List of numbers
Updated: 5/20/2026, 7:04:17 PM Wikipedia source
This is a list of notable numbers and articles about them. The list does not contain all numbers in existence as most of the number sets are infinite. Numbers may be included in the list based on their mathematical, historical or cultural notability, but all numbers have qualities that could arguably make them notable. Even the smallest "uninteresting" number is paradoxically interesting for that very property. This is known as the interesting number paradox. The definition of what is classed as a number is rather diffuse and based on historical distinctions. For example, the pair of numbers (3,4) is commonly regarded as a number when it is in the form of a complex number (3+4i), but not when it is in the form of a vector (3,4). This list will also be categorized with the standard convention of types of numbers. This list focuses on numbers as mathematical objects and is not a list of numerals, which are linguistic devices: nouns, adjectives, or adverbs that designate numbers. The distinction is drawn between the number five (an abstract object equal to 2+3), and the numeral five (the noun referring to the number).
Tables
Table of notable natural numbers · Natural numbers
10
10
0
10
1
11
2
12
3
13
4
14
5
15
6
16
7
17
8
18
9
19
20
20
0
20
1
21
2
22
3
23
4
24
5
25
6
26
7
27
8
28
9
29
30
30
0
30
1
31
2
32
3
33
4
34
5
35
6
36
7
37
8
38
9
39
40
40
0
40
1
41
2
42
3
43
4
44
5
45
6
46
7
47
8
48
9
49
50
50
0
50
1
51
2
52
3
53
4
54
5
55
6
56
7
57
8
58
9
59
60
60
0
60
1
61
2
62
3
63
4
64
5
65
6
66
7
67
8
68
9
69
70
70
0
70
1
71
2
72
3
73
4
74
5
75
6
76
7
77
8
78
9
79
80
80
0
80
1
81
2
82
3
83
4
84
5
85
6
86
7
87
8
88
9
89
90
90
0
90
1
91
2
92
3
93
4
94
5
95
6
96
7
97
8
98
9
99
100
100
0
100
1
101
2
102
3
103
4
104
5
105
6
106
7
107
8
108
9
109
110
110
0
110
1
111
2
112
3
113
4
114
5
115
6
116
7
117
8
118
9
119
120
120
0
120
1
121
2
122
3
123
4
124
5
125
6
126
7
127
8
128
9
129
130
130
0
130
1
131
2
132
3
133
4
134
5
135
6
136
7
137
8
138
9
139
140
140
0
140
1
141
2
142
3
143
4
144
5
145
6
146
7
147
8
148
9
149
150
150
0
150
1
151
2
152
3
153
4
154
5
155
6
156
7
157
8
158
9
159
160
160
0
160
1
161
2
162
3
163
4
164
5
165
6
166
7
167
8
168
9
169
170
170
0
170
1
171
2
172
3
173
4
174
5
175
6
176
7
177
8
178
9
179
180
180
0
180
1
181
2
182
3
183
4
184
5
185
6
186
7
187
8
188
9
189
190
190
0
190
1
191
2
192
3
193
4
194
5
195
6
196
7
197
8
198
9
199
200
200
0
200
1
201
2
202
3
203
4
204
5
205
6
206
7
207
8
208
9
209
210
210
0
210
1
211
2
212
3
213
4
214
5
215
6
216
7
217
8
218
9
219
220
220
0
220
1
221
2
222
3
223
4
224
5
225
6
226
7
227
8
228
9
229
230
230
0
230
1
231
2
232
3
233
4
234
5
235
6
236
7
237
8
238
9
239
240
240
0
240
1
241
2
242
3
243
4
244
5
245
6
246
7
247
8
248
9
249
250
250
0
250
1
251
2
252
3
253
4
254
5
255
6
256
7
257
8
258
9
259
260
260
0
260
1
261
2
262
3
263
4
264
5
265
6
266
7
267
8
268
9
269
270
270
0
270
1
271
2
272
3
273
4
274
5
275
6
276
7
277
8
278
9
279
280
280
0
280
1
281
2
282
3
283
4
284
5
285
6
286
7
287
8
288
9
289
290
290
0
290
1
291
2
292
3
293
4
294
5
295
6
296
7
297
8
298
9
299
300
300
0
300
1
301
2
302
3
303
4
304
5
305
6
306
7
307
8
308
9
309
310
310
0
310
1
311
2
312
3
313
4
314
5
315
6
316
8
318
360
360
0
360
3
363
5
365
9
369
400
400
0
400
420
420
0
420
440
440
0
440
500
500
0
500
1
501
600
600
0
600
610
610
0
610
3
613
6
616
700
700
0
700
720
720
