancient counting systems, such as theBabylonians',and the basis for many modern measuring systems.
• 360,the number ofsexagesimal degreesin a fullcircle.
• 365,the number of days in the common year, while there are 366 days in aleap yearof the solarGregorian calendar.

List of integers notable in computing

• 4,the number ofbitsin anibble.
• 8,the number of bits in anoctetand usually in abyte.
• 256,The number of possible combinations within8 bits,or an octet.
• 1024,the number of bytes in akibibyte,and bits in akibibit.
• 65535,2¹⁶− 1, the maximum value of a16-bitunsigned integer.
• 65536,2¹⁶,the number of possible16-bitcombinations.
• 65537,2¹⁶+ 1, the most popular RSA public key prime exponent in most SSL/TLS certificates on the Web/Internet.
• 16777216,2²⁴,or 16⁶;the hexadecimal "million" (0x1000000), and the total number of possible color combinations in 24/32-bitTrue Colorcomputer graphics.
• 2147483647,2³¹− 1, the maximum value of a32-bitsigned integerusingtwo's complementrepresentation.
• 9223372036854775807,2⁶³− 1, the maximum value of a64-bitsigned integerusingtwo's complementrepresentation.

Classes of natural numbers

Subsets of the natural numbers, such as the prime numbers, may be grouped into sets, for instance based on the divisibility of their members. Infinitely many such sets are possible. A list of notable classes of natural numbers may be found atclasses of natural numbers.

Prime numbers

Main articles:Prime numberandList of prime numbers

A prime number is a positive integer which has exactly twodivisors:1 and itself.

The first 100 prime numbers are:

Highly composite numbers

Main article:Highly composite number

A highly composite number (HCN) is a positive integer with more divisors than any smaller positive integer. They are often used ingeometry,grouping and time measurement.

The first 20 highly composite numbers are:

1,2,4,6,12,24,36,48,60,120,180,240,360,720,840,1260,1680,2520,5040,7560

Perfect numbers

Main article:Perfect number

A perfect number is an integer that is the sum of its positive proper divisors (all divisors except itself).

The first 10 perfect numbers:

1. 6
2. 28
3. 496
4. 8128
5. 33 550 336
6. 8 589 869 056
7. 137 438 691 328
8. 2 305 843 008 139 952 128
9. 2 658 455 991 569 831 744 654 692 615 953 842 176
10. 191 561 942 608 236 107 294 793 378 084 303 638 130 997 321 548 169 216

Integers

Main article:Integer

The integers are asetof numbers commonly encountered inarithmeticandnumber theory.There are manysubsetsof the integers, including thenatural numbers,prime numbers,perfect numbers,etc. Many integers are notable for their mathematical properties. Integers are usually symbolised by a boldfaceZ(orblackboard bold$\mathbb {\mathbb {Z} }$,UnicodeU+2124ℤDOUBLE-STRUCK CAPITAL Z); this became the symbol for the integers based on the German word for "numbers" (Zahlen).

Notable integers include−1,the additive inverse of unity, and0,theadditive identity.

As with the natural numbers, the integers may also have cultural or practical significance. For instance,−40is the equal point in theFahrenheitandCelsiusscales.

SI prefixes

One important use of integers is inorders of magnitude.Apower of 10is a number 10^k,wherekis an integer. For instance, withk= 0, 1, 2, 3,..., the appropriate powers of ten are 1, 10, 100, 1000,... Powers of ten can also be fractional: for instance,k= -3 gives 1/1000, or 0.001. This is used inscientific notation,real numbers are written in the formm× 10ⁿ.The number 394,000 is written in this form as 3.94 × 10⁵.

Integers are used asprefixesin theSI system.Ametric prefixis aunit prefixthat precedes a basic unit of measure to indicate amultipleorfractionof the unit. Each prefix has a unique symbol that is prepended to the unit symbol. The prefixkilo-,for example, may be added togramto indicatemultiplicationby one thousand: one kilogram is equal to one thousand grams. The prefixmilli-,likewise, may be added tometreto indicatedivisionby one thousand; one millimetre is equal to one thousandth of a metre.

