View source for List of numbers

This is a list of [[Number|numbers]]. This list will always be not finished. This happens because there are an infinite amount of numbers. Only [[Wikipedia:Notable|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 [[Wikipedia:Notable|notable]] if they are a big part of [[history]]. A number isn't [[Wikipedia:Notable|notable]] if it is only related to another number. For example, the number (3,4) is a [[Wikipedia:Notable|notable]] number when it is a [[complex number]] (3+4i). When it is only (3,4), however, it's not notable. If a number is not important, that can also make the number important. This is called the [[interesting number paradox]].

== Natural numbers ==
{{main|Natural number}}
[[Natural number|Natural numbers]] are a type of [[Integers|integer]]. They can be used for [[counting]]. Natural numbers can also be used to find out about other number systems. The symbol {{Math|'''N'''}} (or [[blackboard bold]] <math>\mathbb{\N}</math>, Unicode {{Unichar|2115|DOUBLE-STRUCK CAPITAL N}}) is used to symbolize all of the natural numbers.''.'' A [[negative number]] is not a natural number.

[[Zero|0]] is argued on whether or not it is a natural number. In [[computer science]] and [[set theory]], 0 is a natural number. In [[number theory]], it is not. To fix this, people use the terms "non-negative integers". Non-negative integers includes the number 0. "Positive integers" does not.

