List of numbers

Encyclopedia : L : LI : LIS : List of numbers

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

Notable rational numbers

0	1	2	3	4	5	6	7	8	9
10	11	12	13	14	15	16	17	18	19
20	21	22	23	24	25	26	27	28	29
30	31	32	33	34	35	36	37	38	39
40	41	42	43	44	45	46	47	48	49
50	51	52	53	54	55	56	57	58	59
60	61	62	63	64	65	66	67	68	69
70	71	72	73	74	75	76	77	78	79
80	81	82	83	84	85	86	87	88	89
90	91	92	93	94	95	96	97	98	99
100	101	102	103	104	105	106	107	108	109
110	111	112	113	114	115	116	117	118	119
120	121	122	123	124	125	126	127	128	129
130	131	132	133	134	135	136	137	138	139
140	141	142	143	144	145	146	147	148	149
150	151	152	153	154	155	156	157	158	159
160	161	162	163	164	165	166	167	168	169
170	171	172	173	174	175	176	177	178	179
180	181	182	183	184	185	186	187	188	189
190	191	192	193	194	195	196	197	198	199
200	210	220	230	240	250	260	270	280	290
			300	400	500	600	700	800	900
	1000	2000	3000	4000	5000	6000	7000	8000	9000
10k-100k		100k-1M		1M-10M		10M-100M		100M-1000M		Larger #s

Powers of ten

See: Orders of magnitude (numbers)

Notable integers

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

• -40
• -1
• 211
• 221
• 222
• 223
• 227
• 228
• 229
• 233
• 235
• 239
• 241
• 242
• 251
• 255
• 256
• 257
• 263
• 269
• 273
• 284
• 360
• 420
• 451
• 496
• 555
• 666
• 720
• 786
• 911
• 1001
• 1089
• 1337
• 1729
• 3600
• 7744
• 8128
• 69105
• 142857
• 6000000

Named integers

• Graham's number
• Hardy-Ramanujan number
• Skewes' number
• Steinhaus' Mega and Megiston, Moser's number
• Number of the Beast

A prime number is a positive integer greater than one whose only positive divisors are one and itself.

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• List of prime numbers

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The first 100 prime numbers:

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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

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

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The first ten perfect numbers:

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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

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

This table demonstrates the standard English construction of small cardinal numbers up to ten million -- names for which all variants of English agree.

Value	Name	Alternate names
0	Zero	aught, cipher, cypher, naught, nil, none, nought, nowt, null, ought, oh, squat, zed, zilch, zip
1	One	ace, single, singleton, unary, unit, unity
2	Two	binary, brace, couple, couplet, distich, deuce, double, doubleton, duad, duality, duet, duo, dyad, pair, span, twain, twosome, yoke
3	Three	deuce-ace, leash, set, tercet, ternary, ternion, terzetto, threesome, tierce, trey, triad, trine, trinity, trio, triplet, troika
4	Four	foursome, quadruplet, quatern, quaternary, quaternion, 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, septuplet
8	Eight	octad, octet, octonary, octuplet, ogdoad, byte (in computing terms)
9	Nine	ennead
10	Ten	decade
11	Eleven
12	Twelve	dozen
13	Thirteen	baker's dozen, long dozen
14	Fourteen
15	Fifteen
16	Sixteen
17	Seventeen
18	Eighteen
19	Nineteen
20	Twenty	score
21	Twenty-one
22	Twenty-two
23	Twenty-three
24	Twenty-four	two dozen
25	Twenty-five
26	Twenty-six
27	Twenty-seven
28	Twenty-eight
29	Twenty-nine
30	Thirty
31	Thirty-one
40	Forty
50	Fifty	Half - century
60	Sixty	shock
70	Seventy	three-score and ten
80	Eighty	four-score
87	Eighty-seven	four-score and seven
90	Ninety
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, great hundred, (obsolete) hundred
121	One hundred [and] twenty-one
144	One hundred [and] forty-four	gross, dozen dozen, small gross
200	Two hundred
300	Three hundred
666	Six Hundred [and] sixty-six	Number of the Beast
1 000	One thousand	chiliad, grand (or G), thou, yard, kilo (often shortened to K)
1 001	One thousand [and] one
1 010	One thousand [and] ten
1 011	One thousand [and] eleven
1 024	One thousand [and] twenty-four	kilo (in computing) (often shortened to K)
1 100	One thousand one hundred
1 101	One thousand one hundred [and] one
1 728	One thousand seven hundred [and] twenty-eight	great gross, long gross, dozen gross
2 000	Two thousand
10 000	Ten thousand	myriad
100 000	One hundred thousand	lakh
1 000 000	One million	meg, mil, (often shortened to M)
1 048 576	One million forty-eight thousand five hundred [and] seventy-six	meg (in computing) (often shortened to M)
10 000 000	Ten million	crore

English names for powers of 10

This table compares the English names of cardinal numbers according to various American, British, and Continental European conventions. See names of numbers in English or English-language numerals for more information on naming numbers.