0
720
800
800
0
800
1
801
840
840
0
840
880
880
0
880
1
881
8
888
900
900
0
900
1000
1000
0
1000
1
1001
1510
1510
0
1510
1980
1980
0
1980
7
1987
2000
2000
0
2000
2520
2520
0
2520
3000
3000
0
3000
4000
4000
0
4000
5000
5000
0
5000
| 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 | 217 | 218 | 219 |
| 220 | 221 | 222 | 223 | 224 | 225 | 226 | 227 | 228 | 229 |
| 230 | 231 | 232 | 233 | 234 | 235 | 236 | 237 | 238 | 239 |
| 240 | 241 | 242 | 243 | 244 | 245 | 246 | 247 | 248 | 249 |
| 250 | 251 | 252 | 253 | 254 | 255 | 256 | 257 | 258 | 259 |
| 260 | 261 | 262 | 263 | 264 | 265 | 266 | 267 | 268 | 269 |
| 270 | 271 | 272 | 273 | 274 | 275 | 276 | 277 | 278 | 279 |
| 280 | 281 | 282 | 283 | 284 | 285 | 286 | 287 | 288 | 289 |
| 290 | 291 | 292 | 293 | 294 | 295 | 296 | 297 | 298 | 299 |
| 300 | 301 | 302 | 303 | 304 | 305 | 306 | 307 | 308 | 309 |
| 310 | 311 | 312 | 313 | 314 | 315 | 316 | 318 | ||
| 323 | 325 | ||||||||
| 341 | |||||||||
| 353 | 359 | ||||||||
| 360 | 363 | 365 | 369 | ||||||
| 377 | |||||||||
| 384 | |||||||||
| 400 | |||||||||
| 420 | |||||||||
| 440 | |||||||||
| 495 | 496 | ||||||||
| 500 | 501 | ||||||||
| 511 | 512 | ||||||||
| 555 | |||||||||
| 600 | |||||||||
| 610 | 613 | 616 | |||||||
| 666 | |||||||||
| 693 | |||||||||
| 700 |
Table of first 100 prime numbers · Classes of natural numbers › Prime numbers
31
31
2
31
3
37
5
41
7
43
11
47
13
53
17
59
19
61
23
67
29
71
73
73
2
73
3
79
5
83
7
89
11
97
13
101
17
103
19
107
23
109
29
113
127
127
2
127
3
131
5
137
7
139
11
149
13
151
17
157
19
163
23
167
29
173
179
179
2
179
3
181
5
191
7
193
11
197
13
199
17
211
19
223
23
227
29
229
233
233
2
233
3
239
5
241
7
251
11
257
13
263
17
269
19
271
23
277
29
281
283
283
2
283
3
293
5
307
7
311
11
313
13
317
17
331
19
337
23
347
29
349
353
353
2
353
3
359
5
367
7
373
11
379
13
383
17
389
19
397
23
401
29
409
419
419
2
419
3
421
5
431
7
433
11
439
13
443
17
449
19
457
23
461
29
463
467
467
2
467
3
479
5
487
7
491
11
499
13
503
17
509
19
521
23
523
29
541
| 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 |
· Integers › SI prefixes
Kilo
Kilo
Value
1000
1000m
10001
Name
Kilo
Symbol
k
Mega
Mega
Value
1000000
1000m
10002
Name
Mega
Symbol
M
Giga
Giga
Value
1000000000
1000m
10003
Name
Giga
Symbol
G
Tera
Tera
Value
1000000000000
1000m
10004
Name
Tera
Symbol
T
Peta
Peta
Value
1000000000000000
1000m
10005
Name
Peta
Symbol
P
Exa
Exa
Value
1000000000000000000
1000m
10006
Name
Exa
Symbol
E
Zetta
Zetta
Value
1000000000000000000000
1000m
10007
Name
Zetta
Symbol
Z
Yotta
Yotta
Value
1000000000000000000000000
1000m
10008
Name
Yotta
Symbol
Y
Ronna
Ronna
Value
1000000000000000000000000000
1000m
10009
Name
Ronna
Symbol
R
Quetta
Quetta
Value
1000000000000000000000000000000
1000m
100010
Name
Quetta
Symbol
Q
| Value | 1000m | Name | Symbol |
| 1000 | 10001 | Kilo | k |
| 1000000 | 10002 | Mega | M |
| 1000000000 | 10003 | Giga | G |
| 1000000000000 | 10004 | Tera | T |
| 1000000000000000 | 10005 | Peta | P |
| 1000000000000000000 | 10006 | Exa | E |
| 1000000000000000000000 | 10007 | Zetta | Z |
| 1000000000000000000000000 | 10008 | Yotta | Y |
| 1000000000000000000000000000 | 10009 | Ronna | R |
| 1000000000000000000000000000000 | 100010 | Quetta | Q |
Table of notable rational numbers · Rational numbers
1
1
Decimal expansion
1
Fraction
1/1
Notability
One is the multiplicative identity. One is a rational number, as it is equal to 1/1.
