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List of numbers

Updated: 11/6/2025, 1:33:54 AM 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
105
105
0
105
1
106
2
107
3
108
4
109
5
1010
6
1011
7
1012
8
1013
larger numbers, including 10100 and 1010100
larger numbers, including 10100 and 1010100
0
larger numbers, including 10100 and 1010100
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
1.0
1.0
Decimal expansion
1.0
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
−0.083 333...
−0.083 333...
Decimal expansion
−0.083 333...
Fraction
⁠−+1/12⁠
Notability
The value assigned to the series 1+2+3... by zeta function regularization and Ramanujan summation.
0.5
0.5
Decimal expansion
0.5
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.
3.142 857...
3.142 857...
Decimal expansion
3.142 857...
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 } .
0.166 666...
0.166 666...
Decimal expansion
0.166 666...
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
1.0
⁠1/1⁠
One is the multiplicative identity. One is a rational number, as it is equal to 1/1.
1
−0.083 333...
⁠−+1/12⁠
The value assigned to the series 1+2+3... by zeta function regularization and Ramanujan summation.
0.5
⁠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.
3.142 857...
⁠22/7⁠
A widely used approximation for the number π {\displaystyle \pi } . It can be proven that this number exceeds π {\displaystyle \pi } .
0.166 666...
⁠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
0.618033988749894848204586834366
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
1.059463094359295264561825294946
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
1.259921049894873164767210607278
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
1.303577269034296391257099112153
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 3 + 1 2 − 1 6 23 3 3 {\displaystyle {\sqrt[{3}]{{\frac {1}{2}}+{\frac {1}{6}}{\sqrt {\frac {23}{3}}}}}+{\sqrt[{3}]{{\frac {1}{2}}-{\frac {1}{6}}{\sqrt {\frac {23}{3}}}}}}
Decimal expansion
1.324717957244746025960908854478
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
1.414213562373095048801688724210
Notability
√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).
Supergolden ratio
Supergolden ratio
Name
Supergolden ratio
Expression
1 + 29 + 3 3 ⋅ 31 2 3 + 29 − 3 3 ⋅ 31 2 3 3 {\displaystyle {\dfrac {1+{\sqrt[{3}]{\dfrac {29+3{\sqrt {3\cdot 31}}}{2}}}+{\sqrt[{3}]{\dfrac {29-3{\sqrt {3\cdot 31}}}{2}}}}{3}}}
Decimal expansion
1.465571231876768026656731225220
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: A000930)
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
1.561552812808830274910704927987
Golden ratio (φ)
Golden ratio (φ)
Name
Golden ratio (φ)
Expression
5 + 1 2 {\displaystyle {\frac {{\sqrt {5}}+1}{2}}}
Decimal expansion
1.618033988749894848204586834366
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
1.732050807568877293527446341506
Notability
√3 = 2 sin 60° = 2 cos 30° . A.k.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 3 + 19 − 3 3 ⋅ 11 3 3 {\displaystyle {\frac {1+{\sqrt[{3}]{19+3{\sqrt {3\cdot 11}}}}+{\sqrt[{3}]{19-3{\sqrt {3\cdot 11}}}}}{3}}}
Decimal expansion
1.839286755214161132551852564653
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 Tribonacci sequence.(OEIS: A000073) Appears in the volume and coordinates of the snub cube and some related polyhedra.
Supersilver ratio
Supersilver ratio
Name
Supersilver ratio
Expression
2 + 43 + 3 3 ⋅ 59 2 3 + 43 − 3 3 ⋅ 59 2 3 3 {\displaystyle {\dfrac {2+{\sqrt[{3}]{\dfrac {43+3{\sqrt {3\cdot 59}}}{2}}}+{\sqrt[{3}]{\dfrac {43-3{\sqrt {3\cdot 59}}}{2}}}}{3}}}
Decimal expansion
2.20556943040059031170202861778
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 sequence. (OEIS: A008998)
Square root of five
Square root of five
Name
Square root of five
Expression
5 {\displaystyle {\sqrt {5}}}
Decimal expansion
2.236067977499789696409173668731
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
2.414213562373095048801688724210
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
3.302775637731994646559610633735
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}}}
0.618033988749894848204586834366
Reciprocal of (and one less than) the golden ratio.