Natural numbers can be used as [[cardinal numbers]] or [[ordinal numbers]].
{| class="wikitable sortable mw-collapsible" style="text-align:center;"
|+ class="nowrap" |Table of small natural numbers
|[[0]]
|[[1 (number)|1]]
|[[2 (number)|2]]
|[[3 (number)|3]]
|[[4 (number)|4]]
|[[5 (number)|5]]
|[[6 (number)|6]]
|[[7 (number)|7]]
|[[8]]
|[[9 (number) |9]]
|-
|[[10 (number)|10]]
|[[11 (number)|11]]
|[[12 (number)|12]]
|[[13 (number)|13]]
|[[14 (number)|14]]
|[[15 (number)|15]]
|[[16 (number)|16]]
|[[17 (number)|17]]
|[[18 (number)|18]]
|[[19 (number)|19]]
|-
|[[20 (number)|20]]
|[[21 (number)|21]]
|[[22 (number)|22]]
|[[23 (number)|23]]
|[[24 (number)|24]]
|[[25 (number)|25]]
|[[26 (number)|26]]
|[[27 (number)|27]]
|[[28 (number)|28]]
|[[29 (number)|29]]
|-
|[[30 (number)|30]]
|[[31 (number)|31]]
|[[32 (number)|32]]
|[[33 (number)|33]]
|[[34 (number)|34]]
|[[35 (number)|35]]
|[[36 (number)|36]]
|[[37 (number)|37]]
|[[38 (number)|38]]
|[[39 (number)|39]]
|-
|[[40 (number)|40]]
|[[41 (number)|41]]
|[[42 (number)|42]]
|[[43 (number)|43]]
|[[44 (number)|44]]
|[[45 (number)|45]]
|[[46 (number)|46]]
|[[47 (number)|47]]
|[[48 (number)|48]]
|[[49 (number)|49]]
|-
|[[50 (number)|50]]
|[[51 (number)|51]]
|[[52 (number)|52]]
|[[53 (number)|53]]
|[[54 (number)|54]]
|[[55 (number)|55]]
|[[56 (number)|56]]
|[[57 (number)|57]]
|[[58 (number)|58]]
|[[59 (number)|59]]
|-
|[[60 (number)|60]]
|[[61 (number)|61]]
|[[62 (number)|62]]
|[[63 (number)|63]]
|[[64 (number)|64]]
|[[65 (number)|65]]
|[[66 (number)|66]]
|[[67 (number)|67]]
|[[68 (number)|68]]
|[[69 (number)|69]]
|-
|[[70 (number)|70]]
|[[71 (number)|71]]
|[[72 (number)|72]]
|[[73 (number)|73]]
|[[74 (number)|74]]
|[[75 (number)|75]]
|[[76 (number)|76]]
|[[77 (number)|77]]
|[[78 (number)|78]]
|[[79 (number)|79]]
|-
|[[80 (number)|80]]
|[[81 (number)|81]]
|[[82 (number)|82]]
|[[83 (number)|83]]
|[[84 (number)|84]]
|[[85 (number)|85]]
|[[86 (number)|86]]
|[[87 (number)|87]]
|[[88 (number)|88]]
|[[89 (number)|89]]
|-
|[[90 (number)|90]]
|[[91 (number)|91]]
|[[92 (number)|92]]
|[[93 (number)|93]]
|[[94 (number)|94]]
|[[95 (number)|95]]
|[[96 (number)|96]]
|[[97 (number)|97]]
|[[98 (number)|98]]
|[[99 (number)|99]]
|-
|[[100 (number)|100]]
|[[101 (number)|101]]
|[[102 (number)|102]]
|[[103 (number)|103]]
|[[104 (number)|104]]
|[[105 (number)|105]]
|[[106 (number)|106]]
|[[107 (number)|107]]
|[[108 (number)|108]]
|[[109 (number)|109]]
|-
|[[110 (number)|110]]
|[[111 (number)|111]]
|[[112 (number)|112]]
|[[113 (number)|113]]
|[[114 (number)|114]]
|[[115 (number)|115]]
|[[116 (number)|116]]
|[[117 (number)|117]]
|[[118 (number)|118]]
|[[119 (number)|119]]
|-
|[[120 (number)|120]]
|[[121 (number)|121]]
|[[122 (number)|122]]
|[[123 (number)|123]]
|[[124 (number)|124]]
|[[125 (number)|125]]
|[[126 (number)|126]]
|[[127 (number)|127]]
|[[128 (number)|128]]
|[[129 (number)|129]]
|-
|[[130 (number)|130]]
|[[131 (number)|131]]
|[[132 (number)|132]]
|[[133 (number)|133]]
|[[134 (number)|134]]
|[[135 (number)|135]]
|[[136 (number)|136]]
|[[137 (number)|137]]
|[[138 (number)|138]]
|[[139 (number)|139]]
|-
|[[140 (number)|140]]
|[[141 (number)|141]]
|[[142 (number)|142]]
|[[143 (number)|143]]
|[[144 (number)|144]]
|[[145 (number)|145]]
|[[146 (number)|146]]
|[[147 (number)|147]]
|[[148 (number)|148]]
|[[149 (number)|149]]
|-
|[[150 (number)|150]]
|[[151 (number)|151]]
|[[152 (number)|152]]
|[[153 (number)|153]]
|[[154 (number)|154]]
|[[155 (number)|155]]
|[[156 (number)|156]]
|[[157 (number)|157]]
|[[158 (number)|158]]
|[[159 (number)|159]]
|-
|[[160 (number)|160]]
|[[161 (number)|161]]
|[[162 (number)|162]]
|[[163 (number)|163]]
|[[164 (number)|164]]
|[[165 (number)|165]]
|[[166 (number)|166]]
|[[167 (number)|167]]
|[[168 (number)|168]]
|[[169 (number)|169]]
|-
|[[170 (number)|170]]
|[[171 (number)|171]]
|[[172 (number)|172]]
|[[173 (number)|173]]
|[[174 (number)|174]]
|[[175 (number)|175]]
|[[176 (number)|176]]
|[[177 (number)|177]]
|[[178 (number)|178]]
|[[179 (number)|179]]
|-
|[[180 (number)|180]]
|[[181 (number)|181]]
|[[182 (number)|182]]
|[[183 (number)|183]]
|[[184 (number)|184]]
|[[185 (number)|185]]
|[[186 (number)|186]]
|[[187 (number)|187]]
|[[188 (number)|188]]
|[[189 (number)|189]]
|-
|[[190 (number)|190]]
|[[191 (number)|191]]
|[[192 (number)|192]]
|[[193 (number)|193]]
|[[194 (number)|194]]
|[[195 (number)|195]]
|[[196 (number)|196]]
|[[197 (number)|197]]
|[[198 (number)|198]]
|[[199 (number)|199]]
|-
|[[200 (number)|200]]
|[[201 (number)|201]]
|[[202 (number)|202]]
|[[203 (number)|203]]
|[[204 (number)|204]]
|[[205 (number)|205]]
|[[206 (number)|206]]
|[[207 (number)|207]]
|[[208 (number)|208]]
|[[209 (number)|209]]
|-
|[[210 (number)|210]]
|[[211 (number)|211]]
|[[212 (number)|212]]
|[[213 (number)|213]]
|[[214 (number)|214]]
|[[215 (number)|215]]
|[[216 (number)|216]]
|[[217 (number)|217]]
|[[218 (number)|218]]
|[[219 (number)|219]]
|-
|[[220 (number)|220]]
|[[221 (number)|221]]
|[[222 (number)|222]]
|[[223 (number)|223]]
|[[224 (number)|224]]
|[[225 (number)|225]]
|[[226 (number)|226]]
|[[227 (number)|227]]
|[[228 (number)|228]]
|[[229 (number)|229]]
|-
|[[230 (number)|230]]
|[[231 (number)|231]]
|[[232 (number)|232]]
|[[233 (number)|233]]
|[[234 (number)|234]]
|[[235 (number)|235]]
|[[236 (number)|236]]
|[[237 (number)|237]]
|[[238 (number)|238]]
|[[239 (number)|239]]
|-
|[[240 (number)|240]]
|[[241 (number)|241]]
|[[242 (number)|242]]
|[[243 (number)|243]]
|[[244 (number)|244]]
|[[245 (number)|245]]
|[[246 (number)|246]]
|[[247 (number)|247]]
|[[248 (number)|248]]
|[[249 (number)|249]]
|-
|[[250 (number)|250]]
|[[251 (number)|251]]
|[[252 (number)|252]]
|[[253 (number)|253]]
|[[254 (number)|254]]
|[[255 (number)|255]]
|[[256 (number)|256]]
|[[257 (number)|257]]
|[[258 (number)|258]]
|[[259 (number)|259]]
|-
|[[260 (number)|260]]
|[[261 (number)|261]]
|[[262 (number)|262]]
|[[263 (number)|263]]
|[[264 (number)|264]]
|[[265 (number)|265]]
|[[266 (number)|266]]
|[[267 (number)|267]]
|[[268 (number)|268]]
|[[269 (number)|269]]
|-
|[[270 (number)|270]]
|[[271 (number)|271]]
|[[272 (number)|272]]
|[[273 (number)|273]]
|[[274 (number)|274]]
|[[275 (number)|275]]
|[[276 (number)|276]]
|[[277 (number)|277]]
|[[278 (number)|278]]
|[[279 (number)|279]]
|-
|[[280 (number)|280]]
|[[281 (number)|281]]
|[[282 (number)|282]]
|[[283 (number)|283]]
|[[284 (number)|284]]
|[[285 (number)|285]]
|[[286 (number)|286]]
|[[287 (number)|287]]
|[[288 (number)|288]]
|[[289 (number)|289]]
|-
|[[290 (number)|290]]
|[[291 (number)|291]]
|[[292 (number)|292]]
|[[293 (number)|293]]
|[[294 (number)|294]]
|[[295 (number)|295]]
|[[296 (number)|296]]
|[[297 (number)|297]]
|[[298 (number)|298]]
|[[299 (number)|299]]
|-
|[[300 (number)|300]]
|[[301 (number)|301]]
|[[302 (number)|302]]
|[[303 (number)|303]]
|[[304 (number)|304]]
|[[305 (number)|305]]
|[[306 (number)|306]]
|[[307 (number)|307]]
|[[308 (number)|308]]
|[[309 (number)|309]]
|-
|[[310 (number)|310]]
|[[311 (number)|311]]
|[[312 (number)|312]]
|[[313 (number)|313]]
|[[314 (number)|314]]
|[[315 (number)|315]]
|[[316 (number)|316]]
|[[317 (number)|317]]
|[[318 (number)|318]]
|[[319 (number)|319]]
|-
|[[320 (number )|320]]
|[[321 (number)|321]]
|[[322 (number)|322]]
|[[323 (number)|323]]
|[[400 (number)|400]]
|[[500 (number)|500]]
|[[600 (number)|600]]
|[[700 (number)|700]]
|[[800 (number)|800]]
|[[900 (number)|900]]
|-
|[[330 (number)|330]]
|[[1000 (number)|1000]]
|[[2000 (number)|2000]]
|[[3000 (number)|3000]]
|[[4000 (number)|4000]]
|[[5000 (number)|5000]]
|[[6000 (number)|6000]]
|[[7000 (number)|7000]]
|[[8000 (number)|8000]]
|[[9000 (number)|9000]]
|-
|[[340 (number)|340]]
|[[10,000]]
|[[20,000]]
|[[30,000]]
|[[40,000]]
|[[50,000]]
|[[60,000]]
|[[70,000]]
|[[80,000]]
|[[90,000]]
|-
|[[100,000|10<sup>5</sup>]]
|[[1,000,000|10<sup>6</sup>]]
|[[10,000,000|10<sup>7</sup>]]
|[[100,000,000|10<sup>8</sup>]]
|[[1,000,000,000|10<sup>9</sup>]]
| colspan="5" |[[Trillion|10<sup>12</sup>]]
|-
| colspan="10" |[[Order of magnitude|larger numbers]], including [[Googol|10<sup>100</sup>]] and [[Googolplex|10<sup>10<sup>100</sup></sup>]]
|}

