List of special numbers
This list of special numbers lists numbers that have one or more conspicuous mathematical properties and numbers that have a special cultural or technical meaning. The latter numbers are listed in the second part of this article.
Numbers with special mathematical properties
Until 0

−2
 Smallest whole number for which the ring is Euclidean .
 Largest trivial zero of the zeta function .

−1
 A unit in the ring of whole numbers and its extension rings.
 Single complex number of the multiplicative order .
 In the body of complex numbers is
 smallest number occurring as a dimension (namely sometimes the empty set)

−0.5
 Functional value of the zeta function

−0.083333333333333 ...
 Functional value of the zeta function

0
 Neutral element of addition in the ring of whole numbers and its expansion rings. (These include the fields of rational , real and complex numbers .)
 "Zero element" of the multiplication (ie, if there is a factor , so is the product)
 only number for which the function has a point of discontinuity (if the definition is followed)
 first index of some countably indexed series, but usually only if this initial (and not “first”) case has a certain triviality that distinguishes it from the others
 first ordinal number ; Ordinal number of the second kind and among these both the only finite and the only nonLimes number
 smallest thickness of a set , at the same time the only one that already clearly defines the set (as the empty set )
 only number where the sum with itself corresponds to the product with itself (this also applies to 2) and in addition the respective results are equal to the number itself.
 smallest characteristic of a ring
 Degree of constant polynomials (excluding the zero polynomial)
Until 1

0.0112359550561797 ... (Follow A021093 in OEIS )
 is the value of the infinite series , the summands of which are the product of the th Fibonacci number with .

0.12345678910111213141516 ... (sequence A033307 in OEIS )
 : The Champernowne number is the first constructed normal number .

0.2078795763507619 ... (Follow A049006 in OEIS )
 : The imaginary unit to the power has the real value (see also Euler's identity ).

0.2247448713915890 ... (see sequence A115754 in OEIS )
 : Relative distance of the optimal support points from the edges of a uniformly loaded beam ( Bessel points ).

0.235711131719232931374143 ... (Follow A33308 in OEIS )
 : The CopelandErdős number is a normal number .

0.2614972128476427 ... (Follow A077761 in OEIS )
 MeisselMertens constant M _{1} (prime number analogue to EulerMascheroni constant )

0.2801694990238691 ... (sequence A073001 in OEIS )
 Bernstein constant β (the error of the best uniform approximation of  x  on [−1,1] by polynomials of even degree n is ~ β / n)

0.3036630028987326… (Follow A038517 in OEIS )
 GaussKusminWirsing constant λ (occurs when describing the convergence of the number distribution in continued fraction expansion )

0.3532363718549959 ... (Follow A085849 in OEIS )
 HafnerSarnakMcCurley constant (asymptotic probability that the determinants of two integer matrices are relatively prime)

0.3678794411714423 ... (Follow A068985 in OEIS )
 Reciprocal of Euler's number
 Minimal digit of the function , since the zero is from and therefore also from .

0.4142135623730950 ... (sequence A014176 in OEIS )
 ; algebraic value of the tangent function for halfinteger argument in degrees
 0.4342944819032518 ... (sequence A002285 in OEIS )

0.5
 ; rational value of the sine and cosine functions

0.5432589653429767 ... (Follow A081760 in OEIS )
 currently the most precise upper limit of the Landau constant (maximum, so that for every holomorphic function ƒ with ƒ ′ (0) = 1 there is a circular disk with a radius in the image of the unit disk )

0.5671432904097838 ... (Follow A019474 in OEIS )
 The Ω constant : solution of the equation and thus the function value of the Lambert W function

0.5772156649015328 ... (sequence A001620 in OEIS )
 Value of the EulerMascheroni constant , where denotes the harmonic series .

0.5960631721178216 ... (Follow A051158 in OEIS )
 Irrational value of the sum of the reciprocal of all Fermat numbers , that is

0.6180339887498948 ... (sequence A094214 in OEIS )
 , i.e. reciprocal of the golden ratio and at the same time the golden ratio reduced by one:
 0.6243299885435508 ... (sequence A084945 in OEIS )

0.6309297535714574 ... (Follow A102525 in OEIS )
 Hausdorff dimension of the fractal Cantor set ,

0.6434105462883380 ... (Follow A118227 in OEIS )
 Cahen constant C ( transcendental number with a simple formation law for the part of the denominator of the fraction expansion )

0.6601618158468695 ... (sequence A005597 in OEIS )
 Prime twin constant C _{2} (part of the HardyLittlewood conjecture about the number of prime twins ≤ x )

0.6627434193491815 ... (sequence A033259 in OEIS )
 Limit of Laplace (maximum eccentricity for which the Laplace series converges to solve the Kepler equation )

0.6922006275553463 ... (sequence A072364 in OEIS )
 value of
 global minimum of the function

0.6931471805599453 ... (sequence A002162 in OEIS )
 Value of the logarithm naturalis of , i.e. value of

0.70258 ... (Follow A118288 in OEIS )
 EmbreeTrefethen constant β * (limit coefficient of generalized random Fibonacci sequences )

0.7071067811865475 ... (Follow A010503 in OEIS )
 , i.e. half of the root of 2 and at the same time its reciprocal
 Value of the sine and cosine at , so

0.7390851332151606 ... (sequence A003957 in OEIS )
 Fixed point of the cosine function , i.e. solution of the equation

0.7642236535892206 ... (Follow A064533 in OEIS )
 LandauRamanujan constant
 This results from the asymptotic determination of the proportion of the total of all natural numbers that can be represented as the sum of two square numbers.

0.8079455065990344 ... (Follow A133741 in OEIS )
 Distance between the centers of two unit circles, each of which overlaps half of its area
 0.8093940205406391… (Follow A085291 in OEIS )
 0.8660254037844386 ... (sequence A010527 in OEIS )

0.87058838 ... (sequence A213007 in OEIS )
 Brun's constant ; Sum of the reciprocal values of all prime quadruplets

0.9159655941772190 ... (sequence A006752 in OEIS )
 Catalan's constant ;
 Functional value of the Dirichlet beta function

1
 neutral element of multiplication in the ring of integers as well as its extension rings (these include the fields of rational , real and complex numbers ).
 thus also the value of the empty product
 formerly the first of the natural numbers
 smallest positive integer
 first index of countably indexed rows, as far as this is not used here (without exception is used for components of vectors and matrices)
 only number in the product itself, the number itself and with itself the potency Faculty match; smallest of the two numbers for which the former two conditions or the latter two conditions apply
 only Fibonacci number occurring more than once (namely twice) ; once (as the second of three) with their own index, once (as the first of three) smaller than their index (this is exactly one larger in all these cases), furthermore (as the first of four) with the distance from exactly to a prime number and which (as the second of four) is a nonfirst power
 Definitions often demanded as the smallest thickness of a set for various applications, for example the smallest order of a ring (and, if an exception is not expressly inserted into the commonly formulated definition, also of a group )
 smallest characteristic of a finite ring
 first ordinal number of the first kind (successor number)
 first Catalan number
Until 10

1.0149416064096536 ... (Follow A143298 in OEIS )
 Gieseking's constant (maximum volume of a hyperbolic tetrahedron )

1.0173430619844491 ... (sequence A013664 in OEIS )
 Functional value of the zeta function

1.0594630943592952645618252949463 (12th root of 2)
 Factor between the frequencies of two neighboring semitones (e.g. C and C #) with equal pitch

1.0823232337111381 ... (sequence A013662 in OEIS )
 Functional value of the zeta function

1.08366 (sequence A228211 in OEIS )
 Legendre constant (occurs in the prime number theorem , turned out to be incorrect)

1.0986858055251870 ... (Follow A086053 in OEIS )
 Lengyel's constant Λ (occurs in the asymptotic analysis of the number of chains from the smallest to the largest element in the lattice of partitions )

1.1319882487943 ... (Follow A078416 in OEIS )
 Viswanath constant K (basis of the asymptotically exponential growth of random Fibonacci sequences )

1.1547005383792515 ... (sequence A020832 in OEIS )
 , Ratio of the circumferential radius to the incircular radius of the regular hexagon, determines the width of the hexagon socket wrench

1.1865691104156254 ... (sequence A100199 in OEIS )
 ChintschinLévy constant ( almost everywhere the limit value for n → ∞ from ( ln q _{n} ) / n, where q _{n is} the denominator of the nth approximate fraction )_{}_{}

1.2020569031595942 ... (Follow A002117 in OEIS )
 Functional value of the zeta function , Apéry constant

1.2618595071429148 ... (Follow A100831 in OEIS )
 Hausdorff dimension of the fractal Koch curve ,

1.2824271291006226 ... (Follow A074962 in OEIS )
 GlaisherKinkelin constant A (occurs when evaluating integrals and series sums )

1.3063778838630806 ... (Follow A051021 in OEIS )
 Mills' constant A (smallest number A> 0, so that for each n = 1, 2, 3, ... is a prime number , provided the Riemann hypothesis is correct)

1.3247179572447460 ... (sequence A060006 in OEIS )
 Plastic number (the unique real solution of the cubic equation )

1.4142135623730950 ... (sequence A002193 in OEIS )
 , d. H. the square root of ( root of 2 )
 Value of the length of the diagonal of a square with the length of the side