Value	1000m	Name	Symbol
1000	10001	Kilo	k
1000000	10002	Mega	M
1000000000	10003	Giga	G
1000000000000	10004	Tera	T
1000000000000000	10005	Peta	P
1000000000000000000	10006	Exa	E
1000000000000000000000	10007	Zetta	Z
1000000000000000000000000	10008	Yotta	Y
1000000000000000000000000000	10009	Ronna	R
1000000000000000000000000000000	100010	Quetta	Q

Rational numbers

Main article:Rational number

A rational number is any number that can be expressed as thequotientorfractionp/qof twointegers,anumeratorpand a non-zerodenominatorq.Sinceqmay be equal to 1, every integer is trivially a rational number. Thesetof all rational numbers, often referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by a boldfaceQ(orblackboard bold$\mathbb {Q}$,UnicodeU+211AℚDOUBLE-STRUCK CAPITAL Q);it was thus denoted in 1895 byGiuseppe Peanoafterquoziente,Italian for "quotient".

Rational numbers such as 0.12 can be represented ininfinitelymany ways, e.g.zero-point-one-two(0.12),three twenty-fifths(⁠3/25⁠),nine seventy-fifths(⁠9/75⁠), etc. This can be mitigated by representing rational numbers in a canonical form as an irreducible fraction.

A list of rational numbers is shown below. The names of fractions can be found atnumeral (linguistics).

Table of notable rational numbers

Decimal expansion	Fraction	Notability
1.0	⁠1/1⁠	One is the multiplicative identity. One is a rational number, as it is equal to 1/1.
1
−0.083 333...	⁠−+1/12⁠	The value assigned to the series1+2+3...byzeta function regularizationandRamanujan summation.
0.5	⁠1/2⁠	One halfoccurs commonly in mathematical equations and in real world proportions. One half appears in the formula for the area of a triangle:⁠1/2⁠× base × perpendicular height and in the formulae forfigurate numbers,such astriangular numbersandpentagonal numbers.
3.142 857...	⁠22/7⁠	A widely used approximation for the number$\pi$.It can beproventhat this number exceeds$\pi$.
0.166 666...	⁠1/6⁠	One sixth. Often appears in mathematical equations, such as in thesum of squares of the integersand in the solution to the Basel problem.

Real numbers

Real numbersare least upper bounds of sets of rational numbers that are bounded above, or greatest lower bounds of sets of rational numbers that are bounded below, or limits of convergent sequences of rational numbers. real numbers that are not rational numbers are calledirrational numbers.The real numbers are categorised as algebraic numbers (which are the root of a polynomial with rational coefficients) or transcendental numbers, which are not; all rational numbers are algebraic.

