# List of numbers

Wikimedia list article

This is a list of numbers. This list will always be not finished. This happens because there are an infinite amount of numbers. Only notable numbers will be added. Numbers can be added as long as they are popular in math, history or culture.

This means that numbers can only be notable if they are a big part of history. A number isn't notable if it is only related to another number. For example, the number (3,4) is a notable number when it is a complex number (3+4i). When it is only (3,4), however, it's not notable.

## Natural numbers

Natural numbers are a type of integer. They can be used for counting. Natural numbers can also be used to find out about other number systems. A negative number is not a natural number.

0 is argued on whether or not it is a natural number. To fix this, people use the terms "non-negative integers", which cover 0 and "positive integers", which does not.

 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 99 100 101 102 103 104 105 107 108 119 120 133 144 200 300 400 500 600 700 800 900 1000 6000 106 109 1012 larger numbers, along with 10100 and 1010100

## Classes of natural numbers

### Prime numbers

A prime number is a natural number which has only two divisors: 1 and itself.

 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 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

### Highly composite numbers

A highly composite number is a natural number that has more divisors than any smaller natural number. They are used a lot in geometry, grouping, and time measurement.

The first 20 highly composite numbers are:

1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560

### Perfect numbers

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

The first 10 perfect numbers:

1.   6
2.   28
3.   496
4.   8128
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

## Integers

Integers are a set of numbers. They usually are in arithmetic and number theory. There are many subsets of integers. These can cover natural numbers, prime numbers, perfect numbers, etc.

Popular integers are −1 and 0.

### Orders of magnitude

Integers can be written in orders of magnitude. This can be written as 10k, where k is an integer. If k = 0, 1, 2, 3, then the powers of ten for them are 1, 10, 100 and 1000. This is used in scientific notation.

Each number has its own prefix. Each prefix has its own symbol. For example, kilo- may be added to the beginning of gram. This changes the meaning of gram to mean that the gram is 1000 times more than a gram: one kilogram is the same as 1000 grams.

Number 1000m Name Symbol

0.0000000001

10-24 Yokto y

0.000000001

10-21 Zepto z

0.00000001

10-18 Atto a

0.0000001

10-15 Femto f

0.000001

10-12 Pico p

0.00001

10-9 Nano n

0.0001

10-6 Micro μ

0.001

10-3 Mili m

0.01

10-2 Centi c

0.1

10-1 Deci d

10

101 Deca da

100

102 Hecto h
1000 103 Kilo k
1000000 106 Mega M
1000000000 109 Giga G
1000000000000 1012 Tera T
1000000000000000 1015 Peta P
1000000000000000000 1018 Exa E
1000000000000000000000 1021 Zetta Z
1000000000000000000000000 1024 Yotta Y

## Rational numbers

A rational number is a number that can be written as a fraction with two integers. The numerator is written as p and the denominator(which cannot be zero) is written as q. Every integer is a rational number. This is because in integers, 1 is always the denominator of a fraction.

Rational numbers can be written in infinitely many ways. For example, 0.12 can be written as three twenty-fifths (3/25), nine seventy-fifths (9/75), etc.

Table of notable rational numbers
Decimal expansion Fraction Reason
1.0 1/1 1/1 is equal to 1, a notable real number.
1
0.5 1/2 1/2 is a popular number in math. For example, you can use 1/2 to find the area of a Triangle.
3.142 857... 22/7 22/7 is a number slightly above $\pi$  and is an approximation of $\pi$ .
0.166 666... 1/6 One sixth is seen in a lot of equations. For example, the solution to the Basel problem uses 1/6.

## Irrational numbers

Irrational numbers are numbers that cannot be written as a fraction. These are written as algebraic numbers or transcendental numbers.

### Algebraic numbers

Name Expression Decimal expansion Reason
Square root of two ${\sqrt {2}}$  1.414213562373095048801688724210 The Square root of 2(also called Pythagoras' constant) is a number used in math a lot. It can be used to find the ratio of diagonal to side length in a square.
Triangular root of 2 ${\frac {{\sqrt {17}}-1}{2}}$  1.561552812808830274910704927987
Phi, Golden ratio $\phi$  1.618033988749894848204586834366 The golden ratio is a famous number used in both math and science.

### Transcendental numbers

Name Symbol

or

Formula

Decimal expansion Reason
e, Euler's number e 2.718281828459045235360287471352662497757247... e is the base of a natural logarithm.
Pi π 3.141592653589793238462643383279502884197169... Pi is an irrational number that is the result of dividing the circumference of a circle by its diameter.

### Real numbers

The real numbers are a superset(or category) of numbers. They cover algebraic and transcendental numbers.

### Real but not known if irrational or transcendental

Name and symbol Decimal expansion Notes
Euler–Mascheroni constant, γ 0.577215664901532860606512090082... The Euler–Mascheroni constant is used in limits and logarithms. It is thought to be transcendental but not proven to be so.
Twin prime constant, C2 0.660161815846869573927812110014...

## Hypercomplex numbers

A hypercomplex number is a word for an element of a unital algebra over the field of real numbers.

### Algebraic complex numbers

• i, Imaginary unit: ${\textstyle i=-1}$

## Transfinite numbers

Transfinite numbers are numbers that are "infinite". They are larger than any finite number. They are, however, not absolutely infinite.

## Physical Constants

Physical constants are constants that can be used in the universe to figure out information.

## Named numbers

• Googol, 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
• Googolplex, 10(10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000)
• Graham's number, G
• Skewes's number, S