1.4513692348833810 ... (Follow A070769 in OEIS )
 RamanujanSoldner constant , the only positive zero of the integral logarithm

1.4560749485826896 ... (Follow A072508 in OEIS )
 Backhouse constant B (−1 / B is the zero of the power series with 1 and the prime numbers as coefficients)

1.4670780794339754 ... (Follow A086237 in OEIS )
 Porter's constant (occurs in formulas of the asymptotic mean number of divisions in the Euclidean algorithm )

1.5849625007211561… (Follow A020857 in OEIS )
 Hausdorff dimension of the fractal Sierpinski triangle ,

1.6066951524152917 ... (sequence A065442 in OEIS )
 ErdősBorwein constant (sum of the reciprocal values of all Mersenne numbers )
 1.6180339887498948 ... (sequence A001622 in OEIS )

1.6449340668482264 ... (Follow A013661 in OEIS )
 Functional value of the zeta function

1.7052111401053677 ... (Follow A033150 in OEIS )
 Niven constant ( limit of the arithmetic mean of the maximum exponents of the prime factorization of the first natural numbers for )
 1.7320508075688772 ... (Follow A002194 in OEIS )

1.7724538509055160 ... (Follow A002161 in OEIS )
 , the root of the circle number (root )
 Function value of the gamma function
 Value of the error integral
 1.851937052 ... (Follow A036792 in OEIS )

1.90216058 ... (Follow A065421 in OEIS )
 Brun's constant (sum of the reciprocal values of all prime twins )

2
 Smallest positive even number , defining for the even numbers
 Least prime number
 Single even prime number
 Only number that is an odd phi function Euler has yet not to himself prime is
 Smallest order of a body (required by definition)
 Smallest characteristic of a finite body
 Second Catalan number
 The smallest basis of a value system , the dual system
 . Hence, the only number where the sum with itself, the product with itself, and the power with itself (and the largest of only two if only the first two or only the last two conditions are required) is
 Greatest number of two that matches its own faculty
 Second of three Fibonacci numbers that are one smaller than their index, second of four that are exactly a prime number apart
 The only natural number for which the equation is nontrivial and nevertheless solvable ( FermatWiles theorem )

2.3025850929940456… (Follow A002392 in OEIS )
 Logarithm naturalis of , i.e. value of

2.4142135623730950 ... (Follow A014176 in OEIS )
 algebraic value of the tangent function
 Silver cut , limit of the ratio of two consecutive numbers in the Pell sequence

2.5029078750958928 ... (Follow A006891 in OEIS )
 One of the two Feigenbaum constants

2.5849817595792532 ... (Follow A062089 in OEIS )
 Sierpiński constant K (occurs when estimating special sums)

2.6220575542921198 ... (Follow A062539 in OEIS )
 Lemniscatic constant , defined as the value of the elliptic integral

2.6651441426902251 ... (Follow A007507 in OEIS )
 The GelfondSchneider constant from the GelfondSchneider theorem
 value of

2.6854520010653064 ... (sequence A002210 in OEIS )
 Khinchin's constant , almost everywhere , the geometric mean of the denominators of the continued fraction expansion
 2.7182818284590452 ... (sequence A001113 in OEIS )

2.8077702420285193… (Follow A058655 in OEIS )
 FransénRobinson constant (area between the x axis and the curve 1 / Γ ( x ) for x > 0)

3
 Least odd prime number
 Fermat number
 Mersenne prime number
 Smallest natural number that is not a function value of the Euler φ function occurs
 Largest Fibonacci number (of three) that is less than its index ( ); third of four Fibonacci numbers that are precisely spaced from a prime number ; only Fibonacci prime whose index is not prime

3.1415926535897932384626433832795 ... (sequence A000796 in OEIS )
 Circle number , ratio of the circumference of a circle to its diameter

3.1428571428571428571428571428571 ... (Follow A068028 in OEIS )
 , Approximation to the circle number as it is often used

3.3598856662431775531720113029189… (Follow A079586 in OEIS )
 ' Fibonacci reciprocal constant', sum of the reciprocal values of all Fibonacci numbers

4th
 Number of corners of the regular polygon, the area of which corresponds exactly to the second power of the edge length, which is why the term square defines both regular quadrilateral and second power
 Smallest composite number
 Number of colors sufficient to color any flat map ( fourcolor theorem )
 First nonFibonacci number
 Smallest Smith number
 Number of faces and corners of a tetrahedron
 Smallest natural number for which every nonnegative integer can be represented as a sum of at most square numbers (see: Waring's problem )
 Number of points of the smallest affine plane
 Smallest order of a noncommutative ring without a single element
 Maximum degree of the general algebraic equation that can be solved using the extraction of roots
 Smallest order of a noncyclic group (the Klein group of four )
 Minimum order of a body which is not a residue field is

4.6692016091029906 ... (sequence A006890 in OEIS )
 Feigenbaum constant : Fixed point of the logistic equation , transition into chaos

5
 Number of platonic solids
 Smallest positive natural number , the square of which can be written as the sum of two positive square numbers : (see also: Pythagorean triple )
 Fermat number
 Largest number of corners of a regular polygon that appears as the side surface of a Platonic solid
 The only component of two prime twins , namely and
 Least Wilson prime
 Smallest possible mirp number , in the system of three the decimal is the same , the decimal is the same
 Third Catalan number
 Largest (third) Fibonacci number that is identical to its own index
 Smallest number for which a polygram exists
 Number of corners of a polygon that has the same number of diagonals (a corner has diagonals)

6th
 Smallest perfect number : it is equal to the sum of their positive divisor other than their own: .
 The number is equal to the product of its real divisors:
 Exact common quotient of the areas of a regular hexagon and triangle for which the same side length is specified
 Number of faces of the cube
 Number of corners of the octahedron
 Number of edges of the tetrahedron
 In the plane, a circle can be touched by a maximum of other circles of the same size so that no overlaps occur.
 Smallest positive integer whose cube can be written as the sum of three positive cubes: .
 Largest order to which no GrecoLatin square exists
 Smallest order of a nonAbelian group , the symmetric group
 Smallest positive natural number that is not a prime power
 Smallest natural number greater than for which no field of order exists
 Smallest, primarily pseudoperfect number
 Number of platonic solids in four dimensions
 The only natural number above for which no connected polygram exists

6.283185307179586 ... (Follow A019692 in OEIS )
 : Scope of the unit circle

7th
 Smallest number of vertices of a regular polygon that is not constructible with ruler and compass is
 Mersenne prime number
 Number of colors that, according to the RingelYoungs Theorem, are sufficient to color any map on a torus
 Smallest nonnegative integer that cannot be written as a sum of less than four square numbers (see: Waring's problem )
 Number of points and lines of the smallest projective plane , the Fano plane
 Smallest positive natural number for which rectangles of different positive edge lengths exist in pairs, which can be combined to form a rectangle

8th
 Number of faces of the octahedron and number of corners of the cube
 third of four Fibonacci numbers that are nonfirst powers and besides the trivial and single cube number; If you consider the Fibonacci number , the value is obtained by raising the value to the power of its index, the index ( ), when multiplying both numbers; is also the largest of four Fibonacci numbers , which are exactly the distance from a prime number
 Least order of a noncommutative unitary ring
 The only number with four divisors, the second largest of which is even.

9
 Every positive natural number that is multiplied by gives the final number after the formation of crosssums of the intermediate results . Examples: or .
 If you take any threedigit number in which the first and last digit differ by at least and take the same number with the reverse order of digits and form the difference between the two numbers, you get a multiple of . If you add this number to the number that has the reverse sequence of digits, you get the number .
 Smallest odd composite number
 Smallest natural number for which every nonnegative integer can be represented as the sum of at most positive cubic numbers (see: Waring's problem )
 Smallest positive natural number for which there are pairs of squares with different positive edge lengths that can be combined to form a rectangle
 Smallest order of a nonDesarguean projective plane

10
 Largest number of corners of a regular polygon that appears as the side of an Archimedean solid
 Smallest natural number for which applies to all natural numbers ( is Euler's φ function .)
 Is also used as an approximation for .
Until 100

11
 Length of the Golay code , the only nontrivial perfect ternary code that can correct more than one error.
 Smallest prime that is not a Mersenne prime .
 Smallest repunit prime

12
 Least abundant number .
 Number of faces of the dodecahedron , number of edges of the cube and octahedron , number of corners of the icosahedron .
 1st sublime number and only one under a trillion
 3. Pentagonal number
 4. Number of rectangles
 Threedimensional kiss number
 Order of the rotating group of the tetrahedron , the alternating group .
 A dozen

13
 Number of Archimedean solids, if no distinction is made between similar solids.
 2. Wilson prime number .
 Smallest number in the decimal system

14th
 Number of threedimensional Bravais grids
 Smallest even natural number that does not appear as a function value of Euler's φfunction .
 Fourth Catalan number .

14,134725141734693 ... (Follow A058303 in OEIS )
 Imaginary part of the absolute smallest nontrivial zero of the zeta function

15th
 Number of Archimedean solids if nonreflection invariant solids are counted twice.
 Smallest composite number for which, apart from isomorphism, only a single group of the order exists.
 Smallest pseudoprime number . Smallest natural number that cannot be written as a sum of less than eight cube numbers (see: Waring's problem ).
 Largest binary value that a 4bit variable can assume:
 Smallest natural number that Euler's φfunction has no prime number in common.