=== Importance in math ===
Natural numbers can be important in [[mathematics]]. This might because it is part of a [[Set theory|set]]. A number can also be important because it has a unique property.{{Collapsible list|[[1 (number)|1]]. If you multiply any number by one, you will get the same number. This is called the [[multiplicative identity]]. It is also the only natural number (other than 0) that is not [[prime number|prime]] or [[composite number|composite]].|[[2 (number)|2]]. It is the base of the [[binary number]] system. This system is used in almost all [[computer]]s.|[[3 (number)|3]]. It is 2<sup>2</sup>-1. It is also the first [[Mersenne prime]]. It is the first odd [[prime number]].|[[4 (number)|4]]. It is the first [[composite number]].|[[6 (number)|6]]. It is the first [[perfect number]].|[[9 (number)|9]]. It is the first [[Parity (mathematics)|odd]] number that is [[Composite number|composite]].|[[11 (number)|11]]. It is the fifth [[prime number|prime]].|[[12 (number)|12]]. It is the first [[sublime number]].|[[17 (number)|17]]. It is the [[sum]] of the 1st 4 [[prime number]]s. It is the only [[prime number]] that is the [[sum]] of 4 [[prime number]]s in a row.|[[24 (number)|24]]. All [[Dirichlet character]]s [[Modular arithmetic|mod]] ''n'' are [[real number|real]] [[if and only if|if]] ''n'' is a [[divisor]] of 24.|[[25 (number)|25]]. It is the first [[centered square number]] (other than 1) that is also a [[square number]].|[[27 (number)|27]], the [[Cube (algebra)|cube]] of 3. This means that it is 3<sup>3</sup>.|[[28 (number)|28]]. It is the second [[perfect number]].|[[30 (number)|30]]. It is the smallest [[sphenic number]].|[[32 (number)|32]]. It is the smallest [[fifth power (algebra)|fifth power]] (other than 1 or 0).|[[36 (number)|36]]. This is the smallest number that is not a [[perfect power]], but not a [[prime power]].|[[70 (number)|70]]. It is the smallest [[weird number]].|[[72 (number)|72]]. It is the smallest [[Achilles number]].|expand=y|framestyle=|titlestyle=|title=List of important [[natural numbers]] in [[mathematics|math]]|liststyle=|hlist=|bullets=on}}

