List of numbers

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

Rational numbers

Natural 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	201	202	203	204	205	206	207	208	209
210	211	212	213	214	215	216
		220	230	240	250	260	270	280	290
		300	400	500	600	700	800	900
1000	2000	3000	4000	5000	6000	7000	8000	9000
10000	20000	30000	40000	50000	60000	70000	80000	90000
100k–1M		1M–10M		10M–100M		100M–1G		1G–10G
Larger numbers

Powers of ten (scientific notation)

Main article: Orders of magnitude (numbers)

Integers

Notable integers

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

• −40, an equal point in the Fahrenheit and Celsius scales.
• −1
• 0, a number which quantifies a count or an amount of null size.
• 42, the Answer to the Ultimate Question of Life, the Universe, and Everything according to the Hitchhikers Guide to the Galaxy
• 112, emergency phone number in most European countries (following Directive 2002/22/EC - Universal Service Directive) and also standard on GSM mobile phones. 112 is used in Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Indonesia, Ireland, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Republic of Macedonia, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey, Ukraine and the United Kingdom (where it is used alongside the older 999 emergency services number).
• 255, 2⁸−1
• 496, a perfect number.
• 786, regarded as sacred by some Muslims although there is no such evidence in the Quran or Hadith.
• 911, the emergency phone number in the United States and Canada.
• 999, the emergency phone number in the United Kingdom.
• 1729, a taxicab number; the smallest number that can be written as the sum of two cubes in two different ways
• 142857, a base 10 cyclic number.
• 2147483647, 2³¹−1, the maximum number that a 32-bit signed integer can reach.
• 9814072356, the largest perfect power that contains no repeated digits

Named integers

• Graham's number
• Moser's number
• Shannon number
• Hardy-Ramanujan number
• Skewes' number
• Number of the Beast
• Leviathan number
• Kaprekar's constant

Prime numbers

Main article: List of prime numbers

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

The first 100 prime numbers:

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

Perfect numbers

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

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, and names for sets of the given size
0	Zero	aught, cipher, cypher, goose egg, love, nada, 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, snake eyes, span, twain, twosome, yoke
3	Three	deuce-ace, leash, set, tercet, ternary, ternion, terzetto, threesome, tierce, trey, triad, trine, trinity, trio, triplet, troika, hat-trick
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, octave, octet, octonary, octuplet, ogdoad
9	Nine	ennead
10	Ten	deca, decade, sawbuck
11	Eleven	onze, ounze, ounce
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	kibi or kilo in computing, see binary prefix (kilo is shortened to k, Kibi to Ki)
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
500 000	Five hundred thousand	crore (Iranian)
1 000 000	One million	Mega, meg, mil, (often shortened to M)
1 048 576	One million forty-eight thousand five hundred [and] seventy-six	Mibi or Mega in computing, see binary prefix (Mega is shortened to M, Mibi to Mi)
10 000 000	Ten million	crore (Indian)

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	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
1075	Quattuorvigintillion	...	...	100024+1	100000012.5
...	...	...		...	...
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 quinvigintillion	Quinvigintilliard	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

In 2001, Russ Rowlett, Director of the Center for Mathematics and Science Education at the University of North Carolina at Chapel Hill proposed that, to avoid confusion, the Latin based short scale and long scale systems should be replaced by an unambiguous system using Greek-derived numerical prefixes for naming large numbers that would be based on powers of one thousand:

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:

Value	Name	Notation
100	One	1
101	Ten	10
102	Hundred	100
103	Ten hundred	1000
104	Myriad	1,0000
105	Ten myriad	10,0000
106	Hundred myriad	100,0000
107	Ten hundred myriad	1000,0000
108	Myllion	1;0000,0000
1012	Myriad myllion	1,0000;0000,0000
1016	Byllion	1:0000,0000;0000,0000
1024	Myllion byllion	1;0000,0000:0000,0000;0000,0000
1032	Tryllion	1'0000,0000;0000,0000:0000,0000;0000,0000
1064	Quadryllion	1'0000,0000;0000,0000:0000,0000;0000,0000​'0000,0000;0000,0000:0000,0000;0000,0000
10128	Quintyllion	1'0000,0000;0000,0000:0000,0000;0000,0000​'0000,0000;0000,0000:0000,0000;0000,0000​'0000,0000;0000,0000:0000,0000;0000,0000​'0000,0000;0000,0000:0000,0000;0000,0000
10256	Sextyllion	1'0000,0000;0000,0000:0000,0000;0000,0000​'0000,0000;0000,0000:0000,0000;0000,0000​'0000,0000;0000,0000:0000,0000;0000,0000​'0000,0000;0000,0000:0000,0000;0000,0000​'0000,0000;0000,0000:0000,0000;0000,0000​'0000,0000;0000,0000:0000,0000;0000,0000​'0000,0000;0000,0000:0000,0000;0000,0000​'0000,0000;0000,0000:0000,0000;0000,0000
10512	Septyllion
101024	Octyllion
102048	Nonyllion
104096	Decyllion
108192	Undecyllion
1016,384	Duodecyllion
1032,768	Tredecyllion
1065,536	Quattuordecyllion
10131,072	Quindecyllion
10262,144	Sexdecyllion
10524,288	Septendecyllion
101,048,576	Octodecyllion
102,097,152	Novemdecyllion
104,194,304	Vigintyllion
108,388,608	Cafarolion
1016,777,216	Saralion
${10}^{\,\!4\cdot 2^{40}}$	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
${10}^{\,\!4\cdot 2^{10000}}$	Myryllion