16
 ; is actually the only number for which mutually distinct natural numbers and exist with .
 Smallest natural number , so that with a finite number of exceptions, every natural number can be written as a sum of at most biquadrates (see: Waring's problem ).
 Order of the smallest unitary ring that is not antiisomorphic to itself.
 Number of binary values that a 4bit variable can accept:

17th
 Fermat number .
 Number of crystallographic groups in the plane .
 Gauss considered the construction of the regular 17sided with compass and ruler to be one of his most important discoveries.

18th
 The first maximum of the number of nonisomorphic cubic cage graphs of a given waist size , which is reached with increasing waist size of these graphs at .
 The only number that is double its checksum.
 Smallest number with six divisors, which are always alternately odd and even, sorted by size.

19th
 Smallest natural number for which every positive natural number can be represented as a sum of at most biquadrates (see: Waring's problem ).
 Largest nonsquare integer for which the ring is Euclidean .

20th
 Number of faces of the icosahedron and number of corners of the dodecahedron .
 “ God's number ” of the Rubik's cube : maximum number of turns that are necessary to solve a Rubik's cube from any position
 Least abundant number without a perfect divisor

21st
 Smallest positive natural number for which there are pairs of squares with different positive edge lengths that can be put together to form a square.

22nd
 The first coefficient of the continued fraction representation of .

23
 Smallest positive natural number for which cuboids with different positive edge lengths exist, which can be combined to form a cuboid.
 Smallest and next to the only natural number that cannot be written as a sum of less than nine cubic numbers (see Waring's problem ).
 Length of the Golay code , the only nontrivial perfect binary code that can correct more than one error.
 smallest prime number outside of a prime number twin (if one disregards the one whose distance to neighboring prime numbers is even closer than provided in the definition of the prime number twin)

24
 Order of the rotation group symmetrical group of the cube and the octahedron .
 Largest natural number with the property that all natural numbers are less than a divisor of .

25th
 Least square number, the sum of two square numbers is:
 Smallest natural number with a multiplicative tenacity of .

26th
 Number of sporadic groups
 The only natural number that has a square and a cube number as neighbors

27
 The smallest natural number that can be written as the sum of three square numbers in two different ways, namely as .
 The number of lines on a projective cubic surface .

28
 The smallest natural number that can be written as the sum of four square numbers in two different ways, namely as .
 Second perfect number .

29
 Least prime number, which is the sum of three consecutive square numbers:

30th
 Number of edges of the dodecahedron and the icosahedron .
 Area number of the rhombic triacontahedron . Smallest Giuga number .
 The largest natural number with the property that of other than all natural numbers smaller than that to be prime, prime numbers are.
 31

32
 Number of crystal classes in the threedimensional crystal lattice

33
 The largest natural number that cannot be represented as the sum of different triangular numbers.

34
 The smallest number that has the same number of divisors as its predecessor and successor.

35
 The smallest tetrahedral number that is the product of a prime twin .

36
 First (nontrivial) square triangular number , a triangular number at the same time perfect square is.
 The only (nontrivial) triangular number whose square root ( ) is also a triangular number:

37
 Smallest natural number for which every nonnegative whole number can be represented as the sum of at most the fifth powers of nonnegative whole numbers (see: Waring's problem ).
 Least irregular prime number .
 It is the fourth number .

38
 The row sum of the only nontrivial magic hexagon with the side length .

39
 Smallest natural number with a multiplicative tenacity of .

40
 Smallest natural number not in this list .

41
 The polynomial yields for for all prime numbers.

42
 Second primarily pseudoperfect number .
 Fifth Catalan number .
 Smallestdimensional space without a sausage catastrophe .

43
 Largest natural number for which it is impossible to put together Chicken McNuggets in the usual packs of 6, 9 and 20 (see coin problem ).

44
 Number of possibilities to solve the house of St. Nicholas ; another 44 variants are reflections of these paths

49
 Smallest pseudoprime number (number that composed , even though you can see it either on the final number yet on the cross sum)

50
 Smallest natural number that can be written in two different ways as the sum of two square numbers:

56
 At this number, the sausage disaster occurs .

60
 The order of the alternating group , i.e. the smallest non resolvable group and the smallest non Abelian simple group .
 Number of vertices of four Archimedean solids : the truncated dodecahedron , the truncated icosahedron or football body, the small rhombicosidodecahedron and the beveled dodecahedron (Dodekaedron simum).
 Number of edges of two Archimedean solids : the icosidodecahedron and the beveled cube (Cubus simus).
 The smallest natural number that is divided by all natural numbers up to .
 The smallest natural number that is divided by all natural numbers up to .

65
 Smallest natural number that can be written in two different ways as the sum of two different square numbers:

70
 Smallest odd number

71
 Largest supersingular prime . Largest righttrimmable prime number to the base .

72
 Smallest positive integer whose fifth power can be written as the sum of five fifth powers of positive natural numbers: .

73
 It is the 21st prime number, is the product of and .
 Its mirror number is the 12th prime number (again mirror number of ).
 In binary notation it is a palindromic number : . The palindrome has seven digits and contains three times the .
 In octal, there is a palindromic number: . The palindrome has three digits and contains three times the .
 It is the sixth mirp number .

77
 Smallest natural number with a multiplicative tenacity of .

79
 Smallest natural number that cannot be written as the sum of fewer than biquadrates (see: Waring's problem ).

80
 “ God's number ” for the 15 puzzle : maximum number of moves that are necessary to solve the puzzle from any position

85
 85 can be represented in two different ways as the sum of two square numbers:

88
 Number of ways to draw the house of Nicholas , see number

92
 Number of Johnson bodies
 Number of faces of the beveled dodecahedron .
 Number of solutions to the 8 queens problem
Up to 1000

101
 The smallest threedigit prime number
 First threedigit number palindrome

105
 The circular division polynomial is the first whose coefficients are not all , or .

107
 Smallest threedigit number .

108
 Regular pentagon angle

109.47 ...
 Tetrahedron angle

111
 Third smallest repunit number

120
 Maximum number of corners of an Archimedean solid in the large rhombicosidodecahedron
 127

132
 Sixth Catalan number .

143
 Solution of Waring's problem for k = 7

144
 Smallest positive integer whose fifth power can be written as the sum of four fifth powers of positive natural numbers: . This identity was discovered in 1966 and refuted a generalization of Fermat's great theorem suggested by Leonhard Euler in 1769 .
 Largest and fourth fibonacci number (after , and ) that is a nonfirst power, including the only nontrivial square number. It is also the square of its own Fibonacci index.

153
 You start with any natural number divisible by three and continuously build the sum of the cubes of the decimal digits: this sequence will always reach 153 and because of 1³ + 5³ + 3³ = 1 + 125 + 27 = 153 then it will stop there.

163
 Largest number for which class number has. Therefore is unusually close to an integer.

168
 Order of the second smallest nonabelian simple group.

180
 Maximum number of edges of an Archimedean solid in the large rhombicosidodecahedron

191
 Largest righttrimmable prime number to the base .

196
 Smallest and bestknown candidate for a Lychrel number .

210
 Largest Goldbach number .

219
 Number of threedimensional symmetry groups without taking into account the orientation in space ( space group ).

220
 Smallest friendly number , together with the smallest friendly number pair.

223
 The only natural number that cannot be written as the sum of less than positive fifth powers (see: Waring's problem ).

230
 Number of threedimensional symmetry groups taking into account the orientation in space ( space group ).

239
 The largest and the only natural number that cannot be written as the sum of less than nine cubic numbers (see: Waring's problem ).

248
 Dimension of the complex Lie group .

251
 Smallest natural number that can be written as the sum of three cube numbers in two different ways, namely as

255
 Largest binary value that an 8bit variable can assume:

256
 Number of binary values that an 8bit variable can accept:
 257

261
 Number of threedimensional networks in a fourdimensional cube.

284
 Second smallest friendly number , together with the smallest friendly number pair.

292
 Fifth number in the continued fraction expansion of the circle number . Since this number is relatively large, the continued fraction terminated after the fourth digit provides a very good approximation for : The two numbers match in six decimal places, which is a much better approximation than would be expected for an approximate fraction with a denominator of this magnitude.

325
 Smallest number that can be written in three ways as the sum of two square numbers:

341
 Smallest pseudoprime to the base

353
 Smallest positive natural number whose biquadrate can be written as the sum of four positive biquadrates:

373
 The only threedigit number for which the following applies: The digits , and are prime numbers. The numbers and are prime numbers. The number is a prime number. (Special case of prime numbers that can be truncated on both sides )

420
 The smallest natural number that is divided by all numbers from to .

429
 Seventh Catalan number .

454
 Largest natural number that cannot be written as the sum of less than eight cubic numbers (see: Waring's problem ).

466
 Largest natural number that cannot be written as the sum of fewer than positive integer fifths. (see: Waring's problem ).