=== Importance in culture ===
Many numbers are also important in [[culture]].<ref>{{Cite journal|last1=Ayonrinde|first1=Oyedeji A.|last2=Stefatos|first2=Anthi|last3=Miller|first3=Shadé|last4=Richer|first4=Amanda|last5=Nadkarni|first5=Pallavi|last6=She|first6=Jennifer|last7=Alghofaily|first7=Ahmad|last8=Mngoma|first8=Nomusa|date=2020-06-12|title=The salience and symbolism of numbers across cultural beliefs and practice|journal=International Review of Psychiatry|volume=33|issue=1–2|pages=179–188|doi=10.1080/09540261.2020.1769289|issn=0954-0261|pmid=32527165|s2cid=219605482}}</ref> They can also be important for [[measurement]].{{Collapsible list|[[3 (number)|3]]. It is important in [[Christianity]] as the [[Trinity]]. It is also important in [[Hinduism]] ([[Trimurti]], [[Tridevi]]). It is also important in other older [[mythology|mythologies]].|[[4 (number)|4]]. It is an [[Tetraphobia|"unlucky" number]] in modern [[China]], [[Japan]], and [[Korea]]. In their languages, 4 sounds similar to the word "death".|[[7 (number)|7]]. It is the number of days in a [[week]]. It is also called a "lucky" number in Western cultures.|[[8 (number)|8]]. 8 is called a [[Chinese numerology#Eight|"lucky" number in Chinese culture]]. This is because the [[Chinese language|Chinese word]] for "Eight" sounds like prosperity.|[[12 (number)|12]]. 12 things is called a [[dozen]]. There are 12 [[month]]s in a [[year]]. There are 12 [[constellation]]s of the [[Zodiac]] and [[astrological sign]]s. In [[Christianity]], there were 12 [[Apostles in the New Testament|Apostle]]s of [[Jesus]].|[[13 (number)|13]], is called an [[Triskaidekaphobia|"unlucky" number]] in Western [[superstition]]. It is also called a "[[Baker's dozen]]".<ref>{{Cite web |title=Demystified {{!}} Why a baker's dozen is thirteen |url=https://www.britannica.com/video/213933/Demystified-why-is-bakers-dozen-thirteen |access-date=2024-06-05 |website=www.britannica.com |language=en}}</ref>|[[17 (number)|17]]. It is called [[Heptadecaphobia|unlucky]] in [[Greece|Greek]] and [[Latin]] countries.|[[18 (number)|18]]. In [[gematria|Jewish numerology]], 18 is a "lucky" number. This is because it is also the [[Chai (symbol)|Hebrew word for life]]|[[40 (number)|40]]. 40 is important in [[Tengrism]] and [[Turkey|Turkish]] [[folklore]]. There are many [[tradition]]s that use 40.|[[42 (number)|42]]. According to the ''[[The Hitchhiker's Guide to the Galaxy]]'', 42  the "answer to the ultimate question of life, the universe, and everything."|[[69 (number)|69]]. Is a word that can mean [[oral sex]].|expand=y|framestyle=|titlestyle=|title=List of important [[natural numbers]] in [[culture]]|liststyle=|hlist=|bullets=on}}{{Collapsible list|[[10]]. 10 is the number of [[digit]]s in the [[decimal]] number system.|[[12 (number)|12]]. 12 is the [[duodecimal|number base]] to measuring time in many places.|[[14 (number)|14]]. Is the number of days in a [[fortnight]].|[[16 (number)|16]]. 16 is the number of [[digit]]s in the [[hexadecimal]] number system.|[[24 (number)|24]]. 12 is also the number of [[hour]]s in a [[day]].|[[31 (number)|31]]. 31 is the most number of [[day]]s a [[month]] can have.|[[60 (number)|60]]. 60 is the [[sexagesimal|number base]] for some ancient counting systems. For example, the [[Babylonian numerals|Babylonians]] used this number base. Also, 60 is used in some modern measuring systems.|[[360 (number)|360]]. 360 is the number of [[Degree (angle)|degree]]s in a full [[circle]].|[[365 (number)|365]]. 365 is the number of days in the normal [[Gregorian calendar|year]]. In [[leap year]]s, there are 366 days.|expand=y|framestyle=|titlestyle=|title=List of [[natural numbers]] important in [[measurement]]s and [[scale]]s.|liststyle=|hlist=|bullets=on}}{{Collapsible list|[[4]]. 4 is the number of [[bit]]s in a [[nibble]].|[[8]]. 8 is the number of [[bit]]s in an [[Octet (computing)|octet]] and a [[byte]].|[[256 (number)|256]]. 256 is the number of possible numbers in [[8-bit|8 bits]].|[[1024 (number)|1024]]. 1024 is the number of [[byte]]s in a [[kibibyte]]. It is the number of [[bit]]s in a [[kibibit]].|[[65535 (number)|65535]]. 2<sup>16</sup> − 1. It is the largest number in a [[16-bit]] number.|[[65536 (number)|65536]]. 2<sup>16</sup>. It is the number of possible numbers in [[16-bits]].|expand=y|framestyle=|titlestyle=|title=List of [[natural number]]s in [[computer]]s|liststyle=|hlist=|bullets=on}}