1
1
Decimal expansion
1
−0 333...
−0 333...
Decimal expansion
−0 333...
Fraction
−+1/12
Notability
The value assigned to the series 1+2+3... by zeta function regularization and Ramanujan summation.
0
0
Decimal expansion
0
Fraction
1/2
Notability
One half occurs commonly in mathematical equations and in real world proportions. One half appears in the formula for the area of a triangle: 1/2 × base × perpendicular height and in the formulae for figurate numbers, such as triangular numbers and pentagonal numbers.
3 857...
3 857...
Decimal expansion
3 857...
Fraction
22/7
Notability
A widely used approximation for the number
π
{\displaystyle \pi }
. It can be proven that this number exceeds
π
{\displaystyle \pi }
.
0 666...
0 666...
Decimal expansion
0 666...
Fraction
1/6
Notability
One sixth. Often appears in mathematical equations, such as in the sum of squares of the integers and in the solution to the Basel problem.
| Decimal expansion | Fraction | Notability |
| 1 | 1/1 | One is the multiplicative identity. One is a rational number, as it is equal to 1/1. |
| 1 | ||
| −0 333... | −+1/12 | The value assigned to the series 1+2+3... by zeta function regularization and Ramanujan summation. |
| 0 | 1/2 | One half occurs commonly in mathematical equations and in real world proportions. One half appears in the formula for the area of a triangle: 1/2 × base × perpendicular height and in the formulae for figurate numbers, such as triangular numbers and pentagonal numbers. |
| 3 857... | 22/7 | A widely used approximation for the number π {\displaystyle \pi } . It can be proven that this number exceeds π {\displaystyle \pi } . |
| 0 666... | 1/6 | One sixth. Often appears in mathematical equations, such as in the sum of squares of the integers and in the solution to the Basel problem. |
· Real numbers › Algebraic numbers
Golden ratio conjugate (
Φ
{\displaystyle \Phi }
)
Golden ratio conjugate (
Φ
{\displaystyle \Phi }
)
Name
Golden ratio conjugate (
Φ
{\displaystyle \Phi }
)
Expression
5
−
1
2
{\displaystyle {\frac {{\sqrt {5}}-1}{2}}}
Decimal expansion
0
Notability
Reciprocal of (and one less than) the golden ratio.
Twelfth root of two
Twelfth root of two
Name
Twelfth root of two
Expression
2
12
{\displaystyle {\sqrt[{12}]{2}}}
Decimal expansion
1
Notability
Proportion between the frequencies of adjacent semitones in the 12 tone equal temperament scale.
Cube root of two
Cube root of two
Name
Cube root of two
Expression
2
3
{\displaystyle {\sqrt[{3}]{2}}}
Decimal expansion
1
Notability
Length of the edge of a cube with volume two. See doubling the cube for the significance of this number.
Conway's constant
Conway's constant
Name
Conway's constant
Expression
(cannot be written as expressions involving integers and the operations of addition, subtraction, multiplication, division, and the extraction of roots)
Decimal expansion
1
Notability
Defined as the unique positive real root of a certain polynomial of degree 71. The limit ratio between subsequent numbers in the binary Look-and-say sequence (
OEIS: A014715).