495
 Three digit Kaprekar constant

496
 Third perfect number

561
 Smallest Carmichael number

563
 Third and currently largest known Wilson prime

666
 The sum of the squares of the first seven prime numbers
 Is represented in Roman numerals as DCLXVI. Here each numerical value occurs exactly once in the order of decreasing size.
 The sum of the numbers from to
 See also six hundred and sixtysix

679
 Smallest natural number with a multiplicative tenacity of .

840
 The smallest natural number that is divided by all numbers from to .

858
 Second smallest Giuga number with four factors.

880
 Number of fourth order magic squares that do not emerge from one another through reflection or rotation.

945
 Least odd abundant number .

991
 Largest known permutable prime number that is not a success .
Up to 10,000

1009
 Smallest fourdigit number

1089
 For a threedigit number that is not a number palindrome , you create its mirror number (e.g. is the mirror number of ) and subtract the smaller number from the larger number; The reverse number of the result is then added to the result (if the first intermediate result only has two digits, the number is preceded by a zero); this method always gives the result

1093
 First Wieferich prime number

1105
 Smallest number that can be written in four ways as the sum of two square numbers:

1233

1444
 In the decimal system, square numbers can not end in more than three identical ( different) digits. is the smallest square number that has this maximum number of identical digits at the end.

1722
 Third Giuga number .

1729
 Smallest number that can be represented in two different ways as the sum of two third powers: ( Hardy  Ramanujan number).
 The first Carmichael number of the form .

1806
 Third, primarily pseudoperfect number .

2047
 : the smallest Mersenne number with prime exponents that is not prime, i.e. not a Mersenne prime number:

2437
 Largest righttrimmable prime number to the base .

2520
 The smallest natural number that is divided by all numbers from to .
 Eighteenth composite number  it has total divisors. In addition, it is the largest "special" highly composed number: The number of divisors is only exceeded when the numerical value is doubled ( has divisors).

3003
 The only known number so far that appears exactly eight times in Pascal's triangle . See Singmaster conjecture .

3435
 First nontrivial Münchhausen number as a base , in which the sum of the individual digits, taken even up, results in the original number:

3511
 Second (and largest known) Wieferich prime number

4711
 Is used as a metasyntactic variable for finitely large cardinal numbers; the background is that this figure just does not have special mathematical properties, but a wellknown brand name for colognes is

5525
 Smallest number that can be written in exactly six ways as the sum of two square numbers:

5777 and 5993
 the only two known odd numbers greater than that cannot be written as , where is a prime number and an integer

6174
 Kaprekar constant for fourdigit numbers.

6788
 Smallest natural number with a multiplicative tenacity of .

6841
 Largest righttrimmable prime number to the base .

7825
 Smallest number for which there is no binary coloring of the set up to without a singlecolored Pythagorean triple .

8125
 Smallest number that can be written in exactly five ways as the sum of two square numbers:

8128
 Fourth perfect number
 8191

8833
Up to 1 million

10.100
 (applies to all place value systems )

16,843
 First Wolstenholme prime

27,720
 The smallest natural number that is divided by all natural numbers up to .
 The smallest natural number that is divided by all natural numbers up to .

29,341
 10. Carmichael number , smallest pseudoprime to the bases , , , and .

41,041
 Smallest Carmichael number with four prime factors

47,058
 Fourth primarily pseudo perfect number .
 63,973

65,533
 Functional value of the Ackermann function .

65,535
 Largest binary value that a 16bit variable can assume:

65,536
 Number of binary values that a 16bit variable can accept:

65,537
 Fermat number , largest known (and probably also largest) Fermat prime number

66.198
 Fourth Giuga number .

68,889
 Smallest natural number with a multiplicative tenacity of .

78,557
 Smallest known Sierpiński number .

108,863
 Largest righttrimmable prime number to the base .
 131,071

142,857
 Smallest nontrivial cyclic number .

148,349
 The only number that is equal to the sum of its subfaculty digits.

177.147
 Number of possibilities ( ) in the football pool (penalty bet).

271,441
 The smallest Perrinsche pseudo prime number , .
 294,409

360.360
 The smallest natural number that is divided by all natural numbers up to .
 The smallest natural number that is divided by all natural numbers up to .
 The smallest natural number that is divided by all natural numbers up to .

509.203
 Smallest known trickle number .
 524.287

549.945
 1. Kaprekar constant for sixdigit numbers.

617.716
 The th triangular number , a palindrome of numbers ; Discovered by Charles Trigg .

631.764
 2. Kaprekar constant for sixdigit numbers.

720.720
 The smallest natural number that is divided by all natural numbers up to .

990.100
Up to 1 billion

2,082,925
 Smallest number that can be written in different ways as the sum of two square numbers :

2,124,679
 Second Wolstenholme prime number

2,677,889
 Smallest natural number with a multiplicative tenacity of .

4,005,625
 Smallest number that can be written in ways as the sum of two square numbers

4,497,359
 Largest righttrimmable prime number to the base .

5,882,353

5,928,325
 Smallest number that can be written in ways as the sum of two square numbers

9,721,368
 Largest number made up of different digits (in the decimal system) from which any digit can be crossed out so that the rest can be divided by the crossed out digit

26,888,999
 Smallest natural number with a multiplicative tenacity of .

33,550,336
 Fifth perfect number
 56.052.361

73.939.133
 Largest righttrimmable prime number in the decimal system : For the number, when the last digit is deleted, a prime number with precisely this property is created; ie , , , , , , also prime numbers.

87,539,319
 Smallest number that can be represented in three different ways as the sum of two cubic numbers: Taxicab number

94.122.353
 118.901.521
 146.511.208
 172,947,529
 216.821.881
 228.842.209

275.305.224
 Number of fifth order magic squares that do not emerge from one another by mirroring or rotating.
 472.335.975
 534.494.836

635.318.657
 Smallest number that can be written in two different ways as the sum of two biquadrates, namely as .

906.150.257
 Smallest counterexample to the conjecture of Pólya
 912.985.153
Up to 1 trillion
 1,299,963,601

1,355,840,309
 Largest righttrimmable prime number to the base .

1,765,038,125
 2,147,483,647

2,214,408,306
 Fifth Giuga number .

2,214,502,422
 Fifth primarily pseudo perfect number .
 2,301,745,249

2,584,043,776

3,778,888,999
 Smallest natural number with a multiplicative tenacity of .

3,816,547,290
 The only pandigital number whose first digits (read as numbers) are divisible by: the first digit by , the first two digits by , the first three digits by , etc.

4,294,967,295
 Largest value that can be represented as an unsigned 32bit integer :

4,294,967,296
 Number of binary values that a 32bit variable can accept:

4,294,967,297
 Using this number, Euler refuted a conjecture made by Fermat  see Fermat's prime number .
 4,679,307,774

5,391,411,025
 Smallest abundant number that is neither divisible by nor by .

6,172,882,716
 The th triangular number , a palindrome of numbers . Discovered by Charles Trigg .

7,416,043,776

8.235.038.125

8,589,869,056
 Sixth perfect number , discovered by Cataldi in 1588 .

15.170.835.645
 Smallest number that can be written in three different ways as the sum of two cube numbers each , namely as

24,423,128,562
 Sixth Giuga number .
 32.164.049.650

52.495.396.602
 Sixth primarily pseudo perfect number .

116.788.321.168

123.288.328.768

137,438,691,328
 Seventh perfect number , discovered by Cataldi in 1588 .
 192.739.365.541

200.560.490.131
 Is the prime number , where is the product of all prime numbers from to (see also Euclid's theorem , prime faculty ).
 461.574.735.553

876.712.328.768

883.212.321.168
Up to 1 trillion

7,625,597,484,987
 10,028,704,049,893

28,116,440,335,967

61,728,399,382,716
 The th triangular number , a palindrome of numbers .

277,777,788,888,899
 Smallest natural number with a multiplicative tenacity of .

432.749.205.173.838
 The seventh Giuga number

4,338,281,769,391,370

9,585,921,133,193,329
 The smallest Carmichael number according to the Richard GE Pinch system

14.737.133.470.010.574
 The eighth Giuga number

21,897,142,587,612,075

48,988,659,276,962,496
 The smallest number that can be written in five different ways as the sum of two cubic numbers each, namely as

262,537,412,640,768,743.9999999999992500 ... (Follow A060295 in OEIS )
 is called Ramanujan's constant , is a transcendent number and is very close to an integer.

550.843.391.309.130.318
 The ninth Giuga number
Over 1 trillion

1,517,841,543,307,505,039

2,305,843,008,139,952,128
 The eighth perfect number , discovered by Leonhard Euler in 1750 .

2,305,843,009,213,693,951
 Mersenne prime number

12,157,692,622,039,623,539

18,446,744,073,709,551,615
 Largest binary value that a 64bit variable can assume:

18,446,744,073,709,551,616
 Number of binary values that a 64bit variable can accept:

63,105,425,988,599,693,916

128,468,643,043,731,391,252

357,686,312,646,216,567,629,137
 Largest prime number that can be truncated to the left in the decimal system: If you remove any part of the number from the front (left), a prime number always remains.

244,197,000,982,499,715,087,866,346
 The tenth known Giuga number

618,970,019,642,690,137,449,562,111
 Mersenne prime number

554.079.914.617.070.801.288.578.559.178
 The eleventh known Giuga number .

8,490,421,583,559,688,410,706,771,261,086
 The seventh primarily pseudoperfect number .

162.259.276.829.213.363.391.578.010.288.127
 Mersenne prime number

1,910,667,181,420,507,984,555,759,916,338,506
 The twelfth known Giuga number .