SI-derived

Value	SI prefix	Name	Binary prefix	Value
1 000	k	Kilo (k)	Ki	1 024
1 000 000	M	Mega (M)	Mi	1 048 576
1 000 000 000	G	Giga	Gi	1 073 741 824

Fractional numbers

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.

Value	Fraction	Common names	Alternative names
1	$1 \over 1$	One	0.999...
0.9	$9 \over 10$	Nine tenths, [zero] point nine
0.8	$4 \over 5$	Four fifths, eight tenths, [zero] point eight
0.7	$7 \over 10$	Seven tenths, [zero] point seven
0.6	$3 \over 5$	Three fifths, six tenths, [zero] point six
0.5	$1 \over 2$	One half, five tenths, [zero] point five
0.4	$2 \over 5$	Two fifths, four tenths, [zero] point four
0.3 (333 333)...	$1 \over 3$	One third
0.3	$3 \over 10$	Three tenths, [zero] point three
0.25	$1 \over 4$	One quarter, one fourth, twenty-five hundredths, [zero] point two five
0.2	$1 \over 5$	One fifth, two tenths, [zero] point two
0.16 (666 666)...	$1 \over 6$	One sixth
0.142 857 (142 857)...	$1 \over 7$	One seventh
0.125	$1 \over 8$	One eighth, one-hundred-[and-]twenty-five thousandths, [zero] point one two five
0.1 (111 111)...	$1 \over 9$	One ninth
0.1	$1 \over 10$	One tenth, [zero] point one	One perdecime, one perdime
0.090 (909 090)...	$1 \over 11$	One eleventh
0.09	$9 \over 100$	Nine hundredths, [zero] point zero nine
0.083 (333 333)...	$1 \over 12$	One twelfth
0.08	$2 \over 25$	Two twenty-fifths, eight hundredths, [zero] point zero eight
0.0625	$1 \over 16$	One sixteenth, six-hundred-[and-]twenty-five ten-thousandths, [zero] point zero six two five
0.05	$1 \over 20$	One twentieth, [zero] point zero five
0.047 619 (047 619)...	$1 \over 21$	One twenty-first
0.045 (454 545)...	$1 \over 22$	One twenty-second
0.043 478 260 869 565 217 3913 (043 478)...	$1 \over 23$	One twenty-third
0.03 (333 333)...	$1 \over 30$	One thirtieth
0.016 (666 666)...	$1 \over 60$	One sixtieth	One minute
0.012345679 (012345679)...	$1 \over 81$	One eighty-first
0.01	$1 \over 100$	One hundredth, [zero] point zero one	One percent
0.001	$1 \over 1000$	One thousandth, [zero] point zero zero one	One permille
0.000 27 (777 777)...	$1 \over 3600$	One thirty-six hundredth	One second
0.000 1	$1 \over 10000$	One ten-thousandth, [zero] point zero zero zero one	One myriadth, one permyria, one permyriad, one basis point
0.000 01	$1 \over 10^{5}$	One hundred-thousandth	One lakhth, one perlakh
0.000 001	$1 \over 10^{6}$	One millionth	One perion, one ppm
0.000 000 1	$1 \over 10^{7}$	One ten-millionth	One crorth, one percrore
0.000 000 01	$1 \over 10^{8}$	One hundred-millionth	One awkth, one perawk
0.000 000 001	$1 \over 10^{9}$	One billionth (in some dialects)	One ppb
0	$0 \over 1$	Zero

