Jonathan Bowers

Jonathan Bowers, mathematician (November 27, 1969–)

Polychora

One of the participants in the Uniform Polychora Project, an attempt to name higher-dimensional polychora. He independently began his search for polychora in 1990. Circa 1993, he invented his short names for the uniform polychora, which have come to be known as the Bowers style acronyms (or pet name). In 1997, he contacted others who are also interested in the subject, such as Magnus Wenninger, Vincent Matsko, and George Olshevsky.

Very large numbers

Bowers has proposed a series of names (including giggol, gaggol, geegol, goggol, tridecal, tetratri, dutritri, xappol, dimendecal, gongulus, trimentri, goppatoth, golapulus, golapulusplex, golapulusplux, big boowa and guapamonga) for extremely Large numbers, which he terms infinity scrapers (a pun on skyscraper), many of which are so unspeakably and unprecedentedly large as to require special newly-devised extended mathematical notations in order to be expressed.infinity scrapers

He is also the inventor of the Array Notation as a means to represent very large numbers. This notion is very similar to the Conway chained arrow notation and relies on the tetration operator <math>{\ ^{b}a = \atop {\ }} {{\underbrace{a^{a^{\cdot^{\cdot^{a}}}}}} \atop b}</math>, and its higher order analogues: pentation, sexation, heptation. some examples of which are

• <math>\{a,b,1\} = a \{1\} b = a+b\;</math>
• <math>\{a,b,2\} = a \{2\} b = a*b\;</math>
• <math>\{a,b,3\} = a \{3\} b = a^b\;</math>
• <math>\{a,b,4\} = a \{4\} b = \ ^{b}a</math> a tetrated to b.
• <math>\{a,b,5\} = a \{5\} b = \ ^{\ ^{\ ^{\ ^a\cdot}\cdot}a}a</math> - a pentated to b - a tetrated to itself b times.
• <math>\{a,b,c,2\} = a \{\{c\}\}b\;</math>
• <math>\{a,2,1,2\} = a \{\{1\}\}2 = a \{a\}a\;</math>
• <math>\{a,3,1,2\} = a \{\{1\}\}3 = a \{a \{a\}a\}a\;</math>
• <math>\{a,b,1,2\} = a \{\{1\}\}b = a \{a\ldots\{a\}\ldots a\}a\;</math> - a expanded to b.
• <math>\{a,b,2,2\} = a \{\{2\}\}b\;</math> - a expanded to itself b times.

Group	Name	Value	Array notation
Googol group	Googol	<math>10^{100}=10^{10^2}</math>	{10,100,2} = 10 {2} 100
	Googolplex	<math>10^{10^{100}}=10^{10^{10^2}}</math>	{10,{10,100,2},2} = 10 {2} 10 {2} 100
	Googolduplex	<math>10^{10^{10^{100}}}</math>	{10,{10,{10,100,2},2},2} = 10 {2} 10 {2} 10 {2} 100
Giggol group		<math>\ ^{10}10</math>	{10,10,4} = 10 {4} 10
	Giggol	<math>\ ^{100}10</math>	{10,100,4} = 10 {4} 10: 10 to the power of itself 100 times.
	Giggolplex		10 {4} 10 {4} 10: 10 tetrated to a giggol
	Giggolduplex		10 {4} 10 {4} 10 {4} 100.
Gaggol group	Gaggol		{10,100,5} = 10 {5} 100: 10 pentated to 100.
	gaggolplex		10 {5} gaggol = 10 {5} 10 {5} 100: 10 tetrated to itself a gaggol times.
	geegol		{10,100,6}=10 {6} 100
	geegolplex		{10,geegol, 6}
	gygol		{10,100,7}
	gygolplex		{10,gygol,7}
	goggol		{10,100,8}
	goggolplex		{10,goggol,8}
	gagol		{10,100,9}
	gagolplex		{10,gagol,9}
Infinity Scrapers	Tridecal		{10,10,10} = 10 {10} 10 = 10 decated to 10
	boogol		{10,10,100} = 10 {100} 10

Bowers notation extends beyond even these numbers and includes the Corporal {10,100,1,2}, Grand Tridecal {10,10,10,2}, Tetratri = {3,3,3,3}, General = {10,10,10,10}, Pentadecal = {10,10,10,10,10}, Iteral = {10,10,10,10,10,10,10,10,10,10}. Still larger numbers require an extended array notation and include the Emperal Group, Hyperal Group, Dutritri and Dutridecal. The largest number mentioned is the Guapamongaplex which is still considerably less than infinity, but is much larger than even Graham's number.