== Classes of natural numbers ==

=== Prime numbers ===
{{Main|Prime number|List of prime numbers}}
A [[prime number]] is a type of [[natural number]]. It only has two [[Divisor|divisors]]: 1 and itself.

{| class="wikitable sortable mw-collapsible" style="text-align:center;"
|+ class="nowrap" |The first 100 prime numbers
 |&nbsp;&nbsp;[[2 (number)|2]]
|&nbsp;&nbsp;[[3 (number)|3]]
|&nbsp;&nbsp;[[5 (number)|5]]
|&nbsp;&nbsp;[[7 (number)|7]]
|&nbsp;[[11 (number)|11]]
|&nbsp;[[13 (number)|13]]
|&nbsp;[[17 (number)|17]]
|&nbsp;[[19 (number)|19]]
|&nbsp;[[23 (number)|23]]
|&nbsp;[[29 (number)|29]]
 |-
 |&nbsp;[[31 (number)|31]]
|&nbsp;[[37 (number)|37]]
|&nbsp;[[41 (number)|41]]
|&nbsp;[[43 (number)|43]]
|&nbsp;[[47 (number)|47]]
|&nbsp;[[53 (number)|53]]
|&nbsp;[[59 (number)|59]]
|&nbsp;[[61 (number)|61]]
|&nbsp;[[67 (number)|67]]
|&nbsp;[[71 (number)|71]]
 |-
 |&nbsp;[[73 (number)|73]]
|&nbsp;[[79 (number)|79]]
|&nbsp;[[83 (number)|83]]
|&nbsp;[[89 (number)|89]]
|&nbsp;[[97 (number)|97]]
|[[101 (number)|101]]
|[[103 (number)|103]]
|[[107 (number)|107]]
|[[109 (number)|109]]
|[[113 (number)|113]]
 |-
 |[[127 (number)|127]]
|[[131 (number)|131]]
|[[137 (number)|137]]
|[[139 (number)|139]]
|[[149 (number)|149]]
|[[151 (number)|151]]
|[[157 (number)|157]]
|[[163 (number)|163]]
|[[167 (number)|167]]
|[[173 (number)|173]]
 |-
 |[[179 (number)|179]]
|[[181 (number)|181]]
|[[191 (number)|191]]
|[[193 (number)|193]]
|[[197 (number)|197]]
|[[199 (number)|199]]
|[[211 (number)|211]]
|[[223 (number)|223]]
|[[227 (number)|227]]
|[[229 (number)|229]]
 |-
 |[[233 (number)|233]]
|[[239 (number)|239]]
|[[241 (number)|241]]
|[[251 (number)|251]]
|[[257 (number)|257]]
|[[263 (number)|263]]
|[[269 (number)|269]]
|[[271 (number)|271]]
|[[277 (number)|277]]
|[[281 (number)|281]]
 |-
 |[[283 (number)|283]]
|[[293 (number)|293]]
|[[307 (number)|307]]
|[[311 (number)|311]]
|[[313 (number)|313]]
|[[317 (number)|317]]
|[[331 (number)|331]]
|[[337 (number)|337]]
|[[347 (number)|347]]
|[[349 (number)|349]]
 |-
 |[[353 (number)|353]]
|[[359 (number)|359]]
|[[367 (number)|367]]
|[[373 (number)|373]]
|[[379 (number)|379]]
|[[383 (number)|383]]
|[[389 (number)|389]]
|[[397 (number)|397]]
|[[401 (number)|401]]
|[[409 (number)|409]]
 |-
 |[[419 (number)|419]]
|[[421 (number)|421]]
|[[431 (number)|431]]
|[[433 (number)|433]]
|[[439 (number)|439]]
|[[443 (number)|443]]
|[[449 (number)|449]]
|[[457 (number)|457]]
|[[461 (number)|461]]
|[[463 (number)|463]]
 |-
 |[[467 (number)|467]]
|[[479 (number)|479]]
|[[487 (number)|487]]
|[[491 (number)|491]]
|[[499 (number)|499]]
|[[503 (number)|503]]
|[[509 (number)|509]]
|[[521 (number)|521]]
|[[523 (number)|523]]
|[[541 (number)|541]]
 |}