Irrational and suspected irrational numbers

Algebraic numbers

Expression	Approximate value	Notes
${{\sqrt {5}}-1} \over 2$	0.618 033 988 749 894 848 204 586 834 366	Golden ratio conjugate $\Phi \,$, reciprocal of and one less than the golden ratio.
${\sqrt[{12}]{2}}$	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.
${\sqrt[{3}]{2}}$	1.259 921 049 894 873 164 767 210 607 278	Cube root of two. Length of the edge of a cube with volume two. See doubling the cube for the significance of this number.
n/a	1.303 577 269 034 296 391 257 099 112 153	Conway's constant, defined as the unique positive real root of a certain polynomial of degree 71.
${\sqrt[{3}]{{\frac {1}{2}}+{\frac {1}{6}}{\sqrt {\frac {23}{3}}}}}+$ ${\sqrt[{3}]{{\frac {1}{2}}-{\frac {1}{6}}{\sqrt {\frac {23}{3}}}}}$	1.324 717 957 244 746 025 960 908 854 478	Plastic 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).
${{\sqrt {5}}+1} \over 2$	1.618 033 988 749 894 848 204 586 834 366	Golden ratio $\left(\phi \right)$, the larger of the two real roots of $x^{2}=x+1\,.$
${\sqrt {3}}$	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. Twice the altitude of an equilateral triangle with side length 1. Altitude of a regular hexagon with side length 1 and diagonal length 2.
${\sqrt {5}}$	2.236 067 977 499 789 696 409 173 668 731	Square 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.
${\sqrt {2}}+1$	2.414 213 562 373 095 048 801 688 724 210	Silver ratio $\left(\delta _{S}\right)$, the larger of the two real roots of $x^{2}=2x+1\,.$
${\sqrt {6}}$	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 ${\sqrt {3}}$.
${\sqrt {7}}$	2.645 751 311 064 590 590 501 615 753 639	Length 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.
${\sqrt {8}}$	2.828 427 124 746 190 097 603 377 448 419	$2{\sqrt {2}}$ 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 ${\sqrt {5}}$.
${\sqrt {11}}$	3.316 624 790 355 399 849 114 932 736 671	Length 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.
${\sqrt {12}}$	3.464 101 615 137 754 587 054 892 683 012	$2{\sqrt {3}}$ 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

• Liouville constant: c = 0.110001000000000000000001000...
• Champernowne constant: C₁₀ = 0.12345678910111213141516...
• iⁱ: 0.207879576...
• Copeland–Erdős constant: 0.235711131719232931374143...
• The inverse of π: 0.318309886183790671537767526745028724068919291480...
• The inverse of e: 0.367879441171442321595523770161460867445811131031...
• Prouhet–Thue–Morse constant: τ = 0.412454033640...
• Cahen's constant: c = 0.64341054629...
• π/√18 = 0.7404... the maxium density of sphere packing in three dimensional Euclidean space according to the Kepler conjecture
• Gauss's constant: G = 0.8346268...
• Khinchin–Lévy constant: 1.1865691104...[1]
• Favard constant: K₁ = 1.57079633...
• log₂ 3: 1.584962501..., in fact, the logarithm of any positive integer to any integer base greater than one is either rational or transcendental.
• √2^√2: 1.6325269...
• Komornik–Loreti constant: q = 1.787231650...
• Parabolic constant: P₂ = 2.29558714939...
• Gelfond–Schneider constant: 2.665144143...
• Euler's number: e = 2.718281828459045235360287471353...
• Pi: π = 3.141592653589793238462643383279...
• Tau, or 2π: τ = 6.283185307179586..., The ratio of the circumference to a radius, and the number of radians in a complete circle
• Gelfond's constant: 23.14069263277925...
• Ramanujan's constant: e^(π√163) = 262537412640768743.99999999999925...