Algebraic numbers

Main article:Algebraic number

Name	Expression	Decimal expansion	Notability
Golden ratio conjugate($\Phi$)	${\frac {{\sqrt {5}}-1}{2}}$	0.618033988749894848204586834366	Reciprocalof (and one less than) thegolden ratio.
Twelfth root of two	${\sqrt[{12}]{2}}$	1.059463094359295264561825294946	Proportion between the frequencies of adjacentsemitonesin the12 tone equal temperamentscale.
Cube rootof two	${\sqrt[{3}]{2}}$	1.259921049894873164767210607278	Length of the edge of acubewith volume two. Seedoubling the cubefor the significance of this number.
Conway's constant	(cannot be written as expressions involving integers and the operations of addition, subtraction, multiplication, division, and the extraction of roots)	1.303577269034296391257099112153	Defined as the unique positive real root of a certain polynomial of degree 71. The limit ratio between subsequent numbers in the binaryLook-and-say sequence(OEIS:A014715).
Plastic ratio	${\sqrt[{3}]{{\frac {1}{2}}+{\frac {1}{6}}{\sqrt {\frac {23}{3}}}}}+{\sqrt[{3}]{{\frac {1}{2}}-{\frac {1}{6}}{\sqrt {\frac {23}{3}}}}}$	1.324717957244746025960908854478	The only real solution of$x^{3}=x+1$.(OEIS:A060006) The limit ratio between subsequent numbers in theVan der Laan sequence.(OEIS:A182097)
Square root of two	${\sqrt {2}}$	1.414213562373095048801688724210	√2= 2 sin 45° = 2 cos 45°Square root of twoa.k.a.Pythagoras' constant.Ratio ofdiagonalto side length in asquare.Proportion between the sides ofpaper sizesin theISO 216series (originallyDIN476 series).
Supergolden ratio	${\dfrac {1+{\sqrt[{3}]{\dfrac {29+3{\sqrt {3\cdot 31}}}{2}}}+{\sqrt[{3}]{\dfrac {29-3{\sqrt {3\cdot 31}}}{2}}}}{3}}$	1.465571231876768026656731225220	The only real solution of$x^{3}=x^{2}+1$.(OEIS:A092526) The limit ratio between subsequent numbers inNarayana's cows sequence.(OEIS:A000930)
Triangular rootof 2	${\frac {{\sqrt {17}}-1}{2}}$	1.561552812808830274910704927987
Golden ratio(φ)	${\frac {{\sqrt {5}}+1}{2}}$	1.618033988749894848204586834366	The larger of the two real roots ofx2=x+ 1.
Square root of three	${\sqrt {3}}$	1.732050807568877293527446341506	√3= 2 sin 60° = 2 cos 30°. A.k.a.the measure of the fishor Theodorus' constant. Length of thespace diagonalof acubewith edge length 1.Altitudeof anequilateral trianglewith side length 2. Altitude of aregular hexagonwith side length 1 and diagonal length 2.
Tribonacci constant	${\frac {1+{\sqrt[{3}]{19+3{\sqrt {3\cdot 11}}}}+{\sqrt[{3}]{19-3{\sqrt {3\cdot 11}}}}}{3}}$	1.839286755214161132551852564653	The only real solution of$x^{3}=x^{2}+x+1$.(OEIS:A058265) The limit ratio between subsequent numbers in theTribonacci sequence.(OEIS:A000073) Appears in the volume and coordinates of thesnub cubeand some related polyhedra.
Supersilver ratio	${\dfrac {2+{\sqrt[{3}]{\dfrac {43+3{\sqrt {3\cdot 59}}}{2}}}+{\sqrt[{3}]{\dfrac {43-3{\sqrt {3\cdot 59}}}{2}}}}{3}}$	2.20556943040059031170202861778	The only real solution of$x^{3}=2x^{2}+1$.(OEIS:A356035) The limit ratio between subsequent numbers in thethird-order Pell sequence.(OEIS:A008998)
Square root of five	${\sqrt {5}}$	2.236067977499789696409173668731	Length of thediagonalof a 1 × 2rectangle.
Silver ratio(δS)	${\sqrt {2}}+1$	2.414213562373095048801688724210	The larger of the two real roots ofx2= 2x+ 1. Altitude of aregular octagonwith side length 1.
Bronze ratio(S3)	${\frac {{\sqrt {13}}+3}{2}}$	3.302775637731994646559610633735	The larger of the two real roots ofx2= 3x+ 1.