Large numbers that extend the -illion family

Jonathan Bowers has also created a number of names for large numbers that extend the -illion family of much smaller numbers than those mentioned above. Here is a list of the names of large numbers on the extended short scale, long scale and Knuth's extended myriadic scale:

Value	Extended Short scale	Extended Long scale (Modified Chuquet): (Pelletier)	Extended Myriadic (Knuth)	Extended Myriadic (Knuth-Pelletier)	Example of Numbers in this range
0	Zero	Zero	Zero	Zero
<math>{10}^0</math>	One	One	One	One	π, e
<math>{10}^3</math>	Thousand	Thousand	Thousand	Thousand
<math>{10}^4</math>	Ten thousand	Ten thousand	Myriad	Myriad
<math>{10}^6</math>	Million	Million	Hundred myriad	Hundred myriad
<math>{10}^8</math>	Hundred million	Hundred million	Myllion	Myllion
<math>{10}^9</math>	Billion	Milliard	Ten myllion	Ten myllion
<math>{10}^{12}</math>	Trillion	Billion	Myriad myllion	Myriad myllion
<math>{10}^{15}</math>	Quadrillion	Billiard	Thousand myriad myllion	Thousand myriad myllion	Age of universe in seconds
<math>{10}^{16}</math>	Ten quadrillion	Ten billiard	Byllion	Mylliard
<math>{10}^{24}</math>	Septillion	Quadrillion	Myllion byllion	Myllion mylliard	Size (cm) of the homogenous patch
<math>{10}^{32}</math>	Hundred nonillion	Hundred quintillion	Tryllion	Byllion	Temperature of universe (K) in Planck time
<math>{10}^{33}</math>	Decillion	Quintilliard	Ten tryllion	Ten byllion
<math>{10}^{60}</math>	Novemdecillion	Decillion	Myriad myllion byllion tryllion	Myriad myllion mylliard byllion
<math>{10}^{63}</math>	Vigintillion	Decilliard	Thousand myriad myllion byllion tryllion	Thousand myriad myllion mylliard byllion
<math>{10}^{64}</math>	Ten vigintillion	Ten decilliard	Quadryllion	Bylliard	Atoms in universe
<math>{10}^{100}</math>	Googol	?	Myriad tryllion quadryllion	Myriad byllion bylliard	Shannon number
<math>{10}^{128}</math>	Hundred unquadragintillion	Hundred unvigintillion	Quintyllion	Tryllion
<math>{10}^{256}</math>	Ten quattoroctogintillion	Ten duoquadragintilliard	Sextyllion	Trylliard
<math>{10}^{303}</math>	Centillion	Quinquagintilliard	Thousand myriad myllion tryllion sextyllion	Thousand myriad myllion byllion trylliard
<math>{10}^{512}</math>	Hundred Centinovemsexagintillion	Hundred Quinoctogintillion	Septyllion	Quadryllion
<math>{10}^{600}</math>	Centinovemnonagintillion	Centillion	Myllion byllion quadryllion septyllion	Myllion mylliard trylliard quadryllion
<math>{10}^{603}</math>	Ducentillion	Centilliard	Thousand myllion byllion quadryllion septyllion	Thousand myllion mylliard trylliard quadryllion
<math>{10}^{1024}</math>	Ten trecentiquadragintillion	Ten Centiseptuagintillion	Octyllion	Quadrylliard
<math>{10}^{2048}</math>	Hundred Sexincentiunoctogintillion	Hundred Trecentiunquadragintillion	Nonyllion	Quintyllion
<math>{10}^{3003}</math>	Millillion	Quincentilliard?	Thousand myllion byllion tryllion quintyllion sextyllion septyllion nonyllion	Thousand myllion mylliard byllion tryllion trylliard quadryllion quintyllion
<math>{10}^{4096}</math>	Ten Millitrecentiquattuorsexagintillion	Ten Sexincentiduooctagintilliard	Decyllion	Quintylliard
<math>{10}^{6000}</math>	platillion		Millillion	Byllion tryllion sextyllion septyllion octyllion decyllion	Mylliard byllion trylliard quadryllion quadrylliard quintylliard
<math>{10}^{6003}</math>	Dumillillion?	Millilliard	Thousand byllion tryllion sextyllion septyllion octyllion decyllion	Thousand mylliard byllion trylliard quadryllion quadrylliard quintylliard
<math>{10}^{8192}</math>	Hundred Dumilliseptincentinovemvigintillion	Hundred Millitrecentiquinsexagintillion	Undecyllion	Sextyllion