2,658,455,991,569,831,744,654,692,615,953,842,176
 The ninth perfect number , discovered by Pervusin in 1883 .

170,141,183,460,469,231,731,687,303,715,884,105,727
 Mersenne prime number

191,561,942,608,236,107,294,793,378,084,303,638,130,997,321,548,169,216
 The tenth perfect number , discovered by Ralph E. Powers in 1911 .

808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000
 The order of the monster group (the largest sporadic group ).

13,164,036,458,569,648,337,239,753,460,458,722,910,223,472,318,386,943,117,783,728,128
 The eleventh perfect number , discovered by Ralph E. Powers in 1914 .

6,086,555,670,238,378,989,670,371,734,243,169,622,657,830,773,351,885,970,528,324,860,512,791,691,264
 The second raised number , discovered by Kevin Brown

14.474.011.154.664.524.427.946.373.126.085.988.481.573.677.491.474.835.889.066.354.349.131.199.152.128
 The twelfth perfect number , discovered by Lucas in 1876 .

2 ^{520} (2 ^{521}  1)
 The 13th perfect number , discovered by Raphael M. Robinson in 1952 .

2 ^{606} (2 ^{607}  1)
 The 14th perfect number , discovered by Raphael M. Robinson in 1952 .

2 ^{1278} (2 ^{1279}  1)
 The 15th perfect number , discovered by Raphael M. Robinson in 1952 .

2 ^{2202} (2 ^{2203}  1)
 The 16th perfect number , discovered by Raphael M. Robinson in 1952 .

2 ^{2280} (2 ^{2281}  1)
 The 17th perfect number , discovered by Raphael M. Robinson in 1952 .

1.29 x 10 ^{865}
 The lower bound for the maximum number of ones in a holding Busy Beaver with six states

2 ^{3216} (2 ^{3217}  1)
 The 18th perfect number , discovered by Riesel in 1957 .

3 × 10 ^{1730}
 The lower bound for the maximum number of steps a holding Busy Beaver with six states can take

2 ^{4252} (2 ^{4253}  1)
 The 19th perfect number , discovered by Adolf Hurwitz and Selfridge in 1961 .

2 ^{4422} (2 ^{4423}  1)
 The 20th perfect number , discovered by Adolf Hurwitz and Selfridge in 1961 .

2 ^{9688} (2 ^{9689}  1)
 The 21st perfect number , discovered by Gillies in 1963 .

2 ^{9940} (2 ^{9941}  1)
 The 22nd perfect number , discovered by Gillies in 1963 .

2 ^{11,212} (2 ^{11,213}  1)
 The 23rd perfect number , discovered by Gillies in 1963 .

2 ^{19,936} (2 ^{19,937}  1)
 The 24th perfect number , discovered by Tuckermann in 1971 .

2 ^{21,700} (2 ^{21,701}  1)
 The 25th perfect number , discovered by Noll and Nickel in 1978 .

2 ^{23,208} (2 ^{23,209}  1)
 The 26th perfect number , discovered by Noll in 1979 .

2 ^{65,536}  3rd
 Function value of the Ackermann function (decimal number with digits)

2 ^{44,496} (2 ^{44,497}  1)
 The 27th perfect number , discovered by Slowinski and Nelson in 1979 .

2 ^{86,242} (2 ^{86,243}  1)
 The 28th perfect number , discovered by Slowinski in 1982 .

48,047,305,725 × 2 ^{172,403}  1
 Largest known Sophie Germain prime up to 2008 .

2 ^{110.502} (2 ^{110.503}  1)
 The 29th perfect number , discovered by Colquitt and Welsh in 1988 .

2 ^{132 048} (2 ^{132 049}  1)
 The 30th perfect number , discovered by Slowinski in 1983 .

2 ^{216 090} (2 ^{216 091}  1)
 The 31st perfect number , discovered by Slowinski in 1985 .

481,899 × 2 ^{481,899} + 1
 Largest known Cullen prime until 2008

2 ^{756 838} (2 ^{756 839}  1)
 The 32nd perfect number , discovered by Slowinski and Gage in 1992 .

2 ^{859 432} (2 ^{859 433}  1)
 The 33rd perfect number , discovered by Slowinski in 1993 .

3,752,948 × 2 ^{3,752,948}  1
 The largest known Woodall prime

6,679,881 × 2 ^{6,679,881} + 1
 The largest known Cullen prime

2 ^{25,964,951}  1
 The 42nd wellknown Mersenne prime , a number with digits

2 ^{30,402,457}  1
 The 43rd known Mersenne prime , a number with digits

2 ^{32,582,657}  1
 The 44th known Mersenne prime , a number with digits

2 ^{37,156,667}  1st
 The 45th known Mersenne prime , a number with digits

2 ^{42,643,801}  1
 The 46th known Mersenne prime , a number with digits

2 ^{43,112,609}  1
 The 47th known Mersenne prime , a number with digits

70388830… 50240001
 The largest Carmichael number found (up to 1996) that has different prime divisors. It was found by Löh and Niebuhr, a number with digits

2 ^{57,885,161}  1
 The 48th known Mersenne prime , a number with digits

2 ^{74.207.281}  1
 The 49th known Mersenne prime , a number with digits

2 ^{74.207.280} (2 ^{74.207.281}  1)
 The 50th known Mersenne prime , a number with digits

2 ^{82,589,933}  1
 The 51st known Mersenne prime number and thus the largest known prime number (as of December 7, 2018), a number with digits

 Largest number with digits that can be written with three decimal digits

2 ^{2,305,843,009,213,693,951}  1
 This double Mersenne number , which can also be written as and has around 694 quadrillion digits, is possibly a prime number. Refuting this is the declared task of the GIMPS project , which coordinates distributed computing power over the Internet.

 is the largest Fermat number so far (as of January 31, 2020) for which a prime factor is known. It has more than jobs. If you were to write this number on a square piece of paper with 16 digits per cm², the square piece of paper would have an area of approx. 10 ^{1,662,809} square light years, ^{i.e.} a side length of approx. 10 ^{831,404 }light years .^{}^{}

 Skewes number , for a long time (1931–1971) the largest finite number used in a mathematical proof. If you were to write this number on a square sheet of paper with 16 digits per cm², the square sheet of paper would have an area of approximately square light years , i.e. a side length of approximately light years (the exponent therefore has 34 digits).
 Mega
 Megiston
 Moser's number

Graham's number ()
 Ousted Skewes' number from number one in the largest finite numbers used in a mathematical proof.
Infinite sizes

 Infinity, the reciprocal of 0 in certain computing systems , is greater than all numbers in this list and is not itself a number. With can indeed be expected to a limited extent, however, many expressions that contain either himself or (namely the terms and to the extent that no rule of de l'Hospital can be applied) is not defined.

 smaller than all ( whole , rational , real ) numbers, otherwise see above
 in some geometries, but not on the usual number line, applies
 the only negative and only infinite value that can appear as the degree of a polynomial (namely the zero polynomial ).

( aleph ), (small omega )
 is the countable cardinality of the natural , rational and algebraic numbers and thus the smallest transfinite cardinal number . is the smallest ordinal number that is larger than any natural number, and thus the smallest transfinite ordinal number. It is true, but the arithmetic of the ordinal numbers is different from that of the cardinal numbers.
 is the second ordinal number of the second kind (i.e. number without a predecessor). All of these numbers are called Limes numbers , so it is their first.

 The smallest ordinal number that cannot be achieved with a finite number of arithmetic operations (addition, multiplication, exponentiation) . It is still countable , therefore .

 The smallest ordinal number that cannot be counted.

 The next greater thickness, that is . If one accepts the continuum hypothesis, it agrees with the width of the continuum (the set of real numbers).

 The uncountable power of the continuum, the irrational , transcendental , real and complex numbers and quaternions , the power of the power set of natural numbers.

 The uncountable power of the real functions.
Complex numbers
In this sublist special complex numbers are collected and sorted according to their amount.

i
 The imaginary unit. A complex number whose square has the value and which is therefore the solution to the quadratic equation . is fourth root of unity . The formal definition is set (instead of what is also possible ). See also imaginary numbers .

−i
 Reciprocal of the imaginary unit
 or (inverse element of multiplication, but here also of addition:) . is like fourth root of unity .

 The Primitive Third Roots of Unity ; is the third power of these two numbers .

πi
 Returns the value as the argument of the exponential function , see Euler's identity .

2πi
 Period of the complex exponential function.

1/2 + i 14.134725141734693… (sequence A058303 in OEIS )
 Zero of the Riemann zeta function with the smallest, positive imaginary part.
Numbers of particular importance
Until 0

0
 The ice point describes the freezing point of water under normal conditions in degrees Celsius.
 As absolute zero , 0 Kelvin, which corresponds to −273.15 ° C or −459.67 ° F, represents the theoretically lowest possible temperature, which, however, cannot be reached in practice
 Network elimination number in many telephone networks (simply in area codes (D) / area codes (A) and mobile network codes, doubled in country codes)
 Call of the switchboard in many private branch exchanges
Until 1

0.0078749969978123 (sequence A100264 in OEIS )
 Chaitin's constant Ω (approximate, incalculable probability with which a universal Turing machine stops on any input)

0.5
 As a fraction ½ (a half) the only real fraction that has always had a special name in most languages.

1
 Numerical value of the Milesian  Greek number alpha .
 Roman numeral I.
 Symbol of unity and origin
Until 10

1.0594630943592952 ... (sequence A010774 in OEIS )
 , Frequency ratio between two adjacent semitones with equal pitch

1.2589254117941673 ... (sequence A011279 in OEIS )
 , Logarithmic comparative value 1 decibel (dB)

1.4
 Popular approximation for , for example, the aperture range in photography : 1.0; 1.4; 2.0; 2.8; 4.0; 5.6; 8th; 11; 16; 22; ...