	Short scale	Long scale		Power
Value	American & Modern British	Traditional British (Nicolas Chuquet)	Continental European (Jacques Peletier du Mans)	of a thousand	of a million
100	One			1000-1+1	10000000
101	Ten
102	Hundred
103	Thousand			10000+1	10000000.5
106	Million			10001+1	10000001
109	Billion	Thousand million	Milliard	10002+1	10000001.5
1012	Trillion	Billion		10003+1	10000002
1015	Quadrillion	Thousand billion	Billiard	10004+1	10000002.5
1018	Quintillion	Trillion		10005+1	10000003
1021	Sextillion	Thousand trillion	Trilliard	10006+1	10000003.5
1024	Septillion	Quadrillion		10007+1	10000004
1027	Octillion	Thousand quadrillion	Quadrilliard	10008+1	10000004.5
1030	Nonillion	Quintillion		10009+1	10000005
1033	Decillion	Thousand quintillion	Quintilliard	100010+1	10000005.5
1036	Undecillion	Sextillion		100011+1	10000006
1039	Duodecillion	Thousand sextillion	Sextilliard	100012+1	10000006.5
1042	Tredecillion	Septillion		100013+1	10000007
1045	Quattuordecillion	Thousand septillion	Septilliard	100014+1	10000007.5
1048	Quindecillion	Octillion		100015+1	10000008
1051	Sexdecillion	Thousand octillion	Octilliard	100016+1	10000008.5
1054	Septendecillion	Nonillion		100017+1	10000009
1057	Octodecillion	Thousand nonillion	Nonilliard	100018+1	10000009.5
1060	Novemdecillion	Decillion		100019+1	100000010
1063	Vigintillion	Thousand decillion	Decilliard	100020+1	100000010.5
1066	Unvigintillion	Undecillion		100021+1	100000011
1069	Duovigintillion	Thousand undecillion	Undecilliard	100022+1	100000011.5
1072	Trevigintillion	Duodecillion		100023+1	100000012
...	...	...		...	...
1093	Trigintillion	Thousand quindecillion	Quindecilliard	100030+1	100000015.5
...	...	...		...	...
10120	Novemtrigintillion	Vigintillion		100039+1	100000020
10123	Quadragintillion	Thousand vigintillion	Vigintilliard	100040+1	100000020.5
...	...	...		...	...
10153	Quinquagintillion	Thousand duovigintillion	Duovigintilliard	100050+1	100000025.5
...	...	...		...	...
10180	Novemquinquagintillion	Trigintillion		100059+1	100000030
10183	Sexagintillion	Thousand trigintillion	Trigintilliard	100060+1	100000030.5
...	...	...		...	...
10213	Septuagintillion	Thousand quintrigintillion	Quintrigintilliard	100070+1	100000035.5
...	...	...		...	...
10240	Novemseptuagintillion	Quadragintillion		100079+1	100000040
10243	Octogintillion	Thousand quadragintillion	Quadragintilliard	100080+1	100000040.5
...	...	...		...	...
10273	Nonagintillion	Thousand quinquadragintillion	Quinquadragintilliard	100090+1	100000045.5
...	...	...		...	...
10300	Novemnonagintillion	Quinquagintillion		100099+1	100000050
10303	Centillion	Thousand quinquagintillion	Quinquagintilliard	1000100+1	100000050.5
...		...		...	...
10360		Sexagintillion		1000119+1	100000060
10420		Septuagintillion		1000139+1	100000070
10480		Octogintillion		1000159+1	100000080
10540		Nonagintillion		1000179+1	100000090
10600		Centillion		1000199+1	1000000100
10603	ducentillion	Thousand Centillion	Centilliard	1000200+1	1000000100.5

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

Proposed systematic names for powers of 10

Gillion system

As proposed by Russ Rowlett, based on Greek-derived numerical prefixes:

Value Name 103 Thousand 106 Million 109 Gillion 1012 Tetrillion 1015 Pentillion 1018 Hexillion 1021 Heptillion 1024 Oktillion 1027 Ennillion 1030 Dekillion

Value Name 1033 Hendekillion 1036 Dodekillion 1039 Trisdekillion 1042 Tetradekillion 1045 Pentadekillion 1048 Hexadekillion 1051 Heptadekillion 1054 Oktadekillion 1057 Enneadekillion 1060 Icosillion