Twelfth root of two
2 12 {\displaystyle {\sqrt[{12}]{2}}}
1.059463094359295264561825294946
Proportion between the frequencies of adjacent semitones in the 12 tone equal temperament scale.
Cube root of two
2 3 {\displaystyle {\sqrt[{3}]{2}}}
1.259921049894873164767210607278
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)
1.303577269034296391257099112153
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 3 + 1 2 − 1 6 23 3 3 {\displaystyle {\sqrt[{3}]{{\frac {1}{2}}+{\frac {1}{6}}{\sqrt {\frac {23}{3}}}}}+{\sqrt[{3}]{{\frac {1}{2}}-{\frac {1}{6}}{\sqrt {\frac {23}{3}}}}}}
1.324717957244746025960908854478
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}}}
1.414213562373095048801688724210
√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).
Supergolden ratio
1 + 29 + 3 3 ⋅ 31 2 3 + 29 − 3 3 ⋅ 31 2 3 3 {\displaystyle {\dfrac {1+{\sqrt[{3}]{\dfrac {29+3{\sqrt {3\cdot 31}}}{2}}}+{\sqrt[{3}]{\dfrac {29-3{\sqrt {3\cdot 31}}}{2}}}}{3}}}
1.465571231876768026656731225220
The only real solution of x 3 = =x^{2}+1} .(OEIS: A092526) The limit ratio between subsequent numbers in Narayana's cows sequence. (OEIS: A000930)
Triangular root of 2
17 − 1 2 {\displaystyle {\frac {{\sqrt {17}}-1}{2}}}
1.561552812808830274910704927987
Golden ratio (φ)
5 + 1 2 {\displaystyle {\frac {{\sqrt {5}}+1}{2}}}
1.618033988749894848204586834366
The larger of the two real roots of x2 = x + 1.
Square root of three
3 {\displaystyle {\sqrt {3}}}
1.732050807568877293527446341506
√3 = 2 sin 60° = 2 cos 30° . A.k.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 3 + 19 − 3 3 ⋅ 11 3 3 {\displaystyle {\frac {1+{\sqrt[{3}]{19+3{\sqrt {3\cdot 11}}}}+{\sqrt[{3}]{19-3{\sqrt {3\cdot 11}}}}}{3}}}
1.839286755214161132551852564653
The only real solution of x 3 = =x^{2}+x+1} .(OEIS: A058265) The limit ratio between subsequent numbers in the Tribonacci sequence.(OEIS: A000073) Appears in the volume and coordinates of the snub cube and some related polyhedra.
Supersilver ratio
2 + 43 + 3 3 ⋅ 59 2 3 + 43 − 3 3 ⋅ 59 2 3 3 {\displaystyle {\dfrac {2+{\sqrt[{3}]{\dfrac {43+3{\sqrt {3\cdot 59}}}{2}}}+{\sqrt[{3}]{\dfrac {43-3{\sqrt {3\cdot 59}}}{2}}}}{3}}}
2.20556943040059031170202861778
The only real solution of x 3 = 2 =2x^{2}+1} .(OEIS: A356035) The limit ratio between subsequent numbers in the third-order Pell sequence. (OEIS: A008998)
Square root of five
5 {\displaystyle {\sqrt {5}}}
2.236067977499789696409173668731
Length of the diagonal of a 1 × 2 rectangle.
Silver ratio (δS)
2 + 1 {\displaystyle {\sqrt {2}}+1}
2.414213562373095048801688724210
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}}}
3.302775637731994646559610633735
The larger of the two real roots of x2 = 3x + 1.
· Real numbers › Transcendental numbers
Gelfond's constant
Gelfond's constant
Name
Gelfond's constant
Symbol or Formula
e π {\displaystyle e^{\pi }}
Decimal expansion
23.14069263277925...