1.4142135623730950 ... (sequence A002193 in OEIS )
 , Aspect ratio of many paper formats , for example DIN A and DIN B formats with the aspect ratio

1.5
 With the special designation “one and a half” traditionally linguistically particularly emphasized fractional number. Other languages (e.g. Russian  полтора́) also have a special name for this number.

1.5396007178390020 ... (Follow A118273 in OEIS )
 Lieb's ice cube constant (residual entropy of ice is N k ln W in an exactly solvable 2D model in statistical physics )

2
 Symbol of opposites.
 In Chinese philosophy, yin and yang .
 Numerical value of the Milesian Greek number beta .
 Code for (English) "to" in abbreviations , for example in B2C = BusinesstoConsumer .
 Number of points that define a straight line.

3
 Number of repetitions for affirmation (affirmation) in mythology and spirituality .
 "Number of all good things."
 So many times Peter denied before a rooster crowed ( Passion ).
 Trinity : Father, Son, Holy Spirit.
 Three theological virtues : faith, hope, love.
 Number of classic aggregate states .
 Third gender for people who deviate from heteronormative rules.
 Numerical value of the Milesian Greek number gamma .
 Number of points to define a plane.
 three modern levels of the Catholic ordination office (also earlier main levels): bishop, priest and deacon

3.2
 The old aperture series in photography is based on multiples of 3.2 (actually of ): 1.1, 1.6, 2.2, 3.2, 4.5, 6.3, 9, 12.5, 18, 25, 36, 50, 71, 100.

4th
 Number of elements in ancient times.
 Four directions . Four seasons .
 Four canonical gospels and evangelists .
 Four cardinal virtues .
 Chinese and Japanese unlucky number (pronounced like "death").
 In the western world it stands for luck (clover leaf).
 Numerical value of the Milesian Greek number Delta .
 Minimum number of points to define a body
 Language short code for (English) "for", for example in 4U = for you.

5
 Number of elements in Asia, partly also in Greek mysticism ( Quintessenz , Aither )
 Base number in ancient Egypt in the sense of ( pyramid ) and in multiples of 5, probably symbolic for the human body: five (four plus one) limbs, fingers, toes.
 The pentagram (fivepointed star) is ascribed a magical peculiarity.
 Numerical value of the mileso Greek number epsilon .
 Prescribed number of legs (possibly with castors) for office swivel chairs in order to avoid accidental tipping, as the contact radius around a (regular) pentagon no longer fluctuates as much as in a square.
 Roman numeral V
 Holy number among the Manichaeans

6th
 Number of quarks (up, down, charm, strange, top and bottom).
 The hexahedron (cube) is one of the platonic solids .
 The Star of David , an example of a hexagram , is a hexagonal star.
 Numerical value of the Milesian Greek number stigma .
 The symmetry of the snowflake is sixfold. Because of the special structure of the water molecules, only angles of 60 ° or 120 ° are possible.

7th
 Number of days in a week .
 Often used in fairy tales :
 The wolf and the seven young goats
 Snow White and the Seven Dwarfs
 Thumbnail and the Seven Mile Boots
 The seven Ravens
 The seven Swabians
 Seven beautiful
 The brave little tailor killed "seven [flies] in one go"
 Numerical value of the Milesian Greek number zeta .
 Number of crystal systems of the threedimensional lattice.
 In Christianity the 7 symbolizes completeness.
 Number of days of the creation cycle
 Noah was to take seven pairs of pure animals into the ark .
 In Revelation : seven churches, seals , trumpets, angels, plagues, bowls, sevenheaded beast.
 In Catholicism 7 sacraments , 7 main virtues (three divine and four cardinal virtues), 7 root sins , (rarely) 7 heavenly virtues (countervirtues to the root sins), 7 gifts of the Holy Spirit , 7 each spiritual and physical works of mercy , 7 classical levels of the Ordination office (without the superordinate and extraordinary episcopal ordination): Ostiarier, lecturer, exorcist, acolyte, subdeacon, deacon and priest (today limited to religious groups)
 Number of celestial bodies visible to the naked eye that appear to be movable from the earth as the central point ( sun , moon , Mercury , Venus , Mars , Jupiter , Saturn )
 Miller's number describes the fact established by George A. Miller that a person can only hold 7 ± 2 information units (chunks) in shortterm memory at the same time
 Cloud seven describes as a winged word a heavenly feeling of happiness in matters of love (in English Cloud 9)

8th
 Lucky number in China
 Holy number in India
 Numerical value of the Milesian Greek number Eta .
 In our solar system , eight planets orbit the sun.
 Language short code for the German syllable "Acht", z. B. "Good N8"
 Language short code for the English syllable "ight / ite / ate", as in "good n8" or "2 L8"
 in Christianity the number of supernatural abundance (compared to perfection 7): resurrection on the 8th day, 8 beatitudes

9
 Numerical value of the Milesian Greek number theta
 holy number of the Baha'i
 special number in Norse mythology , e.g. B. the number of nights that Odin hung wounded on the world tree and devised the runes
 Number of the Self in Satanism
 Emergency call channel in the CB radio on 27.065 MHz AM
 Number of supposed lives of a cat

9.8066500 (Follow A072915 in OEIS )
 (normalized) value of the acceleration due to gravity in m / s²  in practice often rounded to 9.81 or 9.8 or 10

10
 Basis of our number system ( decimal system )
 The Ten Commandments
 Number of fingers and toes
 The 10 is symbolic of earthly perfection
 Numerical value of the Milesian Greek number Iota
 In Christianity and Judaism , the 10 symbolizes completeness (but inferior to the 7).
 Roman numeral X
Until 100

11
 Smallest number of schnapps
 Foolish number in the Rhenish Carnival :
 Beginning of the carnival on 11.11. at 11 a.m. 11
 The Elferrat is the parliament of the foolish kingdom in Carnival, Mardi Gras and Mardi Gras
 The "soccer eleven": each team has eleven players on the field
 Formerly known as the "dirty dozen"
 Number (next to 12), which is not pronounced in decimal but still according to a historical twelve system with "eleven"; the decimal formulation would be "oneteen"

12
 Number of pentominos
 A dozen
 The basis of prehistoric payment systems
 A symbol of perfection
 In the Bible ...
 the 12 tribes of Israel and often references to them
 the 12 apostles of Jesus
 12 is the mean number of hours the sun shows itself during the day and the number of months of the year
 In music, an octave consists of 12 semitones
 There are 12 signs of the zodiac
 12 Olympic gods
 King Eurystheus gave Heracles 12 tasks ("Dodekathlos")
 12 inhabited islands of the Dodecanese
 12 stars on the European flag
 Number (next to 11), which is not pronounced in a decimal but still according to a historical twelve system with "twelve"; the decimal formulation would be "two thirteen"
 According to the old German spelling, it is traditionally the last written number. Today you can also write smaller numbers in digits and larger numbers.

13
 Unlucky number and / or lucky number
 The Wild Thirteen
 In German and in all Germanic languages first composite number (e.g. thirteen in English ), the numbers 11 and 12 have their own names (e.g. in English eleven and twelve ).

14th
 Number of stations on a way of the cross
 Chinese unlucky number (pronounced like "certain death" (without escape))
 Children's prayer "14 angels stand around me" (originally from Engelbert Humperdinck's opera Hansel and Gretel )
 The fourteen emergency helpers

15th
 15 minutes stand for ¼ hour
 Scoring for volleyball in the 5th and beach volleyball in the 3rd set (if there is at least 2 points difference to the opposing team)

16
 At sixteen, in many societies, you reach a preliminary stage of adulthood, for example the age of consent in Switzerland or the driver's license in the USA

17th
 Unlucky number in Italy
 According to Kabbalistic number mysticism , 17 corresponds to the numerical value of the Hebrew word טוב ("good")

18th
 The 18th birthday is the age of majority in most states
 For the Jews, for whom numbers are expressed by letters, the numerical value means 18 lives
 The Israelites had 18 minutes to leave Egypt
 The matzos for the Passach festival may not be made for more than 18 minutes
 Under neoNazis code number for "AH / Adolf Hitler", after the first and eighth letters of the alphabet

19th
 In Islam, the entrance to hell is guarded by 19 angels

20th
 Numerical value of the Milesian Greek number kappa

21st
 Number of points aimed for in the game of Black Jack or 17 and 4
 Scoring for beach volleyball in the 1st and 2nd set (with at least 2 points difference to the opposing team)
 Formerly the age of majority
 Sum of the eyes of a dice
 "Half the truth" as an allusion to the one described in The Hitchhiker's Guide to the Galaxy as an answer to the question about "life, the universe and all the rest" 42

22nd
 Number of letters in the Hebrew alphabet

23
 Plays a role in various conspiracy theories , u. a. as an alleged number of the Illuminati
 Smallest number of people with random birthdays who are more likely to have two birthdays on the same day than to all have birthdays on different days ( birthday problem )
 Humans ( homo sapiens ) have 23 pairs of chromosomes, with the 23rd pair also being the sexspecifying one.