=== Highly composite numbers ===
A highly [[composite number]] is a type of [[natural number]]. It has more [[Divisor|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 (number)|1]], [[2 (number)|2]], [[4 (number)|4]], [[6 (number)|6]], [[12 (number)|12]], [[24 (number)|24]], [[36 (number)|36]], [[48 (number)|48]], [[60 (number)|60]], [[120 (number)|120]], [[180 (number)|180]], [[240 (number)|240]], [[360 (number)|360]], [[720 (number)|720]], [[840 (number)|840]], [[1260 (number)|1260]], [[1680 (number)|1680]], [[2520 (number)|2520]], [[5040 (number)|5040]], [[7560 (number)|7560]]

=== Perfect numbers ===
{{main|Perfect number}}

A [[perfect number]] is a type of [[integer]]. It has the [[sum]] of its [[Positive number|positive]] [[Divisor|divisors]] (all divisors except itself).

The first 10 perfect numbers:

{{ordered list|type=decimal|&nbsp; [[6 (number)|6]]|&nbsp; [[28 (number)|28]]|&nbsp; [[496 (number)|496]]|&nbsp; [[8128 (number)|8128]]|&nbsp; 33 550 336|&nbsp; 8 589 869 056|&nbsp; 137 438 691 328|&nbsp; 2 305 843 008 139 952 128|&nbsp; 2 658 455 991 569 831 744 654 692 615 953 842 176|&nbsp; 191 561 942 608 236 107 294 793 378 084 303 638 130 997 321 548 169 216}}

== Integers ==
{{main|Integer}}

[[Integer|Integers]] are a [[Set (mathematics)|set]] of numbers. They usually are in [[arithmetic]] and [[number theory]]. There are many [[Subset|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 10<sup>''k''</sup>, where ''k'' is an [[integer]].  If ''k''&nbsp;=&nbsp;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 notation|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]].<ref>{{cite web | url=https://www.techtarget.com/searchstorage/definition/Kilo-mega-giga-tera-peta-and-all-that | title=What is Kilo, Mega, Giga, Tera, Peta, Exa, Zetta and All That? }}</ref>

