List of numbers
This is a list of articles about numbers (not about numerals).
Contents
 1 Rational numbers
 2 Irrational and suspected irrational numbers
 3 Hypercomplex numbers
 4 Transfinite numbers
 5 Numbers representing measured quantities
 6 Numbers representing physical quantities
 7 Numbers without specific values
 8 See also
 9 References
 10 Further reading
 11 External links
Rational numbers[edit]
A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a nonzero denominator q.^{[1]} Since q may be equal to 1, every integer is a rational number. The set of all rational numbers, often referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by a boldface Q (or blackboard bold , Unicode ℚ);^{[2]} it was thus denoted in 1895 by Giuseppe Peano after quoziente, Italian for "quotient".
Natural numbers[edit]
Natural numbers are those used for counting (as in "there are six (6) coins on the table") and ordering (as in "this is the third (3rd) largest city in the country"). In common language, words used for counting are "cardinal numbers" and words used for ordering are "ordinal numbers". There are infinitely many natural numbers.
(Note that the status of 0 is ambiguous. In set theory and computer science, 0 is considered a natural number; in number theory, it usually is not.)
Powers of ten (scientific notation)[edit]
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Integers[edit]
Notable integers[edit]
Integers that are notable for their mathematical properties or cultural meanings include:
 −40, the equal point in the Fahrenheit and Celsius scales.
 −1, the additive inverse of unity.
 0, the additive identity.
 1, the multiplicative identity.
 2, the base of the binary number system, used in almost all modern computers and information systems. Also notable as the only even prime number.
 3, significant in Christianity as the Trinity. Also considered significant in Hinduism (Trimurti, Tridevi).
 4, the first composite number, also considered an "unlucky number" in modern China due to its audible similarity to the word "Death."
 6, the first of the series of perfect numbers, whose proper factors sum to the number itself.
 7, considered a "lucky" number in Western cultures.
 8, considered a "lucky" number in Chinese culture.
 9, the first odd number that is composite.
 10, the number base for most modern counting systems.
 12, the number base for some ancient counting systems and the basis for some modern measuring systems. Known as a dozen.
 13, considered an "unlucky" number in Western superstition. Also known as a "Baker's Dozen".
 20, known as a score.
 28, the second perfect number.
 42, the "answer to the ultimate question of life, the universe, and everything" in the popular science fiction work The Hitchhiker's Guide to the Galaxy.
 60, the number base for some ancient counting systems, such as the Babylonians', and the basis for many modern measuring systems.
 69, the name of a sex position.
 86, a slang term that is used in the American popular culture as a transitive verb to mean throw out or get rid of.^{[3]}
 108, considered sacred by the Dharmic Religions. Approximately equal to the ratio of the distance from Earth to Sun and diameter of the Sun.
 144, a dozen times dozen, known as a gross.
 255, 2^{8} − 1, a Mersenne number and the smallest perfect totient number that is neither a power of three nor thrice a prime; it is also the largest number that can be represented using an 8bit unsigned integer.
 420, a codeterm that refers to the consumption of cannabis.
 496, the third perfect number.
 666, the Number of the Beast from the Book of Revelation.
 786, regarded as sacred in the Muslim Abjad numerology.
 1729, the Hardy–Ramanujan number, also known as the second taxicab number; that is, the smallest positive integer that can be written as the sum of two positive cubes in two different ways.^{[4]}
 5040, mentioned by Plato in the Laws as one of the most important numbers for the city. It is also the largest factorial (7! = 5040) that is also a highly composite number.
 8128, the fourth perfect number.
 65535, 2^{16} − 1, the maximum value of a 16bit unsigned integer.
 65537, 2^{16} + 1, the most popular RSA public key prime exponent in most SSL/TLS certificates on the Web/Internet.
 142857, the smallest base 10 cyclic number.
 8675309, Jenny's Number from Tommy Tutone's song 8675309/Jenny
 2147483647, 2^{31} − 1, the maximum value of a 32bit signed integer using two's complement representation.
 9814072356, the largest perfect power that contains no repeated digits in base ten.
 9223372036854775807, 2^{63} − 1, the maximum value of a 64bit signed integer using two's complement representation.
Named numbers[edit]
 Googol (10^{100}) and googolplex (10^{(10100)}) and googolplexian (10^{(10(10100))}) or 1 followed by a googolplex of zeros.
 Graham's number
 Moser's number
 Shannon number
 Hardy–Ramanujan number (1729)
 Skewes' number
 Kaprekar's constant (6174)
Prime numbers[edit]
A prime number is a positive integer which has exactly two divisors: 1 and itself.