24
 Number of hours in a day
 Number of books of the Tanakh
 Number of letters in the Greek alphabet

25th
 Anniversary number ; often referred to as the "Silver Jubilee ", e.g. B. " Silver Wedding " on the 25th wedding anniversary

26th
 Number of letters in the Latin alphabet

27
 Number of books of the New Testament

27,322:
 The number of days it takes for the moon to orbit the earth ( sidereal month )

28
 Under neoNazis code number for "Blood & Honor", after the second and eighth letters of the alphabet
 4 weeks have 28 days
 Number of days in February in the "normal" calendar year
 Number of letters in the Arabic alphabet

29
 Number of days in February in the leap year

29.530588 ...
 Days, synodic period of the moon (after that the moon phases are repeated)

30th
 Number of days in April, June, September, and November
 Numerical value of the Milesian Greek number lambda
 Number of days in a month for the interest calculation (in Germany )

31
 Number of days in January, March, May, July, August, October, and December
 32

36
 Number of cards in Jassen

37
 Number of numbers to bet on in French roulette

39
 Number of books of the Old Testament in the German Protestant Bible editions

40
 Stands as a symbol for testing, probation, initiation, death
 Ali Baba and the 40 thieves
 Minimum age of the Federal President in Germany
 In the Bible ...
 the (actual) flood lasted 40 days
 was Isaac 40 years old, when he Rebekah took to wife
 was Esau 40 years old, when he took to wife Judith
 Moses was with God 40 days and 40 nights to receive the law
 the Israelite exodus from Egypt lasted 40 years
 was Joshua 40 when he was sent out by Moses the country " Kadesh Barnea to spy out"
 was Ishbosheth 40 when he became king over Israel
 King David ruled Israel for 40 years, King Joash also ruled for 40 years
 Elijah fasted forty days and nights and went to Horeb during that time
 fasted Jesus 40 days in the desert (hence the duration of the course, far easier fasting after the church) and was from the devil tried
 the time between the resurrection and the ascension of Jesus lasted 40 days (hence the feast date)
 The plague quarantine lasted 40 days
 Number of cards in the Doppelkopf (version "without Luschen") and in an Ecuadorian card game ("Cuarenta" = German "Forty")
 Numerical value of the Milesian Greek number My

42
 In the novel The Hitchhiker's Guide to the Galaxy , the number 42 appears as an answer to the question about "life, the universe and all the rest"

43
 Atomic number of the first chemical element without stable isotopes ( technetium )
 Spanish liquor Licor 43 (Cuarenta Y Tres)

46
 Typical number of human chromosomes
 Number of books of the (Catholic) Old Testament
 according to the Bible ( Joh 2.20 EU ) the duration of the construction of the Herodian temple
 Numerical value of the name Adam (occurs as an interpretation of the aforementioned Bible passage)

48
 Number of cards in the Doppelkopf (version "with nines")

50
 Anniversary number ; often referred to as the "Golden Jubilee ", e.g. B. “ Golden Wedding ” on the 50th wedding anniversary
 The Jewish weekly festival Shavuot is celebrated 50 days, i.e. seven weeks plus one day after the Passover , based on Pentecost (Greek: Pentekoste) on the fiftieth day after Easter (including Easter)
 Numerical value of the Milesian Greek number Ny
 Roman numeral L
 52

52.1775
 Average number of weeks in a year taking into account leap years

53
 Herbie's starting number in the film "A great Beetle" (VW)
 Book title “53 Eine Claimung” (2009) by Thomas Trenkler, traces the number 53

55
 Good luck, radio operator

60
 One shock, five dozen
 Highest score that can be achieved with a single throw while playing darts
 Number of carbon atoms in the simplest fullerene C _{60}
 Numerical value of the Milesian Greek number Xi

62
 Number of months in a Yuga period

64
 Number of hexagrams in Yijing
 Number of fields on a chessboard

66
 Number of books of the Bible in the German Protestant Bible editions
 In the Englishspeaking world, the opening quotation marks (“) are sometimes jokingly called 66 due to their shape  analogous to 99 for the closing quotation marks (”)
 for one of the first continuous road connections in the USA, Route 66

69
 A sexual position in which both partners simultaneously satisfy each other orally

70
 Numerical value of the Milesian Greek number omicron
 often simplifying for the number of peoples according to the Bible (actually 72)
 72

73
 Number of books in the Catholic Bible
 Many greetings, radio operator code

75
 Fax extension, (in Austria) frequently used telephone extension for fax connection in an office

80
 Number of elements with at least one stable isotope
 Numerical value of the Milesian Greek number Pi

81
 Tetragrams in the IChing = number of verses from Laotse's " Tao te king "
 Abbreviation for the Hells Angels , since H is the eighth letter and A is the first letter of the alphabet
 82

88
 Literally: "No matter how ~"
 Under neoNazis code number for "HH" / Heil Hitler, since H is the eighth letter of the alphabet
 Radio language: "love and kisses"
 In China, abbreviation for "ByeBye" because of the pronunciation of the numbers

90
 Right angle , measured in degrees
 Numerical value of the Milesian Greek number Qoppa

97
 Often chosen as an example for any number; many libraries stamp page 97

99
 Last whole number before the hundred, is often used as a literary element in the sense of “one before completeness”, for example in Nena's 99 balloons, the song “99 bottles of beer” and 99 names of Allah
 Number of months in an octahedral period
 Get out of here, radio operator

100
 Right angle , measured in gons
 Boiling point of water in degrees Celsius under normal conditions
 Numerical value of the Milesian Greek number Rho
 Roman numeral C
Up to 1000

101
 Room 101 appears in several novels and films, for example in the novel 1984 by George Orwell , Matrix , A Beautiful Mind , Kill Bill  Volume 2 etc.
 Taipei 101  nickname of the Taipei Financial Center (Chinese 台北 101, Táiběi yīlíngyī), a skyscraper in Taipei, Taiwan.
 Postcode of the "old town" in Reykjavík and title of the film 101 Reykjavík
 Title of a concert film by DA Pennebaker about Depeche Mode
 Number of Dalmatians in the book Hundertundein Dalmatiner or its Disney film adaptation 101 Dalmatians
 In the USA the term for a basic course and, referring to it, the term for basic knowledge in a discipline.
 108
 110

111
 Sometimes used as a direct dialing in telephone exchange systems for telephone switching because it can be dialed quickly with a rotary dial

112
 Euro (telephone) emergency call since 1991, with special functions on the GSM mobile phone
 Emergency number for the fire brigade in Germany
 114

115
 Uniform authority telephone number in parts of Germany

117
 Emergency number in Switzerland

118
 Number of chemical elements currently (2015) detected

122
 Emergency number for fire brigade in Austria (landline and GSM mobile networks)

128
 Number of characters in a 7bit code ( ASCII )

133
 Emergency number for the police in Austria (landline and GSM mobile networks)

137.035 999 76 (50)
 Reciprocal value of the fine structure constant

144
 1 Gros
 12 dozen
 The height of the wall of the New Jerusalem is 144 cubits in Revelation. 21.17
 Emergency number for rescue in Austria and Switzerland (landline and GSM mobile networks)

147
 Maximum break , but not the highest possible break in snooker

150
 Number of Psalms

153
 Christian number symbolism: according to the Gospel of John ( Joh 21,11 EU ) number of fish caught by Peter as a symbol for all of humanity
 According to the numerology of Pythagoras , the sum of all species in nature is 153

156
 Product of a dozen (12) and a "dozen of the devil" (13)

165
 Number of cards in Samba Canasta

168
 Number of hours in a calendar week

170
 Highest possible finish with darts in "DoubleOut" mode

175
 Until the early 1980s, it was a code word for homosexuals , alluding to Section 175, which at the time was still in the German Criminal Code  StGB  and which sometimes made homosexuality a criminal offense.