Ramanujan's constant
Ramanujan's constant
Name
Ramanujan's constant
Symbol or Formula
e π 163 {\displaystyle e^{\pi {\sqrt {163}}}}
Decimal expansion
262537412640768743.99999999999925...
Gaussian integral
Gaussian integral
Name
Gaussian integral
Symbol or Formula
π {\displaystyle {\sqrt {\pi }}}
Decimal expansion
1.772453850905516...
Komornik–Loreti constant
Komornik–Loreti constant
Name
Komornik–Loreti constant
Symbol or Formula
q {\displaystyle q}
Decimal expansion
1.787231650...
Universal parabolic constant
Universal parabolic constant
Name
Universal parabolic constant
Symbol or Formula
P 2 {\displaystyle P_{2}}
Decimal expansion
2.29558714939...
Gelfond–Schneider constant
Gelfond–Schneider constant
Name
Gelfond–Schneider constant
Symbol or Formula
2 2 {\displaystyle 2^{\sqrt {2}}}
Decimal expansion
2.665144143...
Euler's number
Euler's number
Name
Euler's number
Symbol or Formula
e {\displaystyle e}
Decimal expansion
2.718281828459045235360287471352662497757247...
Notes and notability
Raising e to the power of i {\displaystyle i} π will result in − 1 {\displaystyle -1} .
Pi
Pi
Name
Pi
Symbol or Formula
π {\displaystyle \pi }
Decimal expansion
3.141592653589793238462643383279502884197169399375...
Notes and notability
Pi is a constant irrational number that is the result of dividing the circumference of a circle by its diameter.
Super square-root of 2
Super square-root of 2
Name
Super square-root of 2
Symbol or Formula
2 s {\textstyle {\sqrt {2}}_{s}}
Decimal expansion
1.559610469...
Liouville constant
Liouville constant
Name
Liouville constant
Symbol or Formula
L {\textstyle L}
Decimal expansion
0.110001000000000000000001000...
Champernowne constant
Champernowne constant
Name
Champernowne constant
Symbol or Formula
C 10 {\textstyle C_{10}}
Decimal expansion
0.12345678910111213141516...
Notes and notability
This constant contains every number string inside it, as its decimals are just every number in order. (1,2,3,etc.)
Prouhet–Thue–Morse constant
Prouhet–Thue–Morse constant
Name
Prouhet–Thue–Morse constant
Symbol or Formula
τ {\textstyle \tau }
Decimal expansion
0.412454033640...
Omega constant
Omega constant
Name
Omega constant
Symbol or Formula
Ω {\displaystyle \Omega }
Decimal expansion
0.5671432904097838729999686622...
Cahen's constant
Cahen's constant
Name
Cahen's constant
Symbol or Formula
C {\textstyle C}
Decimal expansion
0.64341054629...
Natural logarithm of 2
Natural logarithm of 2
Name
Natural logarithm of 2
Symbol or Formula
ln 2
Decimal expansion
0.693147180559945309417232121458
Lemniscate constant
Lemniscate constant
Name
Lemniscate constant
Symbol or Formula
ϖ {\textstyle \varpi }
Decimal expansion
2.622057554292119810464839589891...
Notes and notability
The ratio of the perimeter of Bernoulli's lemniscate to its diameter.
Tau
Tau
Name
Tau
Symbol or Formula
τ = 2 π {\displaystyle \tau =2\pi }
Decimal expansion
6.283185307179586476925286766559...
Notes and notability
The ratio of the circumference to a radius, and the number of radians in a complete circle; 2 × {\displaystyle \times } π
Name
Symbol or Formula
Decimal expansion
Notes and notability
Gelfond's constant
e π {\displaystyle e^{\pi }}
23.14069263277925...
Ramanujan's constant
e π 163 {\displaystyle e^{\pi {\sqrt {163}}}}
262537412640768743.99999999999925...