Transcendental numbers

Main article:Transcendental number

Name	Symbol or Formula	Decimal expansion	Notes and notability
Gelfond's constant	$e^{\pi }$	23.14069263277925...
Ramanujan's constant	$e^{\pi {\sqrt {163}}}$	262537412640768743.99999999999925...
Gaussian integral	${\sqrt {\pi }}$	1.772453850905516...
Komornik–Loreti constant	$q$	1.787231650...
Universal parabolic constant	$P_{2}$	2.29558714939...
Gelfond–Schneider constant	$2^{\sqrt {2}}$	2.665144143...
Euler's number	$e$	2.718281828459045235360287471352662497757247...	Raising e to the power of$i$πwill result in$-1$.
Pi	$\pi$	3.141592653589793238462643383279502884197169399375...	Pi is a constant irrational number that is the result of dividing the circumference of a circle by its diameter.
Super square-rootof 2	${\textstyle {\sqrt {2}}_{s}}$	1.559610469...
Liouville constant	${\textstyle L}$	0.110001000000000000000001000...
Champernowne constant	${\textstyle C_{10}}$	0.12345678910111213141516...	This constant contains every number string inside it, as its decimals are just every number in order. (1,2,3,etc.)
Prouhet–Thue–Morse constant	${\textstyle \tau }$	0.412454033640...
Omega constant	$\Omega$	0.5671432904097838729999686622...
Cahen's constant	${\textstyle C}$	0.64341054629...
Natural logarithm of 2	ln 2	0.693147180559945309417232121458
Lemniscate constant	${\textstyle \varpi }$	2.622057554292119810464839589891...	The ratio of the perimeter ofBernoulli's lemniscateto its diameter.
Tau	$\tau =2\pi$	6.283185307179586476925286766559...	The ratio of thecircumferenceto aradius,and the number ofradiansin a complete circle;2$\times$π

Irrational but not known to be transcendental

Some numbers are known to beirrational numbers,but have not been proven to be transcendental. This differs from the algebraic numbers, which are known not to be transcendental.

Name	Decimal expansion	Proof of irrationality	Reference of unknown transcendentality
ζ(3), also known asApéry's constant	1.202056903159594285399738161511449990764986292
Erdős–Borwein constant,E	1.606695152415291763...
Copeland–Erdős constant	0.235711131719232931374143...	Can be proven withDirichlet's theorem on arithmetic progressionsorBertrand's postulate(Hardy and Wright, p. 113) orRamare's theoremthat every even integer is a sum of at most six primes. It also follows directly from its normality.
Prime constant,ρ	0.414682509851111660248109622...	Proof of the number's irrationality is given atprime constant.
Reciprocal Fibonacci constant,ψ	3.359885666243177553172011302918927179688905133731...

Real but not known to be irrational, nor transcendental

For some numbers, it is not known whether they are algebraic or transcendental. The following list includes real numbers that have not been proved to be irrational, nor transcendental.

Name and symbol	Decimal expansion	Notes
Euler–Mascheroni constant,γ	0.577215664901532860606512090082...	Believed to be transcendental but not proven to be so. However, it was shown that at least one of$\gamma$and the Euler-Gompertz constant$\delta$is transcendental.It was also shown that all but at most one number in an infinite list containing${\frac {\gamma }{4}}$have to be transcendental.
Euler–Gompertz constant,δ	0.596 347 362 323 194 074 341 078 499 369...	It was shown that at least one of the Euler-Mascheroni constant$\gamma$and the Euler-Gompertz constant$\delta$is transcendental.
Catalan's constant,G	0.915965594177219015054603514932384110774...	It is not known whether this number is irrational.
Khinchin's constant,K0	2.685452001...	It is not known whether this number is irrational.
1stFeigenbaum constant,δ	4.6692...	Both Feigenbaum constants are believed to betranscendental,although they have not been proven to be so.
2ndFeigenbaum constant,α	2.5029...	Both Feigenbaum constants are believed to betranscendental,although they have not been proven to be so.
Glaisher–Kinkelin constant,A	1.28242712...
Backhouse's constant	1.456074948...
Fransén–Robinson constant,F	2.8077702420...
Lévy's constant,β	1.18656 91104 15625 45282...
Mills' constant,A	1.30637788386308069046...	It is not known whether this number is irrational.(Finch 2003)
Ramanujan–Soldner constant,μ	1.451369234883381050283968485892027449493...
Sierpiński's constant,K	2.5849817595792532170658936...
Totient summatory constant	1.339784...
Vardi's constant,E	1.264084735305...
Somos' quadratic recurrence constant,σ	1.661687949633594121296...
Niven's constant,C	1.705211...
Brun's constant,B2	1.902160583104...	The irrationality of this number would be a consequence of the truth of the infinitude oftwin primes.
Landau's totient constant	1.943596...
Brun's constant for prime quadruplets,B4	0.8705883800...
Viswanath's constant	1.1319882487943...
Khinchin–Lévy constant	1.1865691104...	This number represents the probability that three random numbers have nocommon factorgreater than 1.
Landau–Ramanujan constant	0.76422365358922066299069873125...
C(1)	0.77989340037682282947420641365...
Z(1)	−0.736305462867317734677899828925614672...
Heath-Brown–Moroz constant,C	0.001317641...
Kepler–Bouwkamp constant,K'	0.1149420448...
MRB constant,S	0.187859...	It is not known whether this number is irrational.
Meissel–Mertens constant,M	0.2614972128476427837554268386086958590516...
Bernstein's constant,β	0.2801694990...
Gauss–Kuzmin–Wirsing constant,λ1	0.3036630029...
Hafner–Sarnak–McCurley constant,σ	0.3532363719...
Artin's constant,CArtin	0.3739558136...
S(1)	0.438259147390354766076756696625152...
F(1)	0.538079506912768419136387420407556...
Stephens' constant	0.575959...
Golomb–Dickman constant,λ	0.62432998854355087099293638310083724...
Twin prime constant,C2	0.660161815846869573927812110014...
Feller–Tornier constant	0.661317...
Laplace limit,ε	0.6627434193...
Embree–Trefethen constant	0.70258...