<math>{10}^{16384}</math>	Ten Quinmilliquadrincentisexagintillion	Ten Dumilliseptincentitrigintilliard	Duodecyllion	Sextylliard
<math>{10}^{30,003}</math>	Myrillion	Quinmillilliard?	Thousand byllion tryllion sextyllion octyllion decyllion undecyllion duodecyllion	Thousand mylliard byllion trylliard quadrylliard quintylliard sextyllion sextylliard
<math>{10}^{60,000}</math>	Myrianonmillinoncentinovemnonagintillion	Myrillion	Tryllion quadryllion septyllion nonyllion undecyllion duodecyllion tredecyllion	Byllion bylliard quadryllion quintyllion sextyllion sextylliard septyllion
<math>{10}^{60,003}</math>	Dumyrillion?	Myrilliard	Thousand tryllion quadryllion septyllion nonyllion undecyllion duodecyllion tredecyllion	Thousand byllion bylliard quadryllion quintyllion sextyllion sextylliard septyllion
<math>{10}^{300,003}</math>	Decemyrillion	Quinmyrilliard	Thousand tryllion quadryllion quintyllion sextyllion septyllion decyllion tredecyllion sexdecyllion	Thousand byllion bylliard tryllion trylliard quadryllion quintylliard septyllion octylliard
<math>{10}^{600,000}</math>	Novemnonagintanoncentinonmillinovamyriadecemyrillion	Decemyrillion	Quadryllion quintyllion sextyllion septyllion octyllion undecyllion quattordecyllion septemdecyllion	Bylliard tryllion trylliard quadryllion quadrylliard sextyllion septylliard nonyllion
<math>{10}^{600,003}</math>	Dudecemyrillion	Decemyrilliard	Thousand quadryllion quintyllion sextyllion septyllion octyllion undecyllion quattordecyllion septemdecyllion	Thousand bylliard tryllion trylliard quadryllion quadrylliard sextyllion septylliard nonyllion
<math>{10}^{2,097,152}</math>	Ten Decemyrianoncentiunquadragintillion	Ten Tredecemyriaquadrincentisexseptuagintillion	Novemdecyllion	Decyllion	Number of books in the Library of Babel is 251,312,000?2×101,834,097.
<math>{10}^{3,000,003}</math>	Micrillion	?	?	?
<math>{10}^{4,194,304}</math>	?	?	Vigintyllion	Decylliard
<math>{10}^{6,000,000}</math>	?	Micrillion	?	?
<math>{10}^{8,388,608}</math>	?	?	Unvigintyllion	Undecylliard
<math>{10}^{2,147,483,648}</math>	?	?	Novemvigintyllion	Quindecyllion
<math>{10}^{3,000,000,003}</math>	Nanillion	?	?	?
<math>{10}^{4,294,967,296}</math>	?	?	Trigintyllion	Quindecylliard
<math>{10}^{6,000,000,000}</math>	?	Micrilliard	?	?
<math>{10}^{8,589,934,592}</math>	?	?	Untrigintyllion	Sexdecyllion
<math>{10}^{{3 * {{10}^{12}}} + 3}</math>	Picillion	?	?	?
<math>{10}^{6 * {{10}^{12}}}</math>	?	Nanillion	?	?
<math>{10}^{{3 * {{10}^{15}}} + 3}</math>	Femtillion	?	?	?
<math>{10}^{6 * {{10}^{15}}}</math>	?	Nanilliard	?	?
<math>{10}^{{3 * {{10}^{18}}} + 3}</math>	Attillion	?	?	?
<math>{10}^{6 * {{10}^{18}}}</math>	?	Picillion	?	?
<math>{10}^{{3 * {{10}^{21}}} + 3}</math>	Zeptillion	?	?	?
<math>{10}^{6 * {{10}^{21}}}</math>	?	Picilliard	?	?
<math>{10}^{{3 * {{10}^{24}}} + 3}</math>	Yoctillion	?	?	?
<math>{10}^{6 * {{10}^{24}}}</math>	?	Femtillion	?	?
<math>{10}^{{3 * {{10}^{27}}} + 3}</math>	Xonillion	?	?	?
<math>{10}^{6 * {{10}^{27}}}</math>	?	Femtilliard	?	?
<math>{10}^{{3 * {{10}^{30}}} + 3}</math>	Dekillion Vecillion Contillion	?	?	?
<math>{10}^{6 * {{10}^{30}}}</math>	?	Attillion	?	?
<math>{{10}^2}^{102}</math>	?	?	Centyllion	Quinquagintylliard
<math>{10}^{{3 * {{10}^{33}}} + 3}</math>	Mecillion	?	?	?
<math>{10}^{6 * {{10}^{33}}}</math>	?	Attilliard	?	?
<math>{10}^{{3 * {{10}^{36}}} + 3}</math>	Duecillion	?	?	?
<math>{10}^{6 * {{10}^{36}}}</math>	?	Zeptillion	?	?
<math>{10}^{{3 * {{10}^{39}}} + 3}</math>	Trecillion	?	?	?
<math>{10}^{6 * {{10}^{39}}}</math>	?	Zeptilliard	?	?
<math>{10}^{{3 * {{10}^{42}}} + 3}</math>	Tetrecillion	?	?	?
<math>{10}^{6 * {{10}^{42}}}</math>	?	Yoctillion	?	?
<math>{10}^{{3 * {{10}^{45}}} + 3}</math>	Pentecillion	?	?	?
<math>{10}^{6 * {{10}^{45}}}</math>	?	Yoctilliard	?	?