Gaussian integral
π {\displaystyle {\sqrt {\pi }}}
1.772453850905516...
Komornik–Loreti constant
1.787231650...
Universal parabolic constant
}
2.29558714939...
Gelfond–Schneider constant
2 2 {\displaystyle 2^{\sqrt {2}}}
2.665144143...
Euler's number
2.718281828459045235360287471352662497757247...
π will result in − 1 {\displaystyle -1} .
Pi
π {\displaystyle \pi }
3.141592653589793238462643383279502884197169399375...
Pi is a constant irrational number that is the result of dividing the circumference of a circle by its diameter.
Super square-root of 2
2 }_{s}}
1.559610469...
Liouville constant
0.110001000000000000000001000...
Champernowne constant
}
0.12345678910111213141516...
This constant contains every number string inside it, as its decimals are just every number in order. (1,2,3,etc.)
Prouhet–Thue–Morse constant
τ {\textstyle \tau }
0.412454033640...
Omega constant
Ω {\displaystyle \Omega }
0.5671432904097838729999686622...
Cahen's constant
0.64341054629...
Natural logarithm of 2
ln 2
0.693147180559945309417232121458
Lemniscate constant
ϖ {\textstyle \varpi }
2.622057554292119810464839589891...
The ratio of the perimeter of Bernoulli's lemniscate to its diameter.
Tau
τ = 2 π {\displaystyle \tau =2\pi }
6.283185307179586476925286766559...
The ratio of the circumference to a radius, and the number of radians in a complete circle; 2 × {\displaystyle \times } π
· Real numbers › Irrational but not known to be transcendental
ζ(3), also known as Apéry's constant
ζ(3), also known as Apéry's constant
Name
ζ(3), also known as Apéry's constant
Decimal expansion
1.202056903159594285399738161511449990764986292
Erdős–Borwein constant, E
Erdős–Borwein constant, E
Name
Erdős–Borwein constant, E
Decimal expansion
1.606695152415291763...
Reference of unknown transcendentality
[citation needed]
Copeland–Erdős constant
Copeland–Erdős constant
Name
Copeland–Erdős constant
Decimal expansion
0.235711131719232931374143...
Proof of irrationality
Can be proven with Dirichlet's theorem on arithmetic progressions or Bertrand's postulate (Hardy and Wright, p. 113) or Ramare's theorem that every even integer is a sum of at most six primes. It also follows directly from its normality.
Reference of unknown transcendentality
[citation needed]
Prime constant, ρ
Prime constant, ρ
Name
Prime constant, ρ
Decimal expansion
0.414682509851111660248109622...
Proof of irrationality
Proof of the number's irrationality is given at prime constant.
Reference of unknown transcendentality
[citation needed]
Reciprocal Fibonacci constant, ψ
Reciprocal Fibonacci constant, ψ
Name
Reciprocal Fibonacci constant, ψ
Decimal expansion
3.359885666243177553172011302918927179688905133731...
Name
Decimal expansion
Proof of irrationality
Reference of unknown transcendentality
ζ(3), also known as Apéry's constant
1.202056903159594285399738161511449990764986292
Erdős–Borwein constant, E
1.606695152415291763...
[citation needed]
Copeland–Erdős constant
0.235711131719232931374143...
Can be proven with Dirichlet's theorem on arithmetic progressions or Bertrand's postulate (Hardy and Wright, p. 113) or Ramare's theorem that every even integer is a sum of at most six primes. It also follows directly from its normality.
[citation needed]
Prime constant, ρ
0.414682509851111660248109622...
Proof of the number's irrationality is given at prime constant.
[citation needed]
Reciprocal Fibonacci constant, ψ
3.359885666243177553172011302918927179688905133731...
· Real numbers › Real but not known to be irrational, nor transcendental
Euler–Mascheroni constant, γ
Euler–Mascheroni constant, γ
Name and symbol
Euler–Mascheroni constant, γ
Decimal expansion
0.577215664901532860606512090082...