Plastic ratio
Plastic ratio
Name
Plastic ratio
Expression
1
2
+
1
6
23
3
Decimal expansion
1
Notability
The only real solution of
x
3
=
x
+
1
{\displaystyle x^{3}=x+1}
.(
OEIS: A060006) The limit ratio between subsequent numbers in the Van der Laan sequence. (
OEIS: A182097)
Square root of two
Square root of two
Name
Square root of two
Expression
2
{\displaystyle {\sqrt {2}}}
Decimal expansion
1
Notability
√2 = 2 sin 45° = 2 cos 45° Square root of two 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).
Supergolden ratio
Supergolden ratio
Name
Supergolden ratio
Expression
1
+
29
+
3
3
⋅
Decimal expansion
1
Notability
The only real solution of
x
3
=
x
2
+
1
{\displaystyle x^{3}=x^{2}+1}
.(
OEIS: A092526) The limit ratio between subsequent numbers in Narayana's cows sequence. (
OEIS:
Triangular root of 2
Triangular root of 2
Name
Triangular root of 2
Expression
17
−
1
2
{\displaystyle {\frac {{\sqrt {17}}-1}{2}}}
Decimal expansion
1
Golden ratio (φ)
Golden ratio (φ)
Name
Golden ratio (φ)
Expression
5
+
1
2
{\displaystyle {\frac {{\sqrt {5}}+1}{2}}}
Decimal expansion
1
Notability
The larger of the two real roots of x2 = x + 1.
Square root of three
Square root of three
Name
Square root of three
Expression
3
{\displaystyle {\sqrt {3}}}
Decimal expansion
1
Notability
√3 = 2 sin 60° = 2 cos 30° . A . the measure of the fish or Theodorus' constant. Length of the space diagonal of a cube with edge length 1. Altitude of an equilateral triangle with side length 2. Altitude of a regular hexagon with side length 1 and diagonal length 2.
Tribonacci constant
Tribonacci constant
Name
Tribonacci constant
Expression
1
+
19
+
3
3
⋅
11
Decimal expansion
1
Notability
The only real solution of
x
3
=
x
2
+
x
+
1
{\displaystyle x^{3}=x^{2}+x+1}
.(
OEIS: A058265) The limit ratio between subsequent numbers in the Tribona
Supersilver ratio
Supersilver ratio
Name
Supersilver ratio
Expression
2
+
43
+
3
3
⋅
Decimal expansion
2
Notability
The only real solution of
x
3
=
2
x
2
+
1
{\displaystyle x^{3}=2x^{2}+1}
.(
OEIS: A356035) The limit ratio between subsequent numbers in the third-order Pell s
Square root of five
Square root of five
Name
Square root of five
Expression
5
{\displaystyle {\sqrt {5}}}
Decimal expansion
2
Notability
Length of the diagonal of a 1 × 2 rectangle.
Silver ratio (δS)
Silver ratio (δS)
Name
Silver ratio (δS)
Expression
2
+
1
{\displaystyle {\sqrt {2}}+1}
Decimal expansion
2
Notability
The larger of the two real roots of x2 = 2x + 1.
Altitude of a regular octagon with side length 1.
Bronze ratio (S3)
Bronze ratio (S3)
Name
Bronze ratio (S3)
Expression
13
+
3
2
{\displaystyle {\frac {{\sqrt {13}}+3}{2}}}
Decimal expansion
3
Notability
The larger of the two real roots of x2 = 3x + 1.