Suspected transcendentals

• Heath-Brown–Moroz constant: C = 0.001317641...
• Kepler–Bouwkamp constant: 0.1149420448...
• MRB constant: 0.187859...
• Meissel–Mertens constant: M = 0.2614972128476427837554268386086958590516...
• Bernstein's constant: β = 0.2801694990...
• Strongly carefree constant: 0.286747...
• The Logarithm of 2 to base 10, used to find the number of digits in a power of 2: 0.30029995663981...
• Gauss–Kuzmin–Wirsing constant: λ₁ = 0.3036630029...[2]
• Hafner–Sarnak–McCurley constant: 0.3532363719...
• Artin's constant: 0.3739558136...
• Prime constant: ρ = 0.414682509851111660248109622...
• Carefree constant: 0.428249...
• The Logarithm of e to base 10: 0.434294481903251827651128918916605082294397005803...
• Omega constant: Ω = 0.5671432904097838729999686622...
• Stephens' constant: 0.575959...
• Euler–Mascheroni constant: γ = 0.577215664901532860606512090082...
• Golomb–Dickman constant: λ = 0.62432998854355087099293638310083724...
• Twin prime constant: C₂ = 0.660161815846869573927812110014...
• Feller-Tornier constant: 0.661317...
• Laplace limit: ε = 0.6627434193...[3]
• Taniguchi's constant: 0.678234...
• ln 2: 0.693147180559945309417232121458...
• Embree–Trefethen constant: β* = 0.70258...
• Sarnak's constant: 0.723648...
• Landau–Ramanujan constant: 0.76422365358922066299069873125...
• Brun's constant for prime quadruplets: B₂ = 0.8705883800...
• Quadratic class number constant: 0.881513...
• Catalan's constant: G = 0.915965594177219015054603514932384110774...
• Viswanath's constant: σ(1) = 1.13198824...
• Apéry's constant: ζ(3) = 1.202056903159594285399738161511449990764986292...
• Vardi's constant: E = 1.264084735305...
• Glaisher–Kinkelin constant: A = 1.28242712...
• Mills' constant: A = 1.30637788386308069046...
• Totient summatory constant: 1.339784...
• Ramanujan–Soldner constant: μ = 1.451369234883381050283968485892027449493…
• Backhouse's constant: 1.456074948...
• Lieb's square ice constant: 1.5396007...
• √2_s: 1.559610469...
• Erdős–Borwein constant: E = 1.606695152415291763...
• Somos' quadratic recurrence constant: σ = 1.661687949633594121296...
• Niven's constant: c = 1.705211...
• Brun's constant: B₂ = 1.902160583104...
• Landau's totient constant: 1.943596...
• Feigenbaum constant: α = 2.5029...
• Sierpiński's constant: K = 2.5849817595792532170658936...
• Barban's constant: 2.596536...
• Khinchin's constant: K₀ = 2.685452001...[4]
• Fransén–Robinson constant: F = 2.8077702420...
• Murata's constant: 2.826419...
• Lévy's constant: γ = 3.275822918721811159787681882...
• Reciprocal Fibonacci constant: ψ = 3.359885666243177553172011302918927179688905133731...
• Feigenbaum constant: δ = 4.6692...

Numbers not known with high precision

• Landau's constant: 0.4330 < B < 0.472
• Landau's constant: 0.5 < L < 0.544
• Landau's constant: 0.5 < A < 0.7853
• Grothendieck constant: 1.67 < k < 1.79

Hypercomplex numbers

Algebraic complex numbers

• Imaginary unit: $i={\sqrt {-1}}$
• nth roots of unity: $\xi _{n}^{k}=\cos \left(2\pi {\tfrac {k}{n}}\right)+i\sin \left(2\pi {\tfrac {k}{n}}\right)$

Other hypercomplex numbers

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

Transfinite numbers

• Infinity in general: $\infty$
• Aleph-null: $\aleph _{0}$
• Aleph-one: $\aleph _{1}$
• Beth-one: ($\beth _{1}$) is the cardinality of the continuum: $2^{\aleph _{0}}$

Numbers representing 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 (= 12²)
• Great gross: 1728 (= 12³)

Numbers representing scientific quantities

• Planck constant: h = 6.6260689633... ×10^–34 Js
• Electronvolt: eV = 1.60217648740... ×10^–19 J
• Electron relative atomic mass: A_r(e) = 0.0005485799094323...
• Molar mass constant: M_u = 0.001 kg/mol
• Fine structure constant: α = 0.007297352537650...
• Rydberg constant: R_∞ = 10973731.56852773... m⁻¹
• Speed of light in vacuum: c = 299792458 m/s
• Avogadro constant: N_A = 6.0221417930... ×10²³ mol⁻¹

Numbers without specific values

Main article: Indefinite and fictitious numbers

Bases

• Base −10 (negadecimal)
• 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 11 (undecimal)
• Base 12 (duodecimal or dozenal)
• Base 13 (tridecimal or tredecimal)
• Base 14 (tetradecimal)
• Base 15 (pentadecimal)
• Base 16 (hexadecimal)
• Base 20 (vigesimal)
• Base 24 (quadrovigesimal)
• Base 26 (hexavigesimal)
• Base 27 (septemvigesimal)
• Base 30 (trigesimal)
• Base 32 (duotrigesimal)
• Base 36 (hexatridecimal, sexatrigesimal or hexatrigesimal)
• Base 60 (sexagesimal)
• Mixed radix
• Non-integer base (base φ, base plastic number, base e, base π, base √2)
• Complex base (base 2i, base −1±i)

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

See also

• English-language numerals
• Numbers in various languages
• Number prefix
• 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
• The Penguin Dictionary of Curious and Interesting Numbers
• 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 0-7167-4447-3

External links

• The Database of Number Correlations: 1 to 2000+
• What's Special About This Number? A Zoology of Numbers: from 0 to 500
• See how to write big numbers
• The MegaPenny Project - Visualizing 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)