Value Name 1063 Icosihenillion 1066 Icosidillion 1069 Icositrillion 1072 Icositetrillion 1075 Icosipentillion 1078 Icosihexillion 1081 Icosiheptillion 1084 Icosioktillion 1087 Icosiennillion 1090 Triacontillion

Myriad system

Proposed by Donald E. Knuth: ^}] | align="center" | Quadragintyllion |- | [^}] | align="center" | Quinquagintyllion |- | [^}] | align="center" | Sexagintyllion |- | [^}] | align="center" | Septuagintyllion |- | [^}] | align="center" | Octogintyllion |- | [^}] | align="center" | Nonagintyllion |- | [^}] | align="center" | Centillion |- | [^}] | align="center" | Millyllion |- | [^}] | align="center" | Myryllion |- |}

Googol and others

^}] | Googolplex |- | 10^-N | N-minex |- | 10^N | N-plex |- |}

This is a table of English names for positive rational numbers less than 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(\right)], nine seventy-fifths [\left( \right)], six fiftieths [\left(\right)], twelve hundredths [\left(\right)], twenty-four two-hundredths [\left(\right)], etc.

- 1} \over 2] | 0.618 033 988 749 894 848 204 586 834 366... | Golden ratio conjugate [\left(\hat\phi\right)], reciprocal of and one less than the golden ratio. |- | align="center" | [\sqrt[12]] | 1.059 463 094 359 295 264 561 825 294 946... | Twelfth root of two.
Proportion between the frequencies of adjacent semitones in the equal temperament scale. |- | align="center" | [\sqrt[3]+\frac\sqrt}}+\sqrt[3]-\frac\sqrt}}] | 1.324 717 957 244 746 025 960 908 854 478... | Plastic number. |- | align="center" | [\sqrt] | 1.414 213 562 373 095 048 801 688 724 210... | [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). |- | align="center" | [ + 1} \over 2] | 1.618 033 988 749 894 848 204 586 834 366... | Golden ratio [\left(\phi\right)]. |- | align="center" | [\sqrt] | 1.732 050 807 568 877 193 176 604 123 437... | [2 \sin 60^\circ = 2 \cos 30^\circ]
Square root of three a.k.a. the measure of the fish.
Length of the diagonal of a cube with edge length 1.
Length of the diagonal of a [1 \times \sqrt] rectangle.
Altitude of an equilateral triangle with side length 2.
Twice the altitude of an equilateral triangle with side length 1.
Altitude of a regular hexagon with side length 1 and diagonal length 2. |- | align="center" | [\sqrt] | 2.236 067 977 499 789 805 051 477 742 381... | Square root of five.
Length of the diagonal of a [1 \times 2] rectangle.
Length of the diagonal of a [\sqrt \times \sqrt] rectangle.
Length of the diagonal of a [1 \times \sqrt \times \sqrt] rectangular box. |- | align="center" | [\sqrt + 1] | 2.414 213 562 373 095 048 801 688 724 210... | Silver ratio [\left(\delta_S\right)]. |- | align="center" | [\sqrt] | 2.449 489 742 783 177 881 335 632 264 381... | [\sqrt \cdot \sqrt] = area of a [\sqrt \times \sqrt] rectangle.
Length of the diagonal of a [1 \times 1 \times 2] rectangular box.
Length of the diagonal of a [1 \times \sqrt] rectangle.
Length of the diagonal of a [2 \times \sqrt] rectangle.
Length of the diagonal of a [\sqrt \times \sqrt] rectangle. |- | align="center" | [\sqrt] | 2.645 751 311 064 590 716 171 096 573 817... | Length of the diagonal of a [1 \times 2 \times \sqrt] rectangular box.
Length of the diagonal of a [1 \times \sqrt] rectangle.
Length of the diagonal of a [2 \times \sqrt] rectangle.
Length of the diagonal of a [\sqrt \times \sqrt] rectangle. |- | align="center" | [\sqrt] | 2.828 427 124 746 190 290 949 243 717 478... | [2 \sqrt]
Volume of a cube with edge length [\sqrt].
Length of the diagonal of a [2 \times 2] rectangle.
Length of the diagonal of a [1 \times \sqrt] rectangle.
Length of the diagonal of a [\sqrt \times \sqrt] rectangle.
Length of the diagonal of a [\sqrt \times \sqrt] rectangle. |- | align="center" | [\sqrt] | 3.162 277 660 168 379 522 787 063 251 599... | [\sqrt \cdot \sqrt] = area of a [\sqrt \times \sqrt] rectangle.
Length of the diagonal of a [1 \times 3] rectangle.
Length of the diagonal of a [2 \times \sqrt] rectangle.
Length of the diagonal of a [\sqrt \times \sqrt] rectangle.
Length of the diagonal of a [\sqrt \times \sqrt] rectangle. |- | align="center" | [\sqrt] | 3.316 624 790 355 399 849 114 932 736 671 | Length of the diagonal of a [1 \times 1 \times 3] rectangular box.
Length of the diagonal of a [1 \times \sqrt] rectangle.
Length of the diagonal of a [2 \times \sqrt] rectangle.
Length of the diagonal of a [3 \times \sqrt] rectangle.
Length of the diagonal of a [\sqrt \times \sqrt] rectangle.
Length of the diagonal of a [\sqrt \times \sqrt] rectangle. |- | align="center" | [\sqrt] | 3.464 101 615 137 754 587 054 892 683 012... | [2 \sqrt]
Length of the diagonal of a cube with edge length 2.
Length of the diagonal of a [1 \times \sqrt] rectangle.
Length of the diagonal of a [2 \times \sqrt] rectangle.
Length of the diagonal of a [3 \times \sqrt] rectangle.
Length of the diagonal of a [\sqrt \times \sqrt] rectangle.
Length of the diagonal of a [\sqrt \times \sqrt] rectangle.
Length of the diagonal of a [\sqrt \times \sqrt] rectangle. |}