<math>{10}^{{3 * {{10}^{48}}} + 3}</math>	Hexecillion	?	?	?
<math>{10}^{6 * {{10}^{48}}}</math>	?	Xonillion	?	?
<math>{10}^{{3 * {{10}^{51}}} + 3}</math>	Heptecillion	?	?	?
<math>{10}^{6 * {{10}^{51}}}</math>	?	Xonilliard	?	?
<math>{10}^{{3 * {{10}^{54}}} + 3}</math>	Octecillion	?	?	?
<math>{10}^{6 * {{10}^{54}}}</math>	?	Wettillion	?	?
<math>{10}^{{3 * {{10}^{57}}} + 3}</math>	Ennecillion	?	?	?
<math>{10}^{6 * {{10}^{57}}}</math>	?	Wettilliard	?	?
<math>{10}^{{3 * {{10}^{60}}} + 3}</math>	Icocillion Ducontillion	?	?	?
<math>{10}^{6 * {{10}^{60}}}</math>	?	Dekillion	?	?
<math>{10}^{6 * {{10}^{63}}}</math>	?	Dekilliard	?	?
<math>{{10}^2}^{201}</math>	?	?	?	Centyllion
<math>{{10}^2}^{202}</math>	?	?	Ducentyllion?	Centylliard
<math>{10}^{{3 * {{10}^{90}}} + 3}</math>	Triacontillion	?	?	?
<math>{{10}^{10}}^{100}</math>	Googolplex	?	?	?
<math>{10}^{{3 * {{10}^{120}}} + 3}</math>	Tetracontillion	?	?	?
<math>{10}^{{3 * {{10}^{150}}} + 3}</math>	Pentacontillion	?	?	?
<math>{10}^{{3 * {{10}^{180}}} + 3}</math>	Hexacontillion	?	?	?
<math>{10}^{{3 * {{10}^{210}}} + 3}</math>	Heptacontillion	?	?	?
<math>{10}^{{3 * {{10}^{240}}} + 3}</math>	Octacontillion	?	?	?
<math>{10}^{{3 * {{10}^{270}}} + 3}</math>	Ennacontillion	?	?	?
<math>{10}^{{3 * {{10}^{300}}} + 3}</math>	Hectillion Icocontillion	?	?	?
<math>{{10}^2}^{1,002}</math>	?	?	Millyllion	?
<math>{10}^{6 * {{10}^{600}}}</math>	?	Hectillion	?	?
<math>{10}^{6 * {{10}^{603}}}</math>	?	Hectilliard	?	?
<math>{{10}^2}^{2,001}</math>	?	?	?	Millyllion
<math>{{10}^2}^{2,002}</math>	?	?	Dumillyllion	Millylliard
<math>{10}^{{3 * {{10}^{3,000}}} + 3}</math>	Killillion Onillion Zerillion	?	?	?
<math>{{10}^2}^{10,002}</math>	?	?	Myryllion	?
<math>{10}^{6 * {{10}^{6,000}}}</math>	?	Killillion	?	?
<math>{10}^{6 * {{10}^{6,003}}}</math>	?	Killilliard	?	?
<math>{{10}^2}^{20,001}</math>	?	?	?	Myryllion
<math>{{10}^2}^{20,002}</math>	?	?	Dumyryllion	Myrylliard
<math>{10}^{{3 * {{10}^{3,000,000}}} + 3}</math>	Megillion	?	?	?
<math>{10}^{6 * {{10}^{6,000,000}}}</math>	?	Megillion Zerillion	?	?
<math>{10}^{{3 * {{10}^{3,000,000,000}}} + 3}</math>	Gigillion	?	?	?
<math>{10}^{6 * {{10}^{6,000,000,000}}}</math>	?	Megilliard	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{12}}}}} + 3}</math>	Terillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{12}}}}}</math>	?	Gigillion	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{15}}}}} + 3}</math>	Petillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{15}}}}}</math>	?	Gigilliard	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{18}}}}} + 3}</math>	Exillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{18}}}}}</math>	?	Terillion	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{21}}}}} + 3}</math>	Zettillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{21}}}}}</math>	?	Terilliard	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{24}}}}} + 3}</math>	Yottillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{24}}}}}</math>	?	Petillion	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{27}}}}} + 3}</math>	Xennillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{27}}}}}</math>	?	Petilliard	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{30}}}}} + 3}</math>	Teenillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{30}}}}}</math>	?	Exillion	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{33}}}}} + 3}</math>	Mekillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{33}}}}}</math>	?	Exilliard	?	?	First Skewes' number eee79 ( approx. 10101034 )
<math>{10}^{{3 * {{10}^{3 * {{10}^{36}}}}} + 3}</math>	Duekillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{36}}}}}</math>	?	Zettillion	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{39}}}}} + 3}</math>	Trekillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{39}}}}}</math>	?	Zettilliard	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{42}}}}} + 3}</math>	Tetrekillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{42}}}}}</math>	?	Yottillion	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{45}}}}} + 3}</math>	Pentekillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{45}}}}}</math>	?	Yottilliard	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{48}}}}} + 3}</math>	Hexekillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{48}}}}}</math>	?	Xennillion	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{51}}}}} + 3}</math>	Heptekillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{51}}}}}</math>	?	Xennilliard	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{54}}}}} + 3}</math>	Octekillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{54}}}}}</math>	?	Wottillion	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{57}}}}} + 3}</math>	Ennekillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{57}}}}}</math>	?	Wottilliard	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{60}}}}} + 3}</math>	Twentillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{60}}}}}</math>	?	Onillion?	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{90}}}}} + 3}</math>	Thirtillion	?	?	?
<math>{{{10}^{10}}^{10}}^{100}</math>	Googolduplex
<math>{10}^{{3 * {{10}^{3 * {{10}^{120}}}}} + 3}</math>	Fortillion	?	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{150}}}}} + 3}</math>	Fiftillion	?	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{180}}}}} + 3}</math>	Sixtillion	?	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{210}}}}} + 3}</math>	Seventillion	?	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{240}}}}} + 3}</math>	Eightillion	?	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{270}}}}} + 3}</math>	Nintillion	?	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{300}}}}} + 3}</math>	Hundrillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{600}}}}}</math>	?	Onilliard?	?	?	Second Skewes' number (1010101000)
<math>{10}^{{3 * {{10}^{3 * {{10}^{3,000}}}}} + 3}</math>	Thousillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6,000}}}}}</math>	?	Zerilliard	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{30,000}}}}} + 3}</math>	Myriaillion Manillion	?	?	?
<math>{10}^{{3 * {{10}^{6 * {{10}^{60,000}}}}}}</math>	?	Quillion?	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{300,000}}}}} + 3}</math>	Lakhillion	?	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{600,000}}}}} + 3}</math>	?	Quilliard?	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{3,000,000}}}}} + 3}</math>	?	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6,000,000}}}}}</math>	?	Teenillion	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{30,000,000}}}}} + 3}</math>	Crorillion	?	?	?
<math>{10}^{{3 * {{10}^{3 * {{10}^{300,000,000}}}}} + 3}</math>	Awkillion	?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6,000,000,000}}}}}</math>	?	Teenilliard	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{12}}}}}}}</math>	?	Twentillion	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{15}}}}}}}</math>	?	Twentilliard	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{18}}}}}}}</math>	?	Thirtillion	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{21}}}}}}}</math>	?	Thirtilliard	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{24}}}}}}}</math>	?	Fortillion	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{27}}}}}}}</math>	?	Fortilliard	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{30}}}}}}}</math>	?	