Notes
Believed to be transcendental but not proven to be so. However, it was shown that at least one of γ {\displaystyle \gamma } and the Euler-Gompertz constant δ {\displaystyle \delta } is transcendental. It was also shown that all but at most one number in an infinite list containing γ 4 {\displaystyle {\frac {\gamma }{4}}} have to be transcendental.
Euler–Gompertz constant, δ
Euler–Gompertz constant, δ
Name and symbol
Euler–Gompertz constant, δ
Decimal expansion
0.596 347 362 323 194 074 341 078 499 369...
Notes
It was shown that at least one of the Euler-Mascheroni constant γ {\displaystyle \gamma } and the Euler-Gompertz constant δ {\displaystyle \delta } is transcendental.
Catalan's constant, G
Catalan's constant, G
Name and symbol
Catalan's constant, G
Decimal expansion
0.915965594177219015054603514932384110774...
Notes
It is not known whether this number is irrational.
Khinchin's constant, K0
Khinchin's constant, K0
Name and symbol
Khinchin's constant, K0
Decimal expansion
2.685452001...
Notes
It is not known whether this number is irrational.
1st Feigenbaum constant, δ
1st Feigenbaum constant, δ
Name and symbol
1st Feigenbaum constant, δ
Decimal expansion
4.6692...
Notes
Both Feigenbaum constants are believed to be transcendental, although they have not been proven to be so.
2nd Feigenbaum constant, α
2nd Feigenbaum constant, α
Name and symbol
2nd Feigenbaum constant, α
Decimal expansion
2.5029...
Notes
Both Feigenbaum constants are believed to be transcendental, although they have not been proven to be so.
Glaisher–Kinkelin constant, A
Glaisher–Kinkelin constant, A
Name and symbol
Glaisher–Kinkelin constant, A
Decimal expansion
1.28242712...
Backhouse's constant
Backhouse's constant
Name and symbol
Backhouse's constant
Decimal expansion
1.456074948...
Fransén–Robinson constant, F
Fransén–Robinson constant, F
Name and symbol
Fransén–Robinson constant, F
Decimal expansion
2.8077702420...
Lévy's constant,β
Lévy's constant,β
Name and symbol
Lévy's constant,β
Decimal expansion
1.18656 91104 15625 45282...
Mills' constant, A
Mills' constant, A
Name and symbol
Mills' constant, A
Decimal expansion
1.30637788386308069046...
Notes
It is not known whether this number is irrational.(Finch 2003)
Ramanujan–Soldner constant, μ
Ramanujan–Soldner constant, μ
Name and symbol
Ramanujan–Soldner constant, μ
Decimal expansion
1.451369234883381050283968485892027449493...
Sierpiński's constant, K
Sierpiński's constant, K
Name and symbol
Sierpiński's constant, K
Decimal expansion
2.5849817595792532170658936...
Totient summatory constant
Totient summatory constant
Name and symbol
Totient summatory constant
Decimal expansion
1.339784...
Vardi's constant, E
Vardi's constant, E
Name and symbol
Vardi's constant, E
Decimal expansion
1.264084735305...
Somos' quadratic recurrence constant, σ
Somos' quadratic recurrence constant, σ
Name and symbol
Somos' quadratic recurrence constant, σ
Decimal expansion
1.661687949633594121296...
Niven's constant, C
Niven's constant, C
Name and symbol
Niven's constant, C
Decimal expansion
1.705211...
Brun's constant, B2
Brun's constant, B2
Name and symbol
Brun's constant, B2
Decimal expansion
1.902160583104...
Notes
The irrationality of this number would be a consequence of the truth of the infinitude of twin primes.
Landau's totient constant
Landau's totient constant
Name and symbol
Landau's totient constant
Decimal expansion
1.943596...
Brun's constant for prime quadruplets, B4
Brun's constant for prime quadruplets, B4
Name and symbol
Brun's constant for prime quadruplets, B4
Decimal expansion
0.8705883800...
Viswanath's constant
Viswanath's constant
Name and symbol
Viswanath's constant
Decimal expansion
1.1319882487943...