The first 100 prime numbers are:
2  3  5  7  11  13  17  19  23  29 
31  37  41  43  47  53  59  61  67  71 
73  79  83  89  97  101  103  107  109  113 
127  131  137  139  149  151  157  163  167  173 
179  181  191  193  197  199  211  223  227  229 
233  239  241  251  257  263  269  271  277  281 
283  293  307  311  313  317  331  337  347  349 
353  359  367  373  379  383  389  397  401  409 
419  421  431  433  439  443  449  457  461  463 
467  479  487  491  499  503  509  521  523  541 
Highly composite numbers[edit]
A highly composite number (HCN) is a positive integer with more divisors than any smaller positive integer, they are often used in geometry, 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[edit]
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  8 128 
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 
Cardinal numbers[edit]
In the following tables, [and] indicates that the word and is used in some dialects (such as British English), and omitted in other dialects (such as American English).
Small numbers[edit]
This table demonstrates the standard English construction of small cardinal numbers up to one hundred million—names for which all variants of English agree.
Value  Name  Alternate names, and names for sets of the given size 

0  Zero  aught, cipher, cypher, donut, dot, duck, goose egg, love, nada, naught, nil, none, nought, nowt, null, ought, oh, squat, zed, zilch, zip, zippo 
1  One  ace, individual, single, singleton, unary, unit, unity 
2  Two  binary, brace, couple, couplet, distich, deuce, double, doubleton, duad, duality, duet, duo, dyad, pair, span, twain, twin, twosome, yoke 
3  Three  deuceace, leash, set, tercet, ternary, ternion, terzetto, threesome, tierce, trey, triad, trine, trinity, trio, triplet, troika, hattrick 
4  Four  foursome, quadruplet, quatern, quaternary, quaternity, quartet, tetrad 
5  Five  cinque, fin, fivesome, pentad, quint, quintet, quintuplet 
6  Six  half dozen, hexad, sestet, sextet, sextuplet, sise 
7  Seven  heptad, septet, septuple, walking stick 
8  Eight  octad, octave, octet, octonary, octuplet, ogdoad 
9  Nine  ennead 
10  Ten  deca, decade 
11  Eleven  onze, ounze, ounce, banker's dozen 
12  Twelve  dozen 
13  Thirteen  baker's dozen, long dozen^{[5]} 
14  Fourteen  
15  Fifteen  
16  Sixteen  
17  Seventeen  
18  Eighteen  
19  Nineteen  
20  Twenty  score 
21  Twentyone  long score^{[5]} 
22  Twentytwo  Deucedeuce 
23  Twentythree  
24  Twentyfour  two dozen 
25  Twentyfive  
26  Twentysix  
27  Twentyseven  
28  Twentyeight  
29  Twentynine  
30  Thirty  
31  Thirtyone  
32  Thirtytwo  
40  Forty  twoscore 
50  Fifty  halfcentury 
60  Sixty  threescore 
70  Seventy  threescore and ten 
80  Eighty  fourscore 
87  Eightyseven  fourscore and seven 
90  Ninety  fourscore and ten 
100  One hundred  centred, century, ton, short hundred 
101  One hundred [and] one  
110  One hundred [and] ten  
111  One hundred [and] eleven  
120  One hundred [and] twenty  long hundred,^{[5]} great hundred, (obsolete) hundred 
121  One hundred [and] twentyone  
144  One hundred [and] fortyfour  gross, dozen dozen, small gross 
200  Two hundred  
300  Three hundred  
400  Four hundred  
500  Five hundred  
600  Six hundred  
666  Six hundred [and] sixtysix  
700  Seven hundred  
777  Seven hundred [and] seventyseven  
800  Eight hundred  
900  Nine hundred  
1000  One thousand  chiliad, grand, G, thou, yard, kilo, k, millennium 
1001  One thousand [and] one  
1010  One thousand [and] ten  
1011  One thousand [and] eleven  
1024  One thousand [and] twentyfour  kibi or kilo in computing, see binary prefix (kilo is shortened to K, Kibi to Ki) 
1100  One thousand one hundred  Eleven hundred 
1101  One thousand one hundred [and] one  
1728  One thousand seven hundred [and] twentyeight  great gross, long gross, dozen gross 
2000  Two thousand  
3000  Three thousand  
10000  Ten thousand  myriad, wan (China) 
100000  One hundred thousand  lakh 
500000  Five hundred thousand  crore (Iranian) 
1000000  One million  Mega, meg, mil, (often shortened to M) 
1048576  One million fortyeight thousand five hundred [and] seventysix  Mibi or Mega in computing, see binary prefix (Mega is shortened to M, Mibi to Mi) 
10000000  Ten million  crore (Indian)(Pakistan) 
100000000  One hundred million  yi (China) 
English names for powers of 10[edit]
This table compares the English names of cardinal numbers according to various American, British, and Continental European conventions. See English numerals or names of large numbers for more information on naming numbers.
Short scale  Long scale  Power  

Value  American  British (Nicolas Chuquet) 
Continental European (Jacques Peletier du Mans) 
of a thousand  of a million 
10^{0}  One  1000^{−1+1}  1000000^{0}  
10^{1}  Ten  
10^{2}  Hundred  
10^{3}  Thousand  1000^{0+1}  1000000^{0.5}  
10^{6}  Million  1000^{1+1}  1000000^{1}  
10^{9}  Billion  Thousand million  Milliard  1000^{2+1}  1000000^{1.5} 
10^{12}  Trillion  Billion  1000^{3+1}  1000000^{2}  
10^{15}  Quadrillion  Thousand billion  Billiard  1000^{4+1}  1000000^{2.5} 
10^{18}  Quintillion  Trillion  1000^{5+1}  1000000^{3}  
10^{21}  Sextillion  Thousand trillion  Trilliard  1000^{6+1}  1000000^{3.5} 
10^{24}  Septillion  Quadrillion  1000^{7+1}  1000000^{4}  
10^{27}  Octillion  Thousand quadrillion  Quadrilliard  1000^{8+1}  1000000^{4.5} 
10^{30}  Nonillion  Quintillion  1000^{9+1}  1000000^{5}  
10^{33}  Decillion  Thousand quintillion  Quintilliard  1000^{10+1}  1000000^{5.5} 
10^{36}  Undecillion  Sextillion  1000^{11+1}  1000000^{6}  
10^{39}  Duodecillion  Thousand sextillion  Sextilliard  1000^{12+1}  1000000^{6.5} 
10^{42}  Tredecillion  Septillion  1000^{13+1}  1000000^{7}  
10^{45}  Quattuordecillion  Thousand septillion  Septilliard  1000^{14+1}  1000000^{7.5} 
10^{48}  Quindecillion  Octillion  1000^{15+1}  1000000^{8}  
10^{51}  Sexdecillion  Thousand octillion  Octilliard  1000^{16+1}  1000000^{8.5} 
10^{54}  Septendecillion  Nonillion  1000^{17+1}  1000000^{9}  
10^{57}  Octodecillion  Thousand nonillion  Nonilliard  1000^{18+1}  1000000^{9.5} 
10^{60}  Novemdecillion  Decillion  1000^{19+1}  1000000^{10}  
10^{63}  Vigintillion  Thousand decillion  Decilliard  1000^{20+1}  1000000^{10.5} 
10^{66}  Unvigintillion  Undecillion  1000^{21+1}  1000000^{11}  
10^{69}  Duovigintillion  Thousand undecillion  Undecilliard  1000^{22+1}  1000000^{11.5} 
10^{72}  Trevigintillion  Duodecillion  1000^{23+1}  1000000^{12}  
10^{75}  Quattuorvigintillion  Thousand duodecillion  Duodecilliard  1000^{24+1}  1000000^{12.5} 
10^{78}  Quinvigintillion  Tredecillion  1000^{25+1}  1000000^{13}  
10^{81}  Sexvigintillion  Thousand tredecillion  Tredecilliard  1000^{26+1}  1000000^{13.5} 
10^{84}  Septenvigintillion  Quattuordecillion  1000^{27+1}  1000000^{14}  
10^{87}  Octovigintillion  Thousand quattuordecillion  Quattuordecilliard  1000^{28+1}  1000000^{14.5} 
10^{90}  Novemvigintillion  Quindecillion  1000^{29+1}  1000000^{15}  
10^{93}  Trigintillion  Thousand quindecillion  Quindecilliard  1000^{30+1}  1000000^{15.5} 
10^{96}  Untrigintillion  Sexdecillion  1000^{31+1}  1000000^{16}  
10^{99}  Duotrigintillion  Thousand sexdecillion  Sexdecilliard  1000^{32+1}  1000000^{16.5} 
...  ...  ...  ...  ...  
10^{120}  Novemtrigintillion  Vigintillion  1000^{39+1}  1000000^{20}  
10^{123}  Quadragintillion  Thousand vigintillion  Vigintilliard  1000^{40+1}  1000000^{20.5} 
...  ...  ...  ...  ...  
10^{153}  Quinquagintillion  Thousand quinvigintillion  Quinvigintilliard  1000^{50+1}  1000000^{25.5} 
...  ...  ...  ...  ...  
10^{180}  Novemquinquagintillion  Trigintillion  1000^{59+1}  1000000^{30}  
10^{183}  Sexagintillion  Thousand trigintillion  Trigintilliard  1000^{60+1}  1000000^{30.5} 
...  ...  ...  ...  ...  
10^{213}  Septuagintillion  Thousand quintrigintillion  Quintrigintilliard  1000^{70+1}  1000000^{35.5} 
...  ...  ...  ...  ...  
10^{240}  Novemseptuagintillion  Quadragintillion  1000^{79+1}  1000000^{40}  
10^{243}  Octogintillion  Thousand quadragintillion  Quadragintilliard  1000^{80+1}  1000000^{40.5} 
...  ...  ...  ...  ...  
10^{273}  Nonagintillion  Thousand quinquadragintillion  Quinquadragintilliard  1000^{90+1}  1000000^{45.5} 
...  ...  ...  ...  ...  
10^{300}  Novemnonagintillion  Quinquagintillion  1000^{99+1}  1000000^{50}  
10^{303}  Centillion  Thousand quinquagintillion  Quinquagintilliard  1000^{100+1}  1000000^{50.5} 
...  ...  ...  ...  ...  
10^{360}  Cennovemdecillion  Sexagintillion  1000^{119+1}  1000000^{60}  
10^{420}  Cennovemtrigintillion  Septuagintillion  1000^{139+1}  1000000^{70}  
10^{480}  Cennovemquinquagintillion  Octogintillion  1000^{159+1}  1000000^{80}  
10^{540}  Cennovemseptuagintillion  Nonagintillion  1000^{179+1}  1000000^{90}  
10^{600}  Cennovemnonagintillion  Centillion  1000^{199+1}  1000000^{100}  
10^{603}  Ducentillion  Thousand centillion  Centilliard  1000^{200+1}  1000000^{100.5} 
There is no consistent and widely accepted way to extend cardinals beyond centillion (centilliard).
SI prefixes for powers of 10[edit]
Value  1000^{m}  SI prefix  Name  Binary prefix  1024^{m} = 2^{10m}  Value 

1000  1000^{1}  k  Kilo  Ki  1024^{1}  1 024 
1000000  1000^{2}  M  Mega  Mi  1024^{2}  1 048 576 
1000000000  1000^{3}  G  Giga  Gi  1024^{3}  1 073 741 824 
1000000000000  1000^{4}  T  Tera  Ti  1024^{4}  1 099 511 627 776 
1000000000000000  1000^{5}  P  Peta  Pi  1024^{5}  1 125 899 906 842 624 
1000000000000000000  1000^{6}  E  Exa  Ei  1024^{6}  1 152 921 504 606 846 976 
1000000000000000000000  1000^{7}  Z  Zetta  Zi  1024^{7}  1 180 591 620 717 411 303 424 
1000000000000000000000000  1000^{8}  Y  Yotta  Yi  1024^{8}  1 208 925 819 614 629 174 706 176 
Fractional numbers[edit]
This is a table of English names for nonnegative rational numbers less than or equal to 1, it also lists alternative names, but there is no widespread convention for the names of extremely small positive numbers.
Keep in mind that rational numbers like 0.12 can be represented in infinitely many ways, e.g. zeropointonetwo (0.12), twelve percent (12%), three twentyfifths (3/25), nine seventyfifths (9/75), six fiftieths (6/50), twelve hundredths (12/100), twentyfour twohundredths (24/200), etc.
Value  Fraction  Common names  Alternative names 

1  1/1  One  0.999..., Unity 
0.9  9/10  Nine tenths, [zero] point nine  
0.8  4/5  Four fifths, eight tenths, [zero] point eight  
0.7  7/10  Seven tenths, [zero] point seven  
0.6  3/5  Three fifths, six tenths, [zero] point six  
0.5  1/2  One half, five tenths, [zero] point five  
0.4  2/5  Two fifths, four tenths, [zero] point four  
0.333333...  1/3  One third  
0.3  3/10  Three tenths, [zero] point three  
0.25  1/4  One quarter, one fourth, twentyfive hundredths, [zero] point two five  
0.2  1/5  One fifth, two tenths, [zero] point two  
0.166666...  1/6  One sixth  
0.142857142857...  1/7  One seventh  
0.125  1/8  One eighth, onehundred[and]twentyfive thousandths, [zero] point one two five  
0.111111...  1/9  One ninth  
0.1  1/10  One tenth, [zero] point one  One perdecime, one perdime 
0.090909...  1/11  One eleventh  
0.09  9/100  Nine hundredths, [zero] point zero nine  
0.083333...  1/12  One twelfth  
0.08  2/25  Two twentyfifths, eight hundredths, [zero] point zero eight  
0.0625  1/16  One sixteenth, sixhundred[and]twentyfive tenthousandths, [zero] point zero six two five  
0.05  1/20  One twentieth, [zero] point zero five  
0.047619047619...  1/21  One twentyfirst  
0.045454545...  1/22  One twentysecond  
0.043478260869565217391304347...  1/23  One twentythird  
0.033333...  1/30  One thirtieth  
0.016666...  1/60  One sixtieth  One minute 
0.012345679012345679...  1/81  One eightyfirst  
0.01  1/100  One hundredth, [zero] point zero one  One percent 
0.001  1/1000  One thousandth, [zero] point zero zero one  One permille 
0.000277777...  1/3600  One thirtysix hundredth  One second 
0.0001  1/10000  One tenthousandth, [zero] point zero zero zero one  One myriadth, one permyria, one permyriad, one basis point 
0.00001  1/100000  One hundredthousandth  One lakhth, one perlakh 
0.000001  1/1000000  One millionth  One perion, one ppm 
0.0000001  1/10000000  One tenmillionth  One crorth, one percrore 
0.00000001  1/100000000  One hundredmillionth  One awkth, one perawk 
0.000000001  1/1000000000  One billionth (in some dialects)  One ppb 
0  0/1  Zero  Nil 
Irrational and suspected irrational numbers[edit]
Algebraic numbers[edit]
Expression  Approximate value  Notes 

√3/4  012701892219323381861585376 0.433  Area of an equilateral triangle with side length 1. 
√5 − 1/2  033988749894848204586834366 0.618  Golden ratio conjugate Φ, reciprocal of and one less than the golden ratio. 
√3/2  025403784438646763723170753 0.866  Height of an equilateral triangle with side length 1. 
^{12}√2  463094359295264561825294946 1.059  Twelfth root of two. Proportion between the frequencies of adjacent semitones in the equal temperament scale. 
3√2/4  660171779821286601266543157 1.060  The size of the cube that satisfies Prince Rupert's cube. 
^{3}√2  921049894873164767210607278 1.259  Cube root of two. Length of the edge of a cube with volume two. See doubling the cube for the significance of this number. 
—  577269034296391257099112153 1.303  Conway's constant, defined as the unique positive real root of a certain polynomial of degree 71. 
717957244746025960908854478 1.324  Plastic number, the unique real root of the cubic equation x^{3} = x + 1.  
√2  213562373095048801688724210 1.414  √2 = 2 sin 45° = 2 cos 45° Square root of two a.k.a. Pythagoras' constant. Ratio of diagonal to side length in a square. Proportion between the sides of paper sizes in the ISO 216 series (originally DIN 476 series). 
571231876768026656731225220 1.465  The limit to the ratio between subsequent numbers in the binary Lookandsay sequence.  
841768587626701285145288018 1.538  Altitude of a regular pentagon with side length 1.  
√17 − 1/2  552812808830274910704927987 1.561  The Triangular root of 2. 
√5 + 1/2  033988749894848204586834366 1.618  Golden ratio (φ), the larger of the two real roots of x^{2} = x + 1. 
477400588966922759011977389 1.720  Area of a regular pentagon with side length 1.  
√3  050807568877293527446341506 1.732  √3 = 2 sin 60° = 2 cos 30° Square root of three a.k.a. the measure of the fish. Length of the space diagonal of a cube with edge length 1. Length of the diagonal of a 1 × √2 rectangle. Altitude of an equilateral triangle with side length 2. Altitude of a regular hexagon with side length 1 and diagonal length 2. 
286755214161132551852564653 1.839  The Tribonacci constant. Appears in the volume and coordinates of the snub cube and some related polyhedra. It satisfies the equation x + x^{−3} = 2. 

√5  067977499789696409173668731 2.236  Square root of five. Length of the diagonal of a 1 × 2 rectangle. Length of the diagonal of a √2 × √3 rectangle. Length of the space diagonal of a 1 × √2 × √2 rectangular box. 
√2 + 1  213562373095048801688724210 2.414  Silver ratio (δ_{S}), the larger of the two real roots of x^{2} = 2x + 1. Altitude of a regular octagon with side length 1. 
√6  489742783178098197284074706 2.449  √2 · √3 = area of a √2 × √3 rectangle. Length of the space diagonal of a 1 × 1 × 2 rectangular box. Length of the diagonal of a 1 × √5 rectangle. Length of the diagonal of a 2 × √2 rectangle. Length of the diagonal of a square with side length √3. 
3√3/2  076113533159402911695122588 2.598  Area of a regular hexagon with side length 1. 
√7  751311064590590501615753639 2.645  Length of the space diagonal of a 1 × 2 × √2 rectangular box. Length of the diagonal of a 1 × √6 rectangle. Length of the diagonal of a 2 × √3 rectangle. Length of the diagonal of a √2 × √5 rectangle. 
√8  427124746190097603377448419 2.828  2√2 Volume of a cube with edge length √2. Length of the diagonal of a square with side length 2. Length of the diagonal of a 1 × √7 rectangle. Length of the diagonal of a √2 × √6 rectangle. Length of the diagonal of a √3 × √5 rectangle. 
√10  277660168379331998893544433 3.162  √2 · √5 = area of a √2 × √5 rectangle. Length of the diagonal of a 1 × 3 rectangle. Length of the diagonal of a 2 × √6 rectangle. Length of the diagonal of a √3 × √7 rectangle. Length of the diagonal of a square with side length √5. 
√11  624790355399849114932736671 3.316  Length of the space diagonal of a 1 × 1 × 3 rectangular box. Length of the diagonal of a 1 × √10 rectangle. Length of the diagonal of a 2 × √7 rectangle. Length of the diagonal of a 3 × √2 rectangle. Length of the diagonal of a √3 × √8 rectangle. Length of the diagonal of a √5 × √6 rectangle. 
√12  101615137754587054892683012 3.464  2√3 Length of the space diagonal of a cube with edge length 2. Length of the diagonal of a 1 × √11 rectangle. Length of the diagonal of a 2 × √8 rectangle. Length of the diagonal of a 3 × √3 rectangle. Length of the diagonal of a √2 × √10 rectangle. Length of the diagonal of a √5 × √7 rectangle. Length of the diagonal of a square with side length √6. 
Transcendental numbers[edit]
 (−1)^{i} = e^{−π} = 2139183... 0.043
 Liouville constant: c = 001000000000000000001000... 0.110
 Champernowne constant: C_{10} = 45678910111213141516... 0.123
 i^{i} = √e^{−π} = 879576... 0.207
 1/π = 309886183790671537767526745028724068919291480...^{[6]} 0.318
 1/e = 879441171442321595523770161460867445811131031...^{[6]} 0.367
 Prouhet–Thue–Morse constant: τ = 454033640... 0.412
 log_{10} e = 294481903251827651128918916605082294397005803...^{[6]} 0.434
 Omega constant: Ω = 1432904097838729999686622... 0.567
 Cahen's constant: c = 41054629... 0.643
 ln 2: 147180559945309417232121458... 0.693
 π/√18 = 0.7404... the maximum density of sphere packing in three dimensional Euclidean space according to the Kepler conjecture^{[7]}
 Gauss's constant: G = 6268... 0.834
 π/√12 = 0.9068..., the fraction of the plane covered by the densest possible circle packing^{[8]}
 e^{i} + e^{−i} = 2 cos 1 = 60461... 1.080
 π^{4}/90 = ζ(4) = 323...^{[9]} 1.082
 √2_{s}: 610469...^{[10]} 1.559
 log_{2} 3: 962501... (the logarithm of any positive integer to any integer base greater than 1 is either rational or transcendental) 1.584
 Gaussian integral: √π = 453850905516... 1.772
 Komornik–Loreti constant: q = 231650... 1.787
 Universal parabolic constant: P_{2} = 58714939... 2.295
 Gelfond–Schneider constant: √2^{√2} = 144143... 2.665
 e = 281828459045235360287471353... 2.718
 π = 592653589793238462643383279... 3.141
 ^{i}√i = √e^{π} = 477381... 4.810
 Tau, or 2π: τ = 185307179586..., The ratio of the 6.283circumference to a radius, and the number of radians in a complete circle^{[11]}^{[12]}
 Gelfond's constant: 69263277925... 23.140
 Ramanujan's constant: e^{π√163} = 537412640768743.99999999999925... 262
Suspected transcendentals[edit]
These are irrational numbers that are thought to be, but have not yet been proved to be, transcendental.
 Z(1): 305462867317734677899828925614672... −0.736
 HeathBrown–Moroz constant: C = 317641... 0.001
 Kepler–Bouwkamp constant: 9420448... 0.114
 MRB constant: 859... 0.187
 Meissel–Mertens constant: M = 4972128476427837554268386086958590516... 0.261
 Bernstein's constant: β = 1694990... 0.280
 Strongly carefree constant: 747...^{[13]} 0.286
 Gauss–Kuzmin–Wirsing constant: λ_{1} = 6630029...^{[14]} 0.303
 Hafner–Sarnak–McCurley constant: 2363719... 0.353
 Artin's constant: 9558136... 0.373
 Prime constant: ρ = 682509851111660248109622... 0.414
 Carefree constant: 249...^{[15]} 0.428
 S(1): 259147390354766076756696625152... 0.438
 F(1): 079506912768419136387420407556... 0.538
 Stephens' constant: 959...^{[16]} 0.575
 Euler–Mascheroni constant: γ = 215664901532860606512090082... 0.577
 Golomb–Dickman constant: λ = 32998854355087099293638310083724... 0.624
 Twin prime constant: C_{2} = 161815846869573927812110014... 0.660
 Copeland–Erdős constant: 711131719232931374143... 0.235
 Feller–Tornier constant: 317...^{[17]} 0.661
 Laplace limit: ε = 7434193... 0.662[1]
 Taniguchi's constant: 234...^{[18]} 0.678
 Continued Fraction Constant: C = 774657964007982006790592551...^{[19]} 0.697
 Embree–Trefethen constant: β* = 58... 0.702
 Sarnak's constant: 648...^{[20]} 0.723
 Landau–Ramanujan constant: 22365358922066299069873125... 0.764
 C(1): 89340037682282947420641365... 0.779
 1/ζ(3) = 907..., the probability that three random numbers have no 0.831common factor greater than 1.^{[7]}
 Brun's constant for prime quadruplets: B_{2} = 5883800... 0.870
 Quadratic class number constant: 513...^{[21]} 0.881
 Catalan's constant: G = 965594177219015054603514932384110774... 0.915
 Viswanath's constant: σ(1) = 9882487943... 1.131
 Khinchin–Lévy constant: 5691104... 1.186[2]
 ζ(3) = 056903159594285399738161511449990764986292..., also known as 1.202Apéry's constant, known to be irrational, but not known whether or not it is transcendental.^{[22]}
 Vardi's constant: E = 084735305... 1.264
 Glaisher–Kinkelin constant: A = 42712... 1.282
 Mills' constant: A = 37788386308069046... 1.306
 Totient summatory constant: 784...^{[23]} 1.339
 Ramanujan–Soldner constant: μ = 369234883381050283968485892027449493... 1.451
 Backhouse's constant: 074948... 1.456
 Favard constant: K_{1} = 79633... 1.570
 Erdős–Borwein constant: E = 695152415291763... 1.606
 Somos' quadratic recurrence constant: σ = 687949633594121296... 1.661
 Niven's constant: c = 211... 1.705
 Brun's constant: B_{2} = 160583104... 1.902
 Landau's totient constant: 596...^{[24]} 1.943
 exp(−W_{0}(−ln(^{3}√3))) = 05268028830..., the smaller solution to 3^{x} = x^{3} and what, when put to the root of itself, is equal to 3 put to the root of itself.^{[25]} 2.478
 Second Feigenbaum constant: α = 2.5029...
 Sierpiński's constant: K = 9817595792532170658936... 2.584
 Barban's constant: 536...^{[26]} 2.596
 Khinchin's constant: K_{0} = 452001... 2.685[3]
 Fransén–Robinson constant: F = 7702420... 2.807
 Murata's constant: 419...^{[27]} 2.826
 Lévy's constant: γ = 822918721811159787681882... 3.275
 Reciprocal Fibonacci constant: ψ = 885666243177553172011302918927179688905133731... 3.359
 Van der Pauw's constant: π/ln 2 = 36014182719380962...^{[28]} 4.532
 First Feigenbaum constant: δ = 4.6692...
Numbers not known with high precision[edit]
 The constant in the Berry–Esseen Theorem: 0.4097 < C < 0.4748
 Landau's constant: 0.4330 < B < 0.472
 Bloch's constant: 0.4332 < B < 0.4719
 Landau's constant: 0.5 < L < 0.544
 Landau's constant: 0.5 < A < 0.7853
 Grothendieck constant: 1.57 < k < 1.79
Hypercomplex numbers[edit]
Hypercomplex number is a traditional term for an element of a unital algebra over the field of real numbers.
Algebraic complex numbers[edit]
 Imaginary unit: i = √−1
 nth roots of unity: (ξ_{n})^{k} = cos (2π k/n) + i sin (2π k/n), while 0 ≤ k ≤ n−1, GCD(k, n) = 1
Other hypercomplex numbers[edit]
 The quaternions
 The octonions
 The sedenions
 The dual numbers (with an infinitesimal)
Transfinite numbers[edit]
Transfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite.