Fiftillion	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{33}}}}}}}</math>	?	Fiftilliard	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{36}}}}}}}</math>	?	Sixtillion	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{39}}}}}}}</math>	?	Sixtilliard	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{42}}}}}}}</math>	?	Seventillion	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{45}}}}}}}</math>	?	Seventilliard	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{48}}}}}}}</math>	?	Eightillion	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{51}}}}}}}</math>	?	Eightilliard	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{54}}}}}}}</math>	?	Nintillion	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{57}}}}}}}</math>	?	Nintilliard	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{60}}}}}}}</math>	?	Hundrillion	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{63}}}}}}}</math>	?	Hundrilliard	?	?
<math>{{{{{10}^{10}}^{10}}^{10}}^{100}}</math>	Googoltriplex
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{600}}}}}}}</math>	?	Thousillion	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{603}}}}}}}</math>	?	Thousilliard	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{6,000}}}}}}}</math>	?	Myriaillion	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{6,003}}}}}}}</math>	?	Myriailliard	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{60,000}}}}}}}</math>	?	Manillion	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{60,003}}}}}}}</math>	?	Manilliard?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{600,000}}}}}}}</math>	?	Lakhillion	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{600,003}}}}}}}</math>	?	Lakhilliard?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{6,000,000}}}}}}}</math>	?	Wanillion	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{6,000,003}}}}}}}</math>	?	Wanilliard?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{60,000,000}}}}}}}</math>	?	Crorillion	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{60,000,003}}}}}}}</math>	?	Crorilliard?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{600,000,000}}}}}}}</math>	?	Awkillion	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{600,000,003}}}}}}}</math>	?	Awkilliard?	?	?
<math>{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^{6 * {{10}^9}}}}}}}}</math>	Bentrizillion	?	?	?
<math>{{{{{10}^{10}}^{10}}^{10}}^{10}}^{100}</math>	Googolquadriplex	?	?	...
Googolduplex and (98 more plexes)	Googolcentplex	...	...	...
Googolduplex and (998 more plexes)	Googolmilleplex	...	...	...
Googolplex and (999,999 more plexes)	Googolmegaplex	...	...	...
Googolplex and (999,999,999 more plexes)	Googolgigaplex	...	...	...
Googolplex and (999,999,999,999 more plexes)	Googolteraplex	...	...	...
Googolplex and (999,999,999,999,999 more plexes)	Googolpetaplex	...	...	...
Googolplex to the power of a googolplex	Fzgoogolplex	...	...	...
{10,100,5} = 10 {5} 100: 10 pentated to 100	Giggol	...	...	...
{10,100,5} = 10 {5} 100: 10 pentated to 100	Giggolplex	...	...	...
...	Mega	...	...	...
{10,100,5} = 10 {5} 100: 10 pentated to 100	Gaggol	...	...	...
10 {5} gaggol = 10 {5} 10 {5} 100: 10 tetrated to itself a gaggol times	Gaggolplex	...	...	...
...	Megaston	...	...	...
{5,5,5} = 5 {5} 5 = 5 {4} 5 {4} 5 {4} 5 {4} 5	Tripent	...	...	...
{7,7,7} = 7 {7} 7 (7 heptated to 7)	Trisept	...	...	...
{10,100,6}=10 {6} 100	Geegol	...	...	...
{10,geegol, 6}	Geegolplex	...	...	...
{10,100,7}	Gygol	...	...	...
{10,gygol,7}	Gygolplex	...	...	...
{10,100,8}	Goggol	...	...	...
{10,goggol,8}	Goggolplex	...	...	...
{10,100,9}	Gagol	...	...	...
{10,gagol,9}	Gagolplex	...	...	...	Graham's number is much bigger.