| Name | Expression | Decimal expansion | Notability |
| Golden ratio conjugate ( Φ {\displaystyle \Phi } ) | 5 − 1 2 {\displaystyle {\frac {{\sqrt {5}}-1}{2}}} | 0 | Reciprocal of (and one less than) the golden ratio. |
| Twelfth root of two | 2 12 {\displaystyle {\sqrt[{12}]{2}}} | 1 | Proportion between the frequencies of adjacent semitones in the 12 tone equal temperament scale. |
| Cube root of two | 2 3 {\displaystyle {\sqrt[{3}]{2}}} | 1 | Length of the edge of a cube with volume two. See doubling the cube for the significance of this number. |
| Conway's constant | (cannot be written as expressions involving integers and the operations of addition, subtraction, multiplication, division, and the extraction of roots) | 1 | Defined as the unique positive real root of a certain polynomial of degree 71. The limit ratio between subsequent numbers in the binary Look-and-say sequence ( OEIS: A014715). |
| Plastic ratio | 1 2 + 1 6 23 3 | 1 | The only real solution of x 3 = =x+1} .( OEIS: A060006) The limit ratio between subsequent numbers in the Van der Laan sequence. ( OEIS: A182097) |
| Square root of two | 2 {\displaystyle {\sqrt {2}}} | 1 | √2 = 2 sin 45° = 2 cos 45° Square root of two 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). |
| Supergolden ratio | 1 + 29 + 3 3 ⋅ | 1 | The only real solution of x 3 = =x^{2}+1} .( OEIS: A092526) The limit ratio between subsequent numbers in Narayana's cows sequence. ( OEIS: |
| Triangular root of 2 | 17 − 1 2 {\displaystyle {\frac {{\sqrt {17}}-1}{2}}} | 1 | |
| Golden ratio (φ) | 5 + 1 2 {\displaystyle {\frac {{\sqrt {5}}+1}{2}}} | 1 | The larger of the two real roots of x2 = x + 1. |
| Square root of three | 3 {\displaystyle {\sqrt {3}}} | 1 | √3 = 2 sin 60° = 2 cos 30° . A . the measure of the fish or Theodorus' constant. Length of the space diagonal of a cube with edge length 1. Altitude of an equilateral triangle with side length 2. Altitude of a regular hexagon with side length 1 and diagonal length 2. |
| Tribonacci constant | 1 + 19 + 3 3 ⋅ 11 | 1 | The only real solution of x 3 = =x^{2}+x+1} .( OEIS: A058265) The limit ratio between subsequent numbers in the Tribona |
| Supersilver ratio | 2 + 43 + 3 3 ⋅ | 2 | The only real solution of x 3 = 2 =2x^{2}+1} .( OEIS: A356035) The limit ratio between subsequent numbers in the third-order Pell s |
| Square root of five | 5 {\displaystyle {\sqrt {5}}} | 2 | Length of the diagonal of a 1 × 2 rectangle. |
| Silver ratio (δS) | 2 + 1 {\displaystyle {\sqrt {2}}+1} | 2 | The larger of the two real roots of x2 = 2x + 1. Altitude of a regular octagon with side length 1. |
| Bronze ratio (S3) | 13 + 3 2 {\displaystyle {\frac {{\sqrt {13}}+3}{2}}} | 3 | The larger of the two real roots of x2 = 3x + 1. |
References
- "Hardy–Ramanujan Number"http://mathworld.wolfram.com/Hardy-RamanujanNumber.html
- International Review of Psychiatryhttps://doi.org/10.1080%2F09540261.2020.1769289
- wwwhttps://www.britannica.com/video/213933/Demystified-why-is-bakers-dozen-thirteen
- Merriam-Websterhttp://www.merriam-webster.com/dictionary/86
- Discrete Mathematics and its Applications
- "Mathematical Symbols"http://searchdatacenter.techtarget.com/definition/Mathematical-Symbols
- Quick(er) Calculationshttps://dx.doi.org/10.1093/oso/9780198852650.003.0010
- "Nick's Mathematical Puzzles: Solution 29"http://www.qbyte.org/puzzles/p029s.html
- "The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 69
- Sequence OEIS: A019692.
- See Apéry 1979.
- "The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 33
- J. Indian Math. Soc.http://www.renyi.hu/~p_erdos/1948-04.pdf
- Mathematical Proceedings of the Cambridge Philosophical Societyhttps://ui.adsabs.harvard.edu/abs/1992MPCPS.112..141B
- André-Jeannin, Richard; 'Irrationalité de la somme des inverses de certaines suites récurrentes.'; Comptes Rendus de l'A
- S. Kato, 'Irrationality of reciprocal sums of Fibonacci numbers', Master's thesis, Keio Univ. 1996
- Duverney, Daniel, Keiji Nishioka, Kumiko Nishioka and Iekata Shiokawa; 'Transcendence of Rogers-Ramanujan continued frachttps://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/62370/1/1060-10.pdf
- oeishttps://oeis.org/A001620
- Michigan Mathematical Journalhttps://doi.org/10.1307%2Fmmj%2F1339011525
- Bulletin of the American Mathematical Societyhttps://doi.org/10.1090%2FS0273-0979-2013-01423-X