{| class="wikitable sortable mw-collapsible"
!Number
!1000<sup>''m''</sup>
!Name
!Symbol
|-
| style="text-align:right;" |
0.0000000001
|10<sup>-24</sup>
|Yokto
|y
|-
| style="text-align:right;" |
0.000000001
|10<sup>-21</sup>
|Zepto
|z
|-
| style="text-align:right;" |
0.00000001
|10<sup>-18</sup>
|Atto
|a
|-
| style="text-align:right;" |
0.0000001
|10<sup>-15</sup>
|Femto
|f
|-
| style="text-align:right;" |
0.000001
|10<sup>-12</sup>
|Pico
|p
|-
| style="text-align:right;" |
0.00001
|10<sup>-9</sup>
|Nano
|n
|-
| style="text-align:right;" |
0.0001
|10<sup>-6</sup>
|Micro
|μ
|-
| style="text-align:right;" |
0.001
|10<sup>-3</sup>
|Mili
|m
|-
| style="text-align:right;" |
0.01
|10<sup>-2</sup>
|Centi
|c
|-
| style="text-align:right;" |
0.1
|10<sup>-1</sup>
|Deci
|d
|-
| style="text-align:right;" |
10
|10<sup>1</sup>
|Deca
|da
|-
| style="text-align:right;" |
100
|10<sup>2</sup>
|Hecto
|h
|-
| style="text-align:right;" |{{gaps|1|000}}
|10<sup>3</sup>
|[[Kilo-|Kilo]]
|k
|-
| style="text-align:right;" |{{gaps|1|000|000}}
|10<sup>6</sup>
|[[Mega-|Mega]]
|M
|-
| style="text-align:right;" |{{gaps|1|000|000|000}}
|10<sup>9</sup>
|[[Giga-|Giga]]
|G
|-
| style="text-align:right;" |{{gaps|1|000|000|000|000}}
|10<sup>12</sup>
|[[Tera-|Tera]]
|T
|-
| style="text-align:right;" |{{gaps|1|000|000|000|000|000}}
|10<sup>15</sup>
|[[Peta-|Peta]]
|P
|-
| style="text-align:right;" |{{gaps|1|000|000|000|000|000|000}}
|10<sup>18</sup>
|[[Exa-|Exa]]
|E
|-
| style="text-align:right;" |{{gaps|1|000|000|000|000|000|000|000}}
|10<sup>21</sup>
|[[Zetta-|Zetta]]
|Z
|-
| style="text-align:right;" |{{gaps|1|000|000|000|000|000|000|000|000}}
|10<sup>24</sup>
|[[Yotta-|Yotta]]
|Y
|}

== Rational numbers ==
{{main|Rational number}}
A [[rational number]] is a number that can be written as a [[Fraction (mathematics)|fraction]] with two [[Integer|integers]]. The [[numerator]] is written as <math>p</math>. The [[denominator]](which cannot be zero) is written as <math>q</math>.<ref name="Rosen">{{cite book|title=Discrete Mathematics and its Applications|url=https://archive.org/details/discretemathemat00rose_815|last=Rosen|first=Kenneth|publisher=McGraw-Hill|year=2007|isbn=978-0-07-288008-3|edition=6th|location=New York, NY|pages=[https://archive.org/details/discretemathemat00rose_815/page/n130 105], 158–160}}</ref> 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 [[Infinity|infinitely]] many ways. For example, 0.12 can be written as ''three twenty-fifths'' (<math>\frac{3}{25}</math>), ''nine seventy-fifths'' (<math>\frac{9}{75}</math>), etc.

{| class="wikitable sortable mw-collapsible" style="text-align:center; width:800px;"
|+ class="nowrap" |Table of notable rational numbers
!Decimal expansion
!Fraction
!Reason
|-
|1.0
| rowspan="2" style="text-align:center;" |<math>\bar1</math>
| rowspan="2" |<math>\bar1</math> is equal to [[1 (number)|1]], a notable real number.
|-
|1
|- 
|0.5
| style="text-align:center;" |<math>\bar2</math>
|<math>\bar2</math> is a popular number in math. For example, you can use <math>\bar2</math> to find the [[area]] of a [[Triangle]].
|-
|3.142 857...
| style="text-align:center;" |<math>\frac{22}{7}</math>
|<math>\frac{22}{7}</math> is a number slightly above <math>\pi</math> and is an [[approximation]] of <math>\pi</math>.
|-
|0.166 666...
| style="text-align:center;" |<math>\bar6</math>
|One sixth is seen in a lot of [[Equation|equations]]. For example, the solution to the Basel problem uses 1/6.
|}

== Irrational numbers ==
{{main|Irrational number}}[[Irrational number|Irrational numbers]] are numbers that cannot be written as a [[Fraction (mathematics)|fraction]]. These are written as [[Algebraic number|algebraic numbers]] or [[Transcendental number|transcendental numbers]].

=== Algebraic numbers ===
{{main|Algebraic number}}
{| class="wikitable"
!Name
!Expression
!Decimal expansion
!Reason
|-
|[[Square root of two]]
| style="text-align:center;" |<math>\sqrt{2}</math>
|{{val|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 (geometry)|square]].
|-
|[[Triangular number#Triangular roots and tests for triangular numbers|Triangular root]] of 2
| style="text-align:center;" |<math>\frac{\sqrt{17}-1}{2}</math>
|{{val|1.561552812808830274910704927987}}
|
|-
|Phi, [[Golden ratio]]
| style="text-align:center;" |<math>\phi</math>
|{{val|1.618033988749894848204586834366}}
|The golden ratio is a famous number used in both [[Mathematics|math]] and [[science]].
|}

=== Transcendental numbers ===
{{main|Transcendental number}}
{| class="wikitable sortable"
!Name
!Symbol
or

Formula
!Decimal expansion
!Reason
|-
|e, Euler's number
|[[Euler's number|e]]
|{{val|2.718281828459045235360287471352662497757247}}...
|e is the [[Base (mathematics)|base]] of a [[natural logarithm]].
|-
|Pi
|[[Pi|{{pi}}]]
|{{val|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 number|algebraic]] and [[Transcendental number|transcendental]] numbers.