187
 Stands for murder or death threat; comes from the USAmerican police, which codes under the abbreviation '187' murder cases

200
 Numerical value of the Milesian Greek number sigma

212
 Boiling point of water in degrees Fahrenheit under normal conditions

235
 Number of months in Meton's calendar cycle

256
 Number of characters that can be represented with one byte

260
 Number of days in a tonalamatl

300
 Numerical value of the Milesian Greek number tau

354
 Number of days in a lunar year ( )

360
 Number of days in a year for the interest calculation (in Germany )
 Numerical value of the full angle in degrees
 Number of months in the Islamic calendar cycle

365
 Number of days in the calendar year

365.24219 ... (Follow A155540 in OEIS )
 Duration of the tropical year (which determines the seasons) in days

366
 Number of days in the leap year

400
 Numerical value of the full angle in gon
 The civil Gregorian calendar repeats itself after 400 years (i.e. without the Easter date, but the same calendar date always falls on the same day of the week afterwards)
 Numerical value of the Milesian Greek number Ypsilon

420
 420, 4:20 or 4/20 (pronunciation fourtwenty) is a code word for regular cannabis use and is widely used to identify with cannabis culture

440
 Since 1939 the standard concert pitch valid in many countries has been fixed at 440 Hz

451
 Alleged autoignition temperature of paper in degrees Fahrenheit , in the novel Fahrenheit 451 by Ray Bradbury

500
 Greatest value of a euro banknote
 Numerical value of the Milesian Greek number Phi
 Roman numeral D.

532
 The Julian calendar repeats itself after 532 years
 555

600
 Numerical value of the Milesian Greek number Chi

613
 Commandments in the Torah

616
 In some old Bible manuscripts instead of the 666 in Revelation. 13.18

666
 Biblically the "number of the beast" or Antichrist (Rev. 13:18)
 Number of satanists and the devil

700
 Numerical value of the Milesian Greek number Psi

777
 Mystically / biblically the "divine number"; with the importance of absolute perfection

800
 Numerical value of the Milesian Greek number omega

888
 "Christ number", numerical value of the name Jesus (see also the meaning of the number 8 )

911
 Emergency number in North America
 911 also stands for the terrorist act of September 11, 2001 (9/11)

940
 Number of months in a Callipean cycle

969
 Age of Methuselah , the oldest man mentioned in the Bible in Genesis 1 ( Genesis , 5: 2127)

1000
 In the Bible in chapter 20 of Revelation, Millennial Kingdom of Christ; also in National Socialist rhetoric
 Roman numeral M
Up to 10,000

1,001
 Arabic magic number (for example "Tales from the Arabian Nights ")

1,024
 Basis for the IEC binary prefixes . 1 KiB = byte = byte

1,080
 Number of chalakim , the time units of an hour in the Jewish calendar (about 3.33 s)

1,154
 Number of complete tiling of a regular decagon with the Penrose diamonds (36 °; 144 ° and 72 °; 108 °) and the Mukundi crown (concave pentagon (36 °; 108 °; 252 °; 108 °; 36 °)) , whereby two tiling are considered to be different if and only if they cannot be converted into one another by rotation

1,189
 Number of chapters in the Bible
 1,337

1,435
 Standard gauge of the railway in millimeters

1,440
 Number of minutes in a day
 Number of kilobytes on a normally formatted 3.5 ″ floppy disk

2,701
 Important number in the cryptonomicon

6,666
 Alleged number of Āyāt in the Quran

6,585.32
 Length of a Saros cycle in days  see eclipse cycles

7,200
 Number of days in a katun period in the Maya calendar

8,766
 Number of hours in a year according to the Julian calendar
 10,000
Up to 1 million

10,631
 Number of days in an Islamic period

12,000
 biblical : length, width and height of the New Jerusalem in Revelation. 21.16 are 12,000 stadia

18,980
 Is  the number of days in the Mayan calendar period

27,759
 Number of days in the Callipean cycle

31,169
 Number of verses in the Bible

44,760
 Number of Warriors by Reuben (1 Chr 5:18)

86,400
 Number of seconds in a day
 144,000

146.097
 Number of days in the 400year Gregorian calendar cycle

304.805
 Number of letters in the Torah

525,600
 Number of minutes in a year

604,800
 Number of seconds in a week
Up to 1 billion

1,048,576
 1 MiB = byte = byte

3,674,160
 Number of positions of a Rubik's cube of the size (pocket cube) that can be reached by manual rotation

3,447,360
 Number of years in the Jewish calendar cycle

5,700,000
 Number of years in the Gregorian Easter cycle (after that, Easter is always on the same date)

8,145,060
 Number of possibilities in the Swiss and Austrian number lottery "6 out of 45"; the probability of a "six" is 1 in 8,145,060

10,518,300
 Number of possible combinations for a player's card hand at Schafkopf

13,983,816
 Number of possible combinations in the German lottery "6 out of 49"

16,777,216
 ; Use in IT , e.g. B. the number of possible color gradations with 24 bit color depth

76.275.360
 Number of possibilities in the EuroMillions Lotto: 5 out of 50 numbers and 2 out of 9 stars

299,792,458
 The speed of light in a vacuum , defined in m / s
Over 1 billion

1,073,741,824
 1 GiB = byte = byte

3.101.788.170
 Number of DNA base pairs that encode human genetic information (≙ 740 MiB ), approximate value

3,735,928,559
 The numerical value results in the character string DEADBEEF in the hexadecimal system.

4,294,967,296
 Number of possible IP addresses according to the IPv4 protocol:

149,597,870,691
 Length of the astronomical unit (AU) in meters; Mean distance from earth to sun in meters

1,099,511,627,776
 1 TiB = byte = byte

2,753,294,408,504,640
 Number of all possible card distributions in the game of Skat

9,460,730,472,580,800
 One light year (in meters)

99,561,092,450,391,000
 Number of possible card distributions at Schafkopf

710,609,175,188,282,000 to 1
 The likelihood that Mikhail Gorbachev is the Antichrist . Calculated by Robert W. Faid and the Ig Nobel Prize 1993 awarded

18,446,744,073,709,551,615
 ( )
 Number of grains of wheat that Sissa ibn Dahir was supposed to receive from the Indian ruler Shihram for the invention of the game of chess , according to the wheat grain legend

43,252,003,274,489,856,000
 Number of positions of a Rubik's cube of the size that can be achieved by manual rotation

2,248,575,441,654,260,591,964
 Number of all possible card distributions with a double head with nines.

6,670,903,752,021,072,936,960
 Number of possible Sudoku puzzles ( )

6.022 140 76 · 10 ^{23}
 Avogadro constant , number of particles (atoms or molecules) per amount of substance ( mol )

60.176.864.903.260.346.841.600.000
 Number of possible starting positions (" key space ") of the EnigmaM4 , the cryptographically strongest Enigma cipher machine used in World War II

340,282,366,920,938,463,463,374,607,431,768,211,456
 Number of possible IP addresses according to the IPv6 protocol:

7,401,196,841,564,901,869,874,093,974,498,574,336,000,000,000
 ( )
 Number of positions of a Rubik's cube of the size ( Master Cube ) that can be reached by manual rotation

81,171,437,193,104,932,746,936,103,027,318,645,818,654,720,000
 ( )
 Number of possible Sudoku puzzles ( )

282,870,942,277,741,856,536,180,333,107,150,328,293,127,731,985,672,134,721,536,000,000,000,000,000
 ( )
 Number of positions of a Rubik's cube of the size ( Professor's Cube ) that can be reached by manual rotation

10 ^{100}
 A googol

19,500,551,183,731,307,835,329,126,754,019,748,794,904,992,692,043,434,567,152,132,912,323,232,706,135,469,180.065,278,712,755,853,360,682,328,551,719.137,311,299,993,600,000,000,000,000,000,000,000. 000,000,000,000
 ( )
 Number of positions of a Rubik's cube of the size ( VCube 7 ) that can be reached by manual rotation

10 ^{6000} 1
 (a number out of 6000 nines): the highest number that can be named with a classic number name (according to the long scale ). The next number ( , a 1 with 6000 zeros) should (again) be called “Millinillion”. The correct classic name would be many pages long.

10 ^{googol} =
 A googolplex

10 ^{Googolplex}
 A googolplexplex, also called googolplexian

10 ^{Googolplexplex}
 Googolplexplexplex

10 ^{Googolplexplexplex}
 Googolplexplexplexplex
literature
 Walter Kranzer: Mathematics is that interesting . Aulis Verlag , Cologne 1989, ISBN 3761408560 .
 F. Le Lionnais: Les Nombres Remarquables . Hermann, Paris 1983
 David Wells: The Lexicon of Numbers . Fischer, Frankfurt am Main 1991, ISBN 3596101352
Historical literature
 Wilhelm Heinrich Roscher : The number 50 in myth, cult, epic and tactics of the Hellenes and other peoples, especially the Semites. Leipzig 1917 (= treatises of the Saxon Society of Sciences: philologicalhistorical class , 33, 5).
See also
 Number names
 Mathematical constant
 Numerology
 Scales of the order of magnitude of various elementary sizes
 Interesting Numbers Paradox
Web links
Individual evidence
 ↑ Follow A004023 in OEIS
 ↑ Cohn, Jhon E., Square Fibonacci Numbers, etc., Bedford Col lege, University of London, London, NWI http://www.fq.math.ca/Scanned/22/cohn2.pdf
 ↑ Follow A046253 in OEIS
 ↑ spiegel.de
 ↑ nature.com
 ↑ State mathematics competition 2005/2006 Bavaria (accessed on June 19, 2010)
 ↑ Weisstein, Eric W .: Ramanujan Constant. Wolfram MathWorld, accessed December 4, 2015 .
 ↑ Kranzer: p. 144.
 ↑ Eric W. Weisstein : Skewes Number . In: MathWorld (English).
 ↑ Under favorable visibility conditions, Uranus and the minor planet (4) Vesta (asteroid) are also visible to the naked eye.
 ↑ From its discovery in 1930 to the redefinition of the term planet in 2006, Pluto was considered the ninth planet in our solar system.
 ↑ actually there are fewer, see kuranyolunda.com
 ↑ Mathematical semester reports Volume 56, Number 2, 177–185, doi: 10.1007 / s0059100900568 Mathematics in research and application Card distributions for Skat, Doppelkopf, Rummy and Canasta JensP. Bode and Arnfried Kemnitz