Infinity scrapers

Numbers higher than those in the Gaggol group are referred to by Jonathan Bowers as the infinity scrapers. Here's a list of the names of those numbers that are infinity scrapers:

Name	Value
Tridecal	{10,10,10} = 10 {10} 10 = 10 decated to 10
Boogol	{10,10,100} = 10 {100} 10
Boogolplex	{10,10,boogol}
Moser's number	...
Graham's number	...
Corporal	{10,100,1,2}
Corporalplex	{10,corporal,1,2}
Grand Tridecal	{10,10,10,2}
Tetratri	{3,3,3,3}
General	{10,10,10,10}
Generalplex	{10,10,10,general}
Pentatri	{3,3,3,3,3}
Pentadecal	{10,10,10,10,10}
Pentadecalplex	{10,10,10,10,pentadecal}
Hexatri	{3,3,3,3,3,3}
Hexadecal	{10,10,10,10,10,10}
Hexadecalplex	{10,10,10,10,10,hexadecal}
Iteral	{10,10,10,10,10,10,10,10,10,10}
Ultatri	{3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}
Iteralplex	{10,10,10,10,10,10,...........,10,10,10}

The following numbers requre an extended array notation to define. These are defined recursively, using rules such as:

<math>\left\langle\begin{matrix}a&b\\2&\end{matrix}\right\rangle=\{a,a,\ldots,a\}</math> with a repeated b times.

<math>\left\langle\begin{matrix}a&b\\k&\end{matrix}\right\rangle=\left\langle\begin{matrix}a&a&\ldots&a\\k-1\end{matrix}\right\rangle</math> with a repeated b times.

Name	Value
Emperal	<math>\left\langle\begin{matrix}10&10\\10&\end{matrix}\right\rangle</math>
Emperalplex	<math>\left\langle\begin{matrix}10&10\\emperal&\end{matrix}\right\rangle</math>
Hyperal	<math>\left\langle\begin{matrix}10&10\\10&10\end{matrix}\right\rangle</math>
Hyperalplex	<math>\left\langle\begin{matrix}10&10\\10&Hyperal\end{matrix}\right\rangle</math>
Dutritri	<math>\left\langle\begin{matrix}3&3&3\\3&3&3\\3&3&3\end{matrix}\right\rangle</math>
Dutridecal	<math>\left\langle\begin{matrix}10&10&10\\10&10&10\\10&10&10\end{matrix}\right\rangle</math>
Xappol	10 by 10 array of 10's
Xappolplex	xappol by xappol array of 10's
Dimentri	3 x 3 x 3 array of 3's
Colossal	10 x 10 x 10 array of 10's
Colossalplex	colossal x colossal x colossal array of 10's
Dimendecal	10x10x10x10x10x10x10x10x10x10 array of 10's
Gongulus	100 dimensional array of 10's (10^100 array that is)
Gongulusplex	gongulus dimensional array of 10's (10^gongulus array)
Dulatri	(3^3)^2 array of 3's
Trimentri	3^(3^3) array of 3's
Goppatoth	10 tetrated to 100 array of 10's
Goppatothplex	{10,goppatoth,4} array of 10's
Tridecatrix	{10,10,10} array of 10's
Gongulus	a "10^100 array of 10's" array of 10's.
Golapulus	a * "10^100 array of tens" array of tens* array of tens.
Big Boowa	X3, {X3,dutritriX, 2} X
Great Big Boowa	X3,3,3X
Wompogulus	10^10 "100th level" exploded array of 10's
Wompogulusplex	10^10 "wompogulusth level" exploded array of 10's!!
Guapamonga	10^100 array of B's within "# #"
Guapamongaplex	10^100 array of B's within guapamonga-level "# #"

See also

• Uniform polychoron
• Knuth's up-arrow notation

External links

• Jonathan's home page