=== Real but not known if irrational or transcendental ===

{| class="wikitable sortable"
|+
!Name and symbol
!Decimal expansion
!Notes
|-
|[[Euler–Mascheroni constant]], γ
|{{val|0.577215664901532860606512090082}}...<ref>{{Cite web|title=A001620 - OEIS|url=https://oeis.org/A001620|access-date=2020-10-14|website=oeis.org}}</ref>
|The [[Euler–Mascheroni constant]] is used in [[Limit (mathematics)|limits]] and [[Logarithm|logarithms]]. It is thought to be [[Transcendental number|transcendental]] but not [[Proof (mathematics)|proven]] to be so.
|-
|[[Twin prime conjecture#First Hardy–Littlewood conjecture|Twin prime constant]], C<sub>2</sub>
|{{val|0.660161815846869573927812110014}}...
|
|}

== Hypercomplex numbers ==
A hypercomplex number is a word for an [[Element (mathematics)|element]] of a unital [[algebra]] over the [[Field (mathematics)|field]] of [[Real number|real numbers]].

=== Algebraic complex numbers ===

* i, [[Imaginary unit]]: <math display="inline">i=\sqrt{-1}</math>

== Transfinite numbers ==
{{main|Transfinite number}}
[[Transfinite number|Transfinite numbers]] are numbers that are "[[Infinity|infinite]]". They are larger than any [[Finite set|finite]] number. They are, however, not absolutely infinite.

== Physical Constants ==
{{main|Physical constant}}
[[Physical constant|Physical constants]] are [[Constant|constants]] that can be used in the [[universe]] to figure out information.

* [[Avogadro constant]]
* [[Gravitational constant]]
* [[Planck constant]]
* [[Rydberg constant]] 
* [[Speed of light|Speed of light in vacuum]]

== 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<sup>(<sup>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</sup>)</sup>
* [[Graham's number]], G
* [[Skewes's number]], S

== References ==
{{reflist}}

== Bibliography ==

* {{citation|last=Finch|first=Steven R.|title=Mathematical Constants (Encyclopedia of Mathematics and its Applications, Series Number 94)|url=https://isbnsearch.org/isbn/0521818052|pages=[https://archive.org/details/mathematicalcons0000finc/page/130 130–133]|year=2003|contribution=Anmol Kumar Singh|publisher=Cambridge University Press|isbn=0521818052}}
* {{Citation|first=Roger|last=Apéry|title=Irrationalité de <math>\zeta(2)</math> et <math>\zeta(3)</math>|year=1979|journal=Astérisque|volume=61|pages=11–13}}.

== Further reading ==

* ''Kingdom of Infinite Number: A Field Guide'' by Bryan Bunch, W.H. Freeman & Company, 2001. {{isbn|0-7167-4447-3}}

== Other websites ==

* [http://www.virtuescience.com/number.html The Database of Number Correlations: 1 to 2000+] {{Webarchive|url=https://web.archive.org/web/20170724110717/http://www.virtuescience.com/number.html |date=2017-07-24 }}
* [http://www.archimedes-lab.org/numbers/Num1_69.html What's Special About This Number? A Zoology of Numbers: from 0 to 500]
* [http://www.isthe.com/chongo/tech/math/number/number.html Name of a Number]
* [http://www.mathcats.com/explore/reallybignumbers.html See how to write big numbers]
* {{webarchive|url=https://web.archive.org/web/20101127194324/http://pages.prodigy.net/jhonig/bignum/indx.html|title=About big numbers|date=27 November 2010}}
* [http://www.mrob.com/pub/math/largenum.html Robert P. Munafo's Large Numbers page]
* [http://www-users.cs.york.ac.uk/~susan/cyc/b/big.htm Different notations for big numbers – by Susan Stepney]
* [http://www.ibiblio.org/units/large.html Names for Large Numbers], in ''How Many? A Dictionary of Units of Measurement'' by Russ Rowlett
* [http://www.stetson.edu/~efriedma/numbers.html What's Special About This Number?] {{Webarchive|url=https://web.archive.org/web/20180223062027/http://www2.stetson.edu/~efriedma/numbers.html|date=2018-02-23}} (from 0 to 9999)

[[Category:Numbers]]
[[Category:Mathematics lists]]