Googlek is equal to \(16^{256} = 2^{1024}\), or \(2^{2^{10}}\) , intended as a hexadecimal analog of googol.[1] It was described on a page on the site "intuitor.com" which proposes a method for pronouncing numbers in hexadecimal. To the best of our knowledge, the page was written in 2007 by Tom Rogers, a high school teacher in South Carolina, USA. The successor of this number is the 10th fermat number, since 2^1,024 is equal to 2^2^10.
It is approximately \(1.797 \times 10^{308}\), or 179.769 uncentillion in the short scale and about 179.769 unquinquagintillion in the long scale.
It is the smallest power of two not expressible as a double-precision floating point number according to IEEE 754 (a double has an exponent width of 11 bits, one of which is the sign, so the exponent has a maximum of 210 - 1). As a result, it is the floating-point limit for numbers in many programming languages. For example, numbers equal to this or larger in JavaScript will simply be expressed as "Infinity".
JavaScript HyperCalc maxes out at a power tower of tens this many terms high, or \(10\uparrow\uparrow(2^{1024})\).
2^1024 is the maximum amount of money, coins etc. for games like AdVenture Capitalist or Cookie Clicker.
Username5243 calls this number Binary-Goodcolplex.[2]
Oganso calls this number superos.
Transcendentem The Duck calls this number the MathPapa Limit because it is the highest number that could be inputed in the MathPapa online calculator.[3][citation needed]
Digit expansions[]
Its full decimal expansion is:
179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216
Its full hexadecimal expansion is:
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Its full ternary expansion is:
10020200012020012100112000100111100022202212112100000000220012221210111211022000021021222102211022101010001120211122022202222100021002121110212011201100221120022112221101022221202200022002021122102001212012222021020211101221121211111112212000220112111200012222101011002120111121210010000221202111212212120201111102201110102120112002222220121102202020120101202100201020112210002020210120101201112011012000212121121220122021002120202012000102101002101111200111000221021110210202101200212210001210121001000112201210102202000120100002000112100221012002110222022002211011212110111011010112010211220220201010001001202011200010102010101110020211220012021
Its full binary expansion is:
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Approximations[]
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1.797\times10^{308}\) | \(1.798\times10^{308}\) |
| Arrow notation | \(16\uparrow256\) | |
| Steinhaus-Moser Notation | 143[3] | 144[3] |
| Copy notation | 1[309] | 2[309] |
| Taro's multivariable Ackermann function | A(3,1021) | A(3,1022) |
| Pound-Star Notation | #*((560))*11 | #*((561))*11 |
| BEAF & Bird's array notation | {16,256} | |
| Hyper-E notation | E[16]2#2 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)(0)[65536] | |
| Hyperfactorial array notation | 170! | 171! |
| Fast-growing hierarchy | \(f_2(1014)\) | \(f_2(1015)\) |
| Hardy hierarchy | \(H_{\omega^2}(1014)\) | \(H_{\omega^2}(1015)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^2}}(16)\) | |
Sources[]
Googol Regiment
Niloogol · Niloogolplex · Niloogolduplex · Niloogoltriplex · Niloogolquadriplex · Niloogolquintiplex · Niloogolsextiplex · Niloogolseptiplex · Niloogoloctiplex · Niloogolnoniplex · Goonol · Goodol · Gootol · Gooquol · Gooqnol · Goosol · Goospol · Gooctol · Goonvol· Goodcol · Goovol · Gooqtol · Gootirol · Gooqrol · Goohfol · Gooxtol · Goostol · Gootgol · Goontol · Gooducol · Gooqnicol · Goomol · Goomyrol · Binary-Googol · Binary-Goonol · Binary-Goodol · Binary-Gootol · Binary-Gooquol · Binary-Gooqnol · Binary-Goovol · Binary-Gooqtol · Binary-Gootirol · Binary-Goohfol · Binary-Goomol · Binary-Goomyrol · Ternary-Googol · Ternary-Goonol · Ternary-Goodol · Ternary-Gooqnol · Ternary-Goodcol · Ternary-Gooqtol · Ternary-Goohfol · Ternary-Goomol · Ternary-Goomyrol · Quaternary-Googol · Quinary-Googol · Senary-Googol · Septary-Googol · Octal-Googol · Octal-Goonol · Octal-Goodol · Octal-Gooqnol · Octal-Goodcol · Octal-Gooqtol · Octal-Goohfol · Octal-Goomol · Octal-Goomyrol · Novary-Googol · Undecimal-Googol · Duodecimal-Googol · Hexadecimal-Googol · Hexadecimal-Goonol · Hexadecimal-Gooqnol · Hexadecimal-Goodcol · Hexadecimal-Goohfol · Hexadecimal-Goomol · Hexadecimal-Goomyrol · Vigesimal-Googol · Trigesimal-Googol · Sexagesimal-Googol · Googolnilex · Niloogolunex · Goonolplex · Goodolplex · Gootolplex · Gooquolplex · Gooqnolplex · Goosolplex · Goospolplex · Gooctolplex · Goonvolplex · Goodcolplex · Goovolplex · Gooqtolplex · Goohfolplex · Gooducolplex · Goomolplex · Goomyrolplex · Binary-Googolplex · Binary-Goonolplex · Binary-Gooqnolplex · Binary-Goodcolplex · Binary-Goohfolplex · Binary-Goomolplex · Ternary-Googolplex · Quaternary-Googolplex · Quinary-Googolplex · Octal-Googolplex · Duodecimal-Googolplex · Hexadecimal-Googolplex · Vigesimal-Googolplex · Sexagesimal-Googolplex · Googolduplex · Gooqnolduplex · Goodcolduplex · Goomolduplex · Goomyrolduplex · Binary-Googolduplex · Hexadecimal-Googolduplex · Googoltriplex · Goomoltriplex · Googolquadriplex · Googolquintiplex · Googolsextiplex · Googolseptiplex · Googoloctiplex · Googolnoniplex · Googoldeciplex
Doogol Regiment
Doogol · Doonol · Doodol · Dootol · Dooquol · Dooqnol · Doosol · Doospol · Dooctol · Doonvol · Doodcol · Doovol · Dooqtol · Dootrol · Dooqrol · Doohfol · Dooxtol · Doostol · Dootgol · Doontol · Dooducol · Dooqnicol · Doomol · Doomyrol · Binary-Doogol · Binary-Doonol · Binary-Doodol · Binary-Dootol · Binary-Dooquol · Binary-Dooqnol · Binary-Doodcol · Binary-Doovol · Binary-Doohfol · Binary-Doomol · Binary-Doomyrol · Ternary-Doonol · Ternary-Doodol · Ternary-Dooqnol · Ternary-Doodcol · Ternary-Doogol · Ternary-Doomol · Quaternary-Doogol · Quinary-Doogol · Octal-Doogol · Octal-Doonol · Octal-Dooqnol · Octal-Doodcol · Octal-Doomol · Duodecimal-Doogol · Hexadecimal-Doogol · Vigesimal-Doogol · Doogolunex · Doogolduunex · Doogoltriunex · Doogolquadriunex · Googolduex · Goonolduex · Goodolduex · Gooqnolduex · Goodcolduex · Goovolduex · Goohfolduex · Goomolduex · Goomyrolduex · Binary-Googolduex · Binary-Goodcolduex · Binary-Goomolduex · Ternary-Googolduex · Octal-Googolduex · Hexadecimal-Googolduex · Googolplexiduex · Gooqnolplexiduex · Goodcolplexiduex · Goomolplexiduex · Binary-Googolplexiduex · Googolduplexiduex · Goodcolduplexiduex · Googoltriplexiduex · Googolquadriplexiduex · Googolquintiplexiduex · Doogolplex · Doogolduex · Dooqnolplex · Doodcolplex · Doovolplex · Dooqtolplex · Doohfolplex · Doomolplex · Doomyrolplex · Binary-Doogolplex · Binary-Doodcolplex · Binary-Doomolplex · Ternary-Doogolplex · Octal-Doogolplex · Hexadecimal-Doogolplex · Googolduduex · Goodcolduduex · Goomolduduex · Binary-Googolduduex · Googolplexiduduex · Goodcolplexiduduex · Googolduplexiduduex · Googoltriplexiduduex · Googolquadriplexiduduex · Doogolduplex · Doodcolduplex · Doomolduplex · Doomyrolduplex · Binary-Doogolduplex · Googolplexitriduex · Googolduplexitriduex · Doogoltriplex · Googolquadriduex · Googolplexiquadriduex · Doogolquadriplex · Googolquintiduex · Doogolquintiplex · Doogolsextiplex · Doogolseptiplex · Doogoloctiplex · Doogolnoniplex · Doogoldeciplex
Toogol Regiment
Toogol · Toonol · Toodol · Tootol · Tooquol · Tooqnol · Toosol · Toospol · Tooctol · Toonvol · Toodcol · Toovol · Tooqtol · Tootrol · Tooqrol · Toohfol · Tooducol · Toomol · Toomyrol · Binary-Toogol · Binary-Toodol · Binary-Tootol · Binary-Tooquol · Binary-Tooqnol · Binary-Toodcol · Binary-Toohfol · Binary-Toomol · Ternary-Toogol · Ternary-Toodol · Ternary-Tooqnol · Ternary-Toodcol · Ternary-Toomol · Quaternary-Toogol · Octal-Toogol · Octal-Toodcol · Duodecimal-Toogol · Hexadecimal-Toogol · Toogolunex · Toogolduunex · Toogolduex · Toogolplexiduex · Toogolduexiplex · Toogolduduex · Googoltrex · Goonoltrex · Gooqnoltrex · Goodcoltrex · Goohfoltrex · Goomoltrex · Goomyroltrex · Binary-Googoltrex · Ternary-Googoltrex · Octal-Googoltrex · Hexadecimal-Googoltrex · Googolplexitrex · Goodcolplexitrex · Goomolplexitrex · Binary-Googolplexitrex · Googolduplexitrex · Googoltriplexitrex · Googolquadriplexitrex · Doogoltrex · Dooqnoltrex · Doodcoltrex · Doomoltrex · Doomyroltrex · Binary-Doogoltrex · Octal-Doogoltrex · Hexadecimal-Googoltrex · Googolduexitrex · Goodcolduexitrex · Goomolduexitrex · Binary-Googolduexitrex · Googolplexiduexitrex · Googolduplexiduexitrex · Doogolplexitrex · Doodcolplexitrex · Doomolplexitrex · Binary-Doogolplexitrex · Googolduduexitrex · Googolplexiduduexitrex · Doogolduplexitrex · Googