List of numbers

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This is a list of articles about numbers (not about numerals).

Rational numbers[edit]

Main article: Rational number

Natural numbers[edit]

Main article: Natural number
0123456789
10111213141516171819
20212223242526272829
30313233343536373839
40414243444546474849
50515253545556575859
60616263646566676869
70717273747576777879
80818283848586878889
90919293949596979899
100101102103104105106107108109
110111112113114115116117118119
120121122123124125126127128129
130131132133134135136137138139
140141142143144145146147148149
150151152153154155156157158159
160161162163164165166167168169
170171172173174175176177178179
180181182183184185186187188189
190191192193194195196197198199
200201202203204205206207208209
210211212213214215216217218219
220230240250260270280290
300400500600700800900
100020003000400050006000700080009000
100002000030000400005000060000700008000090000
100k–1M1M–10M10M–100M100M–1G1G–10G
Larger numbers

Powers of ten (scientific notation)[edit]

Integers[edit]

Main article: Integer

Notable integers[edit]

Other numbers that are notable for their mathematical properties or cultural meanings include:

Named integers[edit]


Prime numbers[edit]

Main article: Prime numbers

A prime number is a positive integer which has exactly two divisors: one and itself.

  2  3  5  7 11 13 17 19 23 29
 31 37 41 43 47 53 59 61 67 71
 73 79 83 89 97101103107109113
127131137139149151157163167173
179181191193197199211223227229
233239241251257263269271277281
283293307311313317331337347349
353359367373379383389397401409
419421431433439443449457461463
467479487491499503509521523541

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 (the seven values with more divisors than any lesser number than twice itself are in bold):

1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1 260, 1 680, 2 520, 5 040, 7 560

Perfect numbers[edit]

Main article: Perfect number

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

The first 10 perfect numbers:

16
228
3496
48 128
533 550 336
68 589 869 056
7137 438 691 328
82 305 843 008 139 952 128
92 658 455 991 569 831 744 654 692 615 953 842 176
10   191 561 942 608 236 107 294 793 378 084 303 638 130 997 321 548 169 216

Cardinal numbers[edit]

Main article: cardinal number

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.

ValueNameAlternate names, and names for sets of the given size
0Zeroaught, cipher, cypher, donut, goose egg, love, nada, naught, nil, none, nought, nowt, null, ought, oh, squat, zed, zilch, zip
1Oneace, individual, single, singleton, unary, unit, unity
2Twobinary, brace, couple, couplet, distich, deuce, double, doubleton, duad, duality, duet, duo, dyad, pair, span, twain, twin, twosome, yoke
3Threedeuce-ace, leash, set, tercet, ternary, ternion, terzetto, threesome, tierce, trey, triad, trine, trinity, trio, triplet, troika, hat-trick
4Fourfoursome, quadruplet, quatern, quaternary, quaternity, quartet, tetrad
5Fivecinque, fin, fivesome, pentad, quint, quintet, quintuplet
6Sixhalf dozen, hexad, sestet, sextet, sextuplet, sise
7Sevenheptad, septet, septuple
8Eightoctad, octave, octet, octonary, octuplet, ogdoad
9Nineennead
10Tendeca, decade
11Elevenonze, ounze, ounce
12Twelvedozen
13Thirteenbaker's dozen, long dozen[2]
14Fourteen
15Fifteen
16Sixteen
17Seventeen
18Eighteen
19Nineteen
20Twentyscore
21Twenty-onelong score[2]
22Twenty-twoDeuce-deuce
23Twenty-three
24Twenty-fourtwo dozen
25Twenty-five
26Twenty-six
27Twenty-seven
28Twenty-eight
29Twenty-nine
30Thirty
31Thirty-one
40Fortytwo-score
50Fiftyhalf-century
60Sixtythree-score
70Seventythree-score and ten
80Eightyfour-score
87Eighty-sevenfour-score and seven
90Ninety
100One hundredcentred, century, ton, short hundred
101One hundred [and] one
110One hundred [and] ten
111One hundred [and] eleven
120One hundred [and] twentylong hundred,[2] great hundred, (obsolete) hundred
121One hundred [and] twenty-one
144One hundred [and] forty-fourgross, dozen dozen, small gross
169One hundred [and] sixty-ninebaker's gross[citation needed]
200Two hundred
300Three hundred
400Four hundred
500Five hundred
600Six hundred
666Six hundred [and] sixty-sixNumber of the Beast
700Seven hundred
777Seven hundred [and] seventy-sevenNumber of Luck
800Eight hundred
900Nine hundred
1 000One thousandchiliad, grand, G, thou, yard, kilo, k, millennium
1 001One thousand [and] one
1 010One thousand [and] ten
1 011One thousand [and] eleven
1 024One thousand [and] twenty-fourkibi or kilo in computing, see binary prefix (kilo is shortened to K, Kibi to Ki)
1 100One thousand one hundredEleven hundred
1 101One thousand one hundred [and] one
1 728One thousand seven hundred [and] twenty-eightgreat gross, long gross, dozen gross
2 000Two thousand
3 000Three thousand
10 000Ten thousandmyriad, wan (China)
100 000One hundred thousandlakh
500 000Five hundred thousandcrore (Iranian)
1 000 000One millionMega, meg, mil, (often shortened to M)
1 048 576One million forty-eight thousand five hundred [and] seventy-sixMibi or Mega in computing, see binary prefix (Mega is shortened to M, Mibi to Mi)
10 000 000Ten millioncrore (Bhartia)
100 000 000One hundred millionyi (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 scaleLong scalePower
ValueAmericanBritish
(Nicolas Chuquet)
Continental European
(Jacques Peletier du Mans)
of a thousandof a million
100One1000−1+110000000
101Ten
102Hundred
103Thousand10000+110000000.5
106Million10001+110000001
109BillionThousand millionMilliard10002+110000001.5
1012TrillionBillion10003+110000002
1015QuadrillionThousand billionBilliard10004+110000002.5
1018QuintillionTrillion10005+110000003
1021SextillionThousand trillionTrilliard10006+110000003.5
1024SeptillionQuadrillion10007+110000004
1027OctillionThousand quadrillionQuadrilliard10008+110000004.5
1030NonillionQuintillion10009+110000005
1033DecillionThousand quintillionQuintilliard100010+110000005.5
1036UndecillionSextillion100011+110000006
1039DuodecillionThousand sextillionSextilliard100012+110000006.5
1042TredecillionSeptillion100013+110000007
1045QuattuordecillionThousand septillionSeptilliard100014+110000007.5
1048QuindecillionOctillion100015+110000008
1051SexdecillionThousand octillionOctilliard100016+110000008.5
1054SeptendecillionNonillion100017+110000009
1057OctodecillionThousand nonillionNonilliard100018+110000009.5
1060NovemdecillionDecillion100019+1100000010
1063VigintillionThousand decillionDecilliard100020+1100000010.5
1066UnvigintillionUndecillion100021+1100000011
1069DuovigintillionThousand undecillionUndecilliard100022+1100000011.5
1072TrevigintillionDuodecillion100023+1100000012
1075QuattuorvigintillionThousand duodecillionDuodecilliard100024+1100000012.5
1078QuinvigintillionTredecillion100025+1100000013
...............
1093TrigintillionThousand quindecillionQuindecilliard100030+1100000015.5
...............
10120NovemtrigintillionVigintillion100039+1100000020
10123QuadragintillionThousand vigintillionVigintilliard100040+1100000020.5
...............
10153QuinquagintillionThousand quinvigintillionQuinvigintilliard100050+1100000025.5
...............
10180NovemquinquagintillionTrigintillion100059+1100000030
10183SexagintillionThousand trigintillionTrigintilliard100060+1100000030.5
...............
10213SeptuagintillionThousand quintrigintillionQuintrigintilliard100070+1100000035.5
...............
10240NovemseptuagintillionQuadragintillion100079+1100000040
10243OctogintillionThousand quadragintillionQuadragintilliard100080+1100000040.5
...............
10273NonagintillionThousand quinquadragintillionQuinquadragintilliard100090+1100000045.5
...............
10300NovemnonagintillionQuinquagintillion100099+1100000050
10303CentillionThousand quinquagintillionQuinquagintilliard1000100+1100000050.5
............
10360Sexagintillion1000119+1100000060
10420Septuagintillion1000139+1100000070
10480Octogintillion1000159+1100000080
10540Nonagintillion1000179+1100000090
10600Centillion1000199+11000000100
10603DucentillionThousand centillionCentilliard1000200+11000000100.5

There is no consistent and widely accepted way to extend cardinals beyond centillion (centilliard).

Proposed systematic names for powers of 10[edit]

Myriad system[edit]

Proposed by Donald E. Knuth:

ValueNameNotation
100One1
101Ten10
102Hundred100
103Ten hundred1000
104Myriad1,0000
105Ten myriad10,0000
106Hundred myriad100,0000
107Ten hundred myriad1000,0000
108Myllion1;0000,0000
1012Myriad myllion1,0000;0000,0000
1016Byllion1:0000,0000;0000,0000
1024Myllion byllion1;0000,0000:0000,0000;0000,0000
1032Tryllion1'0000,0000;0000,0000:0000,0000;0000,0000
1064Quadryllion1'0000,0000;0000,0000:0000,0000;0000,0000'0000,0000;0000,0000:0000,0000;0000,0000
10128Quintyllion
10256Sextyllion
10512Septyllion
101024Octyllion
102048Nonyllion
104096Decyllion
108192Undecyllion
1016,384Duodecyllion
1032,768Tredecyllion
1065,536Quattuordecyllion
10131,072Quindecyllion
10262,144Sexdecyllion
10524,288Septendecyllion
101,048,576Octodecyllion
102,097,152Novemdecyllion
{10}^{\,\! 4\cdot 2^{20}}Vigintyllion
{10}^{\,\! 4\cdot 2^{30}}Trigintyllion
{10}^{\,\! 4 \cdot 2^{40}}Quadragintyllion
{10}^{\,\! 4 \cdot 2^{50}}Quinquagintyllion
{10}^{\,\! 4 \cdot 2^{60}}Sexagintyllion
{10}^{\,\! 4 \cdot 2^{70}}Septuagintyllion
{10}^{\,\! 4 \cdot 2^{80}}Octogintyllion
{10}^{\,\! 4 \cdot 2^{90}}Nonagintyllion
{10}^{\,\! 4 \cdot 2^{100}}Centyllion
{10}^{\,\! 4 \cdot 2^{1000}}Millyllion
{10}^{\,\! 4 \cdot 2^{10,000}}Myryllion
SI-derived[edit]
Value1000mSI prefixNameBinary prefix1024m=210mValue
1 00010001kKiloKi102411 024
1 000 00010002MMegaMi102421 048 576
1 000 000 00010003GGigaGi102431 073 741 824
1 000 000 000 00010004TTeraTi102441 099 511 627 776
1 000 000 000 000 00010005PPetaPi102451 125 899 906 842 624
1 000 000 000 000 000 00010006EExaEi102461 152 921 504 606 846 976
1 000 000 000 000 000 000 00010007ZZettaZi102471 180 591 620 717 411 303 424
1 000 000 000 000 000 000 000 00010008YYottaYi102481 208 925 819 614 629 174 706 176

Fractional numbers[edit]

This is a table of English names for positive 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. zero-point-one-two (0.12), twelve percent (12%), three twenty-fifths \left({3 \over 25}\right), nine seventy-fifths \left({9 \over 75} \right), six fiftieths \left({6 \over 50}\right), twelve hundredths \left({12 \over 100}\right), twenty-four two-hundredths \left({24 \over 200}\right), etc.

ValueFractionCommon namesAlternative names
11 \over 1One0.999..., Unity
0.99 \over 10Nine tenths, [zero] point nine
0.84 \over 5Four fifths, eight tenths, [zero] point eight
0.77 \over 10Seven tenths, [zero] point seven
0.63 \over 5Three fifths, six tenths, [zero] point six
0.51 \over 2One half, five tenths, [zero] point five
0.42 \over 5Two fifths, four tenths, [zero] point four
0.3 (333 333)...1 \over 3One third
0.33 \over 10Three tenths, [zero] point three
0.251 \over 4One quarter, one fourth, twenty-five hundredths, [zero] point two five
0.21 \over 5One fifth, two tenths, [zero] point two
0.16 (666 666)...1 \over 6One sixth
0.142 857 (142 857)...1 \over 7One seventh
0.1251 \over 8One eighth, one-hundred-[and-]twenty-five thousandths, [zero] point one two five
0.1 (111 111)...1 \over 9One ninth
0.11 \over 10One tenth, [zero] point oneOne perdecime, one perdime
0.090 (909 090)...1 \over 11One eleventh
0.099 \over 100Nine hundredths, [zero] point zero nine
0.083 (333 333)...1 \over 12One twelfth
0.082 \over 25Two twenty-fifths, eight hundredths, [zero] point zero eight
0.06251 \over 16One sixteenth, six-hundred-[and-]twenty-five ten-thousandths, [zero] point zero six two five
0.051 \over 20One twentieth, [zero] point zero five
0.047 619 (047 619)...1 \over 21One twenty-first
0.045 (454 545)...1 \over 22One twenty-second
0.043 478 260 869 565 217 3913 (043 478)...1 \over 23One twenty-third
0.03 (333 333)...1 \over 30One thirtieth
0.016 (666 666)...1 \over 60One sixtiethOne minute
0.012345679 (012345679)...1 \over 81One eighty-first
0.011 \over 100One hundredth, [zero] point zero oneOne percent
0.0011 \over 1000One thousandth, [zero] point zero zero oneOne permille
0.000 27 (777 777)...1 \over 3600One thirty-six hundredthOne second
0.000 11 \over 10000One ten-thousandth, [zero] point zero zero zero oneOne myriadth, one permyria, one permyriad, one basis point
0.000 011 \over 10^5One hundred-thousandthOne lakhth, one perlakh
0.000 0011 \over 10^6One millionthOne perion, one ppm
0.000 000 11 \over 10^7One ten-millionthOne crorth, one percrore
0.000 000 011 \over 10^8One hundred-millionthOne awkth, one perawk
0.000 000 0011 \over 10^9One billionth (in some dialects)One ppb
00 \over 1ZeroNil

Irrational and suspected irrational numbers[edit]

Main article: irrational number

Algebraic numbers[edit]

Main article: Algebraic number
ExpressionApproximate valueNotes
\frac{\sqrt{3}}{4}0.433 012 701 892 219 323 381 861 585 376Area of an equilateral triangle with side length 1.
{\sqrt{5} - 1} \over 20.618 033 988 749 894 848 204 586 834 366Golden ratio conjugate \Phi\,, reciprocal of and one less than the golden ratio.
\frac{\sqrt{3}}{2}0.866 025 403 784 438 646 763 723 170 753Altitude of an equilateral triangle with side length 1.
\sqrt[12]{2}1.059 463 094 359 295 264 561 825 294 946Twelfth root of two.
Proportion between the frequencies of adjacent semitones in the equal temperament scale.
\frac{3 \sqrt{2}}{4}1.060 660 171 779 821 286 601 266 543 157The size of the cube that satisfies Prince Rupert's cube.
\sqrt[3]{2}1.259 921 049 894 873 164 767 210 607 278Cube root of two.
Length of the edge of a cube with volume two. See doubling the cube for the significance of this number.
n/a1.303 577 269 034 296 391 257 099 112 153Conway's constant, defined as the unique positive real root of a certain polynomial of degree 71.
\sqrt[3]{\frac{1}{2}+\frac{1}{6}\sqrt{\frac{23}{3}}}+
\sqrt[3]{\frac{1}{2}-\frac{1}{6}\sqrt{\frac{23}{3}}}
1.324 717 957 244 746 025 960 908 854 478Plastic number, the unique real root of the cubic equation x^3=x+1\, .
\sqrt{2}1.414 213 562 373 095 048 801 688 724 210\sqrt{2} = 2 \sin 45^\circ = 2 \cos 45^\circ
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).
\frac{\sqrt{5+2+\sqrt{5}}}{2}1.538 841 768 587 626 701 285 145 288 018Altitude of a regular pentagon with side length 1.
\frac{\sqrt{17}-1}{2}1.561 552 812 808 830 274 910 704 927 987The Triangular root of 2.
{\sqrt{5} + 1} \over 21.618 033 988 749 894 848 204 586 834 366Golden ratio \left(\phi\right), the larger of the two real roots of x^2=x+1\, .
\frac{5}{4\sqrt{5-2\sqrt{5}}}1.720 477 400 588 966 922 759 011 977 389Area of a regular pentagon with side length 1.
\sqrt{3}1.732 050 807 568 877 293 527 446 341 506\sqrt{3} = 2 \sin 60^\circ = 2 \cos 30^\circ
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 \times \sqrt{2} rectangle.
Altitude of an equilateral triangle with side length 2.
Altitude of a regular hexagon with side length 1 and diagonal length 2.
\frac{1+\sqrt[3]{19+3\sqrt{33}}+\sqrt[3]{19-3\sqrt{33}}}{3}1.839 286 755 214 161 132 551 852 564 653The Tribonacci constant.
Used in the formula for the volume of the snub cube and properties of some of its dual polyhedrons.
It satisfies the equation x + x−3 = 2.
\sqrt{5}2.236 067 977 499 789 696 409 173 668 731Square root of five.
Length of the diagonal of a 1 \times 2 rectangle.
Length of the diagonal of a \sqrt{2} \times \sqrt{3} rectangle.
Length of the space diagonal of a 1 \times \sqrt{2} \times \sqrt{2} rectangular box.
\sqrt{2} + 12.414 213 562 373 095 048 801 688 724 210Silver ratio \left(\delta_S\right), the larger of the two real roots of x^2=2x+1\, .
Altitude of an regular octagon with side length 1.
\sqrt{6}2.449 489 742 783 178 098 197 284 074 706\sqrt{2} \cdot \sqrt{3} = area of a \sqrt{2} \times \sqrt{3} rectangle.
Length of the space diagonal of a 1 \times 1 \times 2 rectangular box.
Length of the diagonal of a 1 \times \sqrt{5} rectangle.
Length of the diagonal of a 2 \times \sqrt{2} rectangle.
Length of the diagonal of a square with side length \sqrt{3}.
\frac{3\sqrt{3}}{2}2.598 076 113 533 159 402 911 695 122 588Area of a regular hexagon with side length 1.
\sqrt{7}2.645 751 311 064 590 590 501 615 753 639Length of the space diagonal of a 1 \times 2 \times \sqrt{2} rectangular box.
Length of the diagonal of a 1 \times \sqrt{6} rectangle.
Length of the diagonal of a 2 \times \sqrt{3} rectangle.
Length of the diagonal of a \sqrt{2} \times \sqrt{5} rectangle.
\sqrt{8}2.828 427 124 746 190 097 603 377 448 4192 \sqrt{2}
Volume of a cube with edge length \sqrt{2}.
Length of the diagonal of a square with side length 2.
Length of the diagonal of a 1 \times \sqrt{7} rectangle.
Length of the diagonal of a \sqrt{2} \times \sqrt{6} rectangle.
Length of the diagonal of a \sqrt{3} \times \sqrt{5} rectangle.
\sqrt{10}3.162 277 660 168 379 331 998 893 544 433\sqrt{2} \cdot \sqrt{5} = area of a \sqrt{2} \times \sqrt{5} rectangle.
Length of the diagonal of a 1 \times 3 rectangle.
Length of the diagonal of a 2 \times \sqrt{6} rectangle.
Length of the diagonal of a \sqrt{3} \times \sqrt{7} rectangle.
Length of the diagonal of a square with side length \sqrt{5}.
\sqrt{11}3.316 624 790 355 399 849 114 932 736 671Length of the space diagonal of a 1 \times 1 \times 3 rectangular box.
Length of the diagonal of a 1 \times \sqrt{10} rectangle.
Length of the diagonal of a 2 \times \sqrt{7} rectangle.
Length of the diagonal of a 3 \times \sqrt{2} rectangle.
Length of the diagonal of a \sqrt{3} \times \sqrt{8} rectangle.
Length of the diagonal of a \sqrt{5} \times \sqrt{6} rectangle.
\sqrt{12}3.464 101 615 137 754 587 054 892 683 0122 \sqrt{3}
Length of the space diagonal of a cube with edge length 2.
Length of the diagonal of a 1 \times \sqrt{11} rectangle.
Length of the diagonal of a 2 \times \sqrt{8} rectangle.
Length of the diagonal of a 3 \times \sqrt{3} rectangle.
Length of the diagonal of a \sqrt{2} \times \sqrt{10} rectangle.
Length of the diagonal of a \sqrt{5} \times \sqrt{7} rectangle.
Length of the diagonal of a square with side length \sqrt{6}.

Transcendental numbers[edit]

Main article: Transcendental number

Suspected transcendentals[edit]

Numbers not known with high precision[edit]

Hypercomplex numbers[edit]

Main article: Hypercomplex number

Algebraic complex numbers[edit]

Other hypercomplex numbers[edit]

Transfinite numbers[edit]

Main article: Transfinite number

Numbers representing measured quantities[edit]

Numbers representing scientific quantities[edit]

Numbers without specific values[edit]

See also[edit]

Notes[edit]

  1. ^ http://mathworld.wolfram.com/Hardy-RamanujanNumber.html
  2. ^ a b c The shipmaster's assistant, and commercial digest
  3. ^ a b c "The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 27.
  4. ^ a b "The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 29.
  5. ^ "The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 30.
  6. ^ "The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 33.
  7. ^ http://www.qbyte.org/puzzles/p029s.html
  8. ^ OEISA163973
  9. ^ "The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 69
  10. ^ Sequence OEISA019692.
  11. ^ OEISA065473
  12. ^ Weisstein, Eric W., "Gauss-Kuzmin-Wirsing Constant", MathWorld.
  13. ^ OEISA065464
  14. ^ OEISA065478
  15. ^ OEISA065493
  16. ^ OEISA175639
  17. ^ http://mathworld.wolfram.com/ContinuedFractionConstant.html
  18. ^ OEISA065476
  19. ^ OEISA065465
  20. ^ "The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 33
  21. ^ OEISA065483
  22. ^ OEISA082695
  23. ^ OEISA166928
  24. ^ OEISA175640
  25. ^ OEISA065485

Further reading[edit]

External links[edit]