 Alephnull: ℵ_{0}: the smallest infinite cardinal, and the cardinality of ℕ, the set of natural numbers
 Alephone: ℵ_{1}: the cardinality of ω_{1}, the set of all countable ordinal numbers
 Bethone: ℶ_{1} the cardinality of the continuum 2^{ℵ0}
 ℭ or : the cardinality of the continuum 2^{ℵ0}
 omega: ω, the smallest infinite ordinal
Numbers representing measured quantities[edit]
Various terms have arisen to describe commonly used measured quantities.
 Pair: 2 (the base of the binary numeral system)
 Dozen: 12 (the base of the duodecimal numeral system)
 Baker's dozen: 13
 Score: 20 (the base of the vigesimal numeral system)
 Gross: 144 (= 12^{2})
 Great gross: 1728 (= 12^{3})
Numbers representing physical quantities[edit]
Physical quantities that appear in the universe are often described using physical constants.
 Avogadro constant: N_{A} = 1417930×10^{23} mol^{−1} 6.022
 Coulomb's constant: k_{e} = 551787368×10^{9} 8.987N·m^{2}/C^{2} (m/F)
 Electronvolt: eV = 17648740×10^{−19} J 1.602
 Electron relative atomic mass: A_{r}(e) = 5485799094323... 0.000
 Fine structure constant: α = 297352537650... 0.007
 Gravitational constant: G = 84×10^{−11} N·(m/kg)^{2} 6.673
 Molar mass constant: M_{u} = 0.001 kg/mol
 Planck constant: h = 0689633×10^{−34} J · s 6.626
 Rydberg constant: R_{∞} = 973731.56852773 m^{−1} 10
 Speed of light in vacuum: c = 792458 m/s 299
 Stefan–Boltzmann constant: σ = 400×10^{−8} W · m^{−2} · K^{−4} 5.670
Numbers without specific values[edit]
Many languages have words expressing indefinite and fictitious numbers—inexact terms of indefinite size, used for comic effect, for exaggeration, as placeholder names, or when precision is unnecessary or undesirable. One technical term for such words is "nonnumerical vague quantifier",^{[29]} such words designed to indicate large quantities can be called "indefinite hyperbolic numerals".^{[30]}
See also[edit]
References[edit]
 ^ Rosen, Kenneth (2007). Discrete Mathematics and its Applications (6th ed.). New York, NY: McGrawHill. pp. 105, 158–160. ISBN 9780072880083.
 ^ Rouse, Margaret. "Mathematical Symbols". Retrieved 1 April 2015.
 ^ "Eightysix – Definition of eightysix by MerriamWebster". merriamwebster.com. Archived from the original on 20130408.
 ^ Weisstein, Eric W. "Hardy–Ramanujan Number". Archived from the original on 20040408.
 ^ ^{a} ^{b} ^{c} Blunt, Joseph (1 January 1837). "The Shipmaster's Assistant, and Commercial Digest: Containing Information Useful to Merchants, Owners, and Masters of Ships". E. & G.W. Blunt – via Google Books.
 ^ ^{a} ^{b} ^{c} "The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 27.
 ^ ^{a} ^{b} "The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 29.
 ^ "The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 30.
 ^ "The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 33.
 ^ "Nick's Mathematical Puzzles: Solution 29". Archived from the original on 20111018.
 ^ "The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 69
 ^ Sequence A019692.
 ^ A065473
 ^ Weisstein, Eric W. "Gauss–Kuzmin–Wirsing Constant". MathWorld.
 ^ A065464
 ^ A065478
 ^ A065493
 ^ A175639
 ^ Weisstein, Eric W. "Continued Fraction Constant". Wolfram Research, Inc. Archived from the original on 20111024.
 ^ A065476
 ^ A065465
 ^ "The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 33
 ^ A065483
 ^ A082695
 ^ A166928
 ^ A175640
 ^ A065485
 ^ A163973
 ^ "Bags of Talent, a Touch of Panic, and a Bit of Luck: The Case of NonNumerical Vague Quantifiers" from Linguista Pragensia, Nov. 2, 2010 Archived 20120731 at Archive.is
 ^ Boston Globe, July 13, 2016: "The surprising history of indefinite hyperbolic numerals"
Further reading[edit]
 Kingdom of Infinite Number: A Field Guide by Bryan Bunch, W.H. Freeman & Company, 2001. ISBN 0716744473
External links[edit]
 The Database of Number Correlations: 1 to 2000+
 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 numbers
 Robert P. Munafo's Large Numbers page
 Different notations for big numbers – by Susan Stepney
 Names for Large Numbers, in How Many? A Dictionary of Units of Measurement by Russ Rowlett
 What's Special About This Number? (from 0 to 9999)