Numbers not known with high precision

See also:Normal numberandUncomputable number

Some real numbers, including transcendental numbers, are not known with high precision.

• The constant in theBerry–Esseen Theorem:0.4097 <C< 0.4748
• De Bruijn–Newman constant:0 ≤ Λ ≤ 0.2
• Chaitin's constantsΩ, which are transcendental and provably impossible to compute.
• Bloch's constant(also2nd Landau's constant): 0.4332 <B< 0.4719
• 1st Landau's constant:0.5 <L< 0.5433
• 3rd Landau's constant:0.5 <A≤ 0.7853
• Grothendieck constant:1.67 <k< 1.79
• Romanov's constant inRomanov's theorem:0.107648 <d< 0.49094093, Romanov conjectured that it is 0.434

Hypercomplex numbers

Main article:Hypercomplex number

Hypercomplex numberis a term for anelementof a unitalalgebraover thefieldofreal numbers.Thecomplex numbersare often symbolised by a boldfaceC(orblackboard bold$\mathbb {\mathbb {C} }$,UnicodeU+2102ℂDOUBLE-STRUCK CAPITAL C), while the set ofquaternionsis denoted by a boldfaceH(orblackboard bold$\mathbb {H}$,UnicodeU+210DℍDOUBLE-STRUCK CAPITAL H).

Algebraic complex numbers

• Imaginary unit:${\textstyle i={\sqrt {-1}}}$
• nthroots of unity:${\textstyle \xi _{n}^{k}=\cos {\bigl (}2\pi {\frac {k}{n}}{\bigr )}+i\sin {\bigl (}2\pi {\frac {k}{n}}{\bigr )}}$,while${\textstyle 0\leq k\leq n-10}$,GCD(k,n) = 1

Other hypercomplex numbers

• Thequaternions
• Theoctonions
• Thesedenions
• Thetrigintaduonions
• Thedual numbers(with aninfinitesimal)

Transfinite numbers

Main article:Transfinite number

Transfinite numbersare numbers that are "infinite"in the sense that they are larger than allfinitenumbers, yet not necessarilyabsolutely infinite.

• Aleph-null:ℵ₀:the smallest infinite cardinal, and the cardinality of$\mathbb {N}$,the set ofnatural numbers
• Aleph-one:ℵ₁:the cardinality of ω₁,the set of all countable ordinal numbers
• Beth-one:$\beth _{1}$:thecardinality of the continuum2^ℵ₀
• ℭ or${\mathfrak {c}}$:thecardinality of the continuum2^ℵ₀
• Omega:ω, the smallestinfinite ordinal

Numbers representing physical quantities

Main articles:Physical constantandList of physical constants

Physical quantities that appear in the universe are often described usingphysical constants.