• Khinchin-Lévy constant: 1.186 569 110 4...[link]
• Napier's constant: e = 2.718 281 828 459 045 235 360 287 471 353 ...
• Pi: π = 3.141 592 653 589 793 238 462 643 383 279 ...

Suspected transcendentals:

• Euler-Mascheroni constant: γ = 0.577 215 664 901 532 860 606 512 090 082 ...
• Gauss-Kuzmin-Wirsing constant: 0.303 663 002 9...[link]
• Laplace limit: ε=0.662 743 419 3...[link]
• Khinchin's constant: 2.685 452 001...[link]
• Feigenbaum constants: δ = 4.6692 ... and α = 2.5029 ...

Algebraic

• Imaginary unit: [i = \sqrt]

Other hypercomplex numbers

• The quaternions
• The octonions
• The sedenions
• The dual numbers (with an infinitesimal)

• Infinity in general: [\infty]
• Aleph-null: [\aleph_0]
• Aleph-one: [\aleph_1]
• Beth-one: ([\beth_1]) is the cardinality of the continuum: [2^]

Numbers representing measured quantities

• Pair: 2
• Dozen: 12
• Baker's dozen: 13
• Score: 20
• Gross: 144
• Avogadro's number: N_A = [6.022... \times 10^]

Numbers without specific values

See placeholder names

Bases

• Base -3 (negaternary)
• Base -2 (negabinary)
• Base 1 (unary)
• Base 2 (binary)
• Base 3 (ternary or trinary, see also balanced ternary)
• Base 4 (quaternary)
• Base 5 (quinary)
• Base 6 (senary or heximal)
• Base 7 (septenary)
• Base 8 (octal)
• Base 9 (nonary)
• Base 10 (decimal)
• Base 12 (duodecimal or dozenal)
• Base 13 (tridecimal or tredecimal)
• Base 16 (hexadecimal)
• Base 20 (vigesimal)
• Base 24 (quadrovigesimal)
• Base 26 (hexavigesimal)
• Base 27 (septemvigesimal)
• Base 32
• Base 36 (hexatridecimal, sexatrigesimal or hexatrigesimal)
• Base 60 (sexagesimal)
• Base 64
• mixed radix
• Base φ (phinary)
• Base 2i (quater-imaginary)

See also positional systems of numeral system for bases which might not be listed here.

See also

• English-language numerals
• Numbers in various languages
• Floating point
• Fraction (mathematics)
• Interesting number paradox
• Large number
• List of prime numbers
• Mathematical constant
• Names of large numbers
• Negative number
• Number names
• Orders of magnitude (numbers)
• Ordinal number
• SI prefix
• Small number
• Surreal number
• Table of prime factors

Further reading

• Kingdom of Infinite Number: A Field Guide by Bryan Bunch, W.H. Freeman & Company, 2001. ISBN 0716744473

External links

• [A list of unusual properties for many of the first 1000 natural numbers]
• [Number Gossip - a searchable database of interesting properties for numbers upto 10000]
• [See how to write big numbers]
• [The MegaPenny Project - Visualizing big numbers]
• [About big numbers]
• [Robert P. Munafo's amazing 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

 

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