Khinchin–Lévy constant
Khinchin–Lévy constant
Name and symbol
Khinchin–Lévy constant
Decimal expansion
1.1865691104...
Notes
This number represents the probability that three random numbers have no common factor greater than 1.
Landau–Ramanujan constant
Landau–Ramanujan constant
Name and symbol
Landau–Ramanujan constant
Decimal expansion
0.76422365358922066299069873125...
C(1)
C(1)
Name and symbol
C(1)
Decimal expansion
0.77989340037682282947420641365...
Z(1)
Z(1)
Name and symbol
Z(1)
Decimal expansion
−0.736305462867317734677899828925614672...
Heath-Brown–Moroz constant, C
Heath-Brown–Moroz constant, C
Name and symbol
Heath-Brown–Moroz constant, C
Decimal expansion
0.001317641...
Kepler–Bouwkamp constant,K'
Kepler–Bouwkamp constant,K'
Name and symbol
Kepler–Bouwkamp constant,K'
Decimal expansion
0.1149420448...
MRB constant,S
MRB constant,S
Name and symbol
MRB constant,S
Decimal expansion
0.187859...
Notes
It is not known whether this number is irrational.
Meissel–Mertens constant, M
Meissel–Mertens constant, M
Name and symbol
Meissel–Mertens constant, M
Decimal expansion
0.2614972128476427837554268386086958590516...
Bernstein's constant, β
Bernstein's constant, β
Name and symbol
Bernstein's constant, β
Decimal expansion
0.2801694990...
Gauss–Kuzmin–Wirsing constant, λ1
Gauss–Kuzmin–Wirsing constant, λ1
Name and symbol
Gauss–Kuzmin–Wirsing constant, λ1
Decimal expansion
0.3036630029...
Hafner–Sarnak–McCurley constant,σ
Hafner–Sarnak–McCurley constant,σ
Name and symbol
Hafner–Sarnak–McCurley constant,σ
Decimal expansion
0.3532363719...
Artin's constant,CArtin
Artin's constant,CArtin
Name and symbol
Artin's constant,CArtin
Decimal expansion
0.3739558136...
S(1)
S(1)
Name and symbol
S(1)
Decimal expansion
0.438259147390354766076756696625152...
F(1)
F(1)
Name and symbol
F(1)
Decimal expansion
0.538079506912768419136387420407556...
Stephens' constant
Stephens' constant
Name and symbol
Stephens' constant
Decimal expansion
0.575959...
Golomb–Dickman constant, λ
Golomb–Dickman constant, λ
Name and symbol
Golomb–Dickman constant, λ
Decimal expansion
0.62432998854355087099293638310083724...
Twin prime constant, C2
Twin prime constant, C2
Name and symbol
Twin prime constant, C2
Decimal expansion
0.660161815846869573927812110014...
Feller–Tornier constant
Feller–Tornier constant
Name and symbol
Feller–Tornier constant
Decimal expansion
0.661317...
Laplace limit, ε
Laplace limit, ε
Name and symbol
Laplace limit, ε
Decimal expansion
0.6627434193...
Embree–Trefethen constant
Embree–Trefethen constant
Name and symbol
Embree–Trefethen constant
Decimal expansion
0.70258...
Name and symbol
Decimal expansion
Notes
Euler–Mascheroni constant, γ
0.577215664901532860606512090082...
Believed to be transcendental but not proven to be so. However, it was shown that at least one of γ {\displaystyle \gamma } and the Euler-Gompertz constant δ {\displaystyle \delta } is transcendental. It was also shown that all but at most one number in an infinite list containing γ 4 {\displaystyle {\frac {\gamma }{4}}} have to be transcendental.
Euler–Gompertz constant, δ
0.596 347 362 323 194 074 341 078 499 369...
It was shown that at least one of the Euler-Mascheroni constant γ {\displaystyle \gamma } and the Euler-Gompertz constant δ {\displaystyle \delta } is transcendental.
Catalan's constant, G
0.915965594177219015054603514932384110774...
It is not known whether this number is irrational.
Khinchin's constant, K0
2.685452001...
It is not known whether this number is irrational.
1st Feigenbaum constant, δ
4.6692...
Both Feigenbaum constants are believed to be transcendental, although they have not been proven to be so.
2nd Feigenbaum constant, α
2.5029...
Both Feigenbaum constants are believed to be transcendental, although they have not been proven to be so.
Glaisher–Kinkelin constant, A
1.28242712...
Backhouse's constant
1.456074948...
Fransén–Robinson constant, F
2.8077702420...
Lévy's constant,β
1.18656 91104 15625 45282...
Mills' constant, A
1.30637788386308069046...
It is not known whether this number is irrational.(Finch 2003)
Ramanujan–Soldner constant, μ
1.451369234883381050283968485892027449493...
Sierpiński's constant, K
2.5849817595792532170658936...
Totient summatory constant
1.339784...
Vardi's constant, E
1.264084735305...
Somos' quadratic recurrence constant, σ
1.661687949633594121296...
Niven's constant, C
1.705211...
Brun's constant, B2
1.902160583104...
The irrationality of this number would be a consequence of the truth of the infinitude of twin primes.
Landau's totient constant
1.943596...
Brun's constant for prime quadruplets, B4
0.8705883800...
Viswanath's constant
1.1319882487943...
Khinchin–Lévy constant
1.1865691104...
This number represents the probability that three random numbers have no common factor greater than 1.
Landau–Ramanujan constant
0.76422365358922066299069873125...
C(1)
0.77989340037682282947420641365...
Z(1)
−0.736305462867317734677899828925614672...
Heath-Brown–Moroz constant, C
0.001317641...
Kepler–Bouwkamp constant,K'
0.1149420448...
MRB constant,S
0.187859...
It is not known whether this number is irrational.
Meissel–Mertens constant, M
0.2614972128476427837554268386086958590516...
Bernstein's constant, β
0.2801694990...
Gauss–Kuzmin–Wirsing constant, λ1
0.3036630029...
Hafner–Sarnak–McCurley constant,σ
0.3532363719...
Artin's constant,CArtin
0.3739558136...
S(1)
0.438259147390354766076756696625152...
F(1)
0.538079506912768419136387420407556...
Stephens' constant
0.575959...
Golomb–Dickman constant, λ
0.62432998854355087099293638310083724...
Twin prime constant, C2
0.660161815846869573927812110014...
Feller–Tornier constant
0.661317...
Laplace limit, ε
0.6627434193...
Embree–Trefethen constant
0.70258...

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    https://physics.nist.gov/cgi-bin/cuu/Value?bg
  40. The NIST Reference on Constants, Units, and Uncertainty
    https://physics.nist.gov/cgi-bin/cuu/Value?mu
  41. The NIST Reference on Constants, Units, and Uncertainty
    https://physics.nist.gov/cgi-bin/cuu/Value?h
  42. The NIST Reference on Constants, Units, and Uncertainty
    https://physics.nist.gov/cgi-bin/cuu/Value?ryd
  43. The NIST Reference on Constants, Units, and Uncertainty
    https://physics.nist.gov/cgi-bin/cuu/Value?c
  44. The NIST Reference on Constants, Units, and Uncertainty
    https://physics.nist.gov/cgi-bin/cuu/Value?ep0
  45. "Bags of Talent, a Touch of Panic, and a Bit of Luck: The Case of Non-Numerical Vague Quantifiers" from Linguista Pragen
    http://versita.metapress.com/content/t98071387u726916/?p=1ad6a085630c432c94528c5548f5c2c4&pi=1
  46. Boston Globe, July 13, 2016: "The surprising history of indefinite hyperbolic numerals"
    https://www.bostonglobe.com/ideas/2016/07/13/the-surprising-history-indefinite-hyperbolic-numerals/qYTKpkP9lyWVfItLXuTHdM/story.html
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