• Avogadro constant:N_A=6.02214076×10²³mol⁻¹‍
• Electron mass:m_e=9.1093837139(28)×10⁻³¹kg‍
• Fine-structure constant:α=0.0072973525643(11)‍
• Gravitational constant:G=6.67430(15)×10⁻¹¹m³⋅kg⁻¹⋅s⁻²‍
• Molar mass constant:M_u=1.00000000105(31)×10⁻³kg⋅mol⁻¹‍
• Planck constant:h=6.62607015×10⁻³⁴J⋅Hz⁻¹‍
• Rydberg constant:R_∞=10973731.568157(12) m⁻¹‍
• Speed of light in vacuum:c=299792458m⋅s⁻¹‍
• Vacuum electric permittivity:ε₀=8.8541878188(14)×10⁻¹²F⋅m⁻¹‍

Numbers representing geographical and astronomical distances

• 6378.137,the average equatorial radius of Earth inkilometers(followingGRS 80andWGS 84standards).
• 40075.0167,the length of theEquatorin kilometers (following GRS 80 and WGS 84 standards).
• 384399,the semi-major axis of theorbit of the Moon,in kilometers, roughly the distance between the center of Earth and that of the Moon.
• 149597870700,the average distance between the Earth and the Sun orAstronomical Unit(AU), in meters.
• 9460730472580800,onelight-year,the distance travelled by light in oneJulian year,in meters.
• 30856775814913673,the distance of oneparsec,another astronomical unit, in whole meters.

Numbers without specific values

Main article:Indefinite and fictitious numbers

Many languages have words expressingindefinite and fictitious numbers—inexact terms of indefinite size, used for comic effect, for exaggeration, asplaceholder names,or when precision is unnecessary or undesirable. One technical term for such words is "non-numerical vague quantifier".Such words designed to indicate large quantities can be called "indefinite hyperbolic numerals".

Named numbers

• Hardy–Ramanujan number,1729
• Kaprekar's constant,6174
• Eddington number,~10⁸⁰
• Googol,10¹⁰⁰
• Shannon number
• Centillion,10³⁰³
• Skewes's number
• Googolplex,10^(10100)
• Mega/Circle(2)
• Moser's number
• Graham's number
• TREE(3)
• SSCG(3)
• Rayo's number
• Kanahiya's Constant,2592

See also

• Absolute infinite
• English numerals
• Floating-point arithmetic
• Fraction
• Integer sequence
• Interesting number paradox
• Large numbers
• List of mathematical constants
• List of prime numbers
• List of types of numbers
• Mathematical constant
• Metric prefix
• Names of large numbers
• Names of small numbers
• Negative number
• Numeral (linguistics)
• Numeral prefix
• Order of magnitude
• Orders of magnitude (numbers)
• Ordinal number
• The Penguin Dictionary of Curious and Interesting Numbers
• Perfect numbers
• Power of two
• Power of 10
• Surreal number
• Table of prime factors

References

• Finch, Steven R. (2003), "Anmol Kumar Singh",Mathematical Constants (Encyclopedia of Mathematics and its Applications, Series Number 94),Cambridge University Press, pp.130–133,ISBN0521818052
• Apéry, Roger (1979), "Irrationalité de$\zeta (2)$et$\zeta (3)$",Astérisque,61:11–13.

Further reading

• Kingdom of Infinite Number: A Field Guideby Bryan Bunch, W.H. Freeman & Company, 2001.ISBN0-7167-4447-3

External links

• What's Special About This Number? A Zoology of Numbers: from 0 to 500
• Name of a Number
• See how to write big numbers
• About big numbersat theWayback Machine(archived 27 November 2010)
• Robert P. Munafo's Large Numbers page
• Different notations for big numbers – by Susan Stepney
• Names for Large Numbers,inHow Many? A Dictionary of Units of Measurementby Russ Rowlett
• What's Special About This Number?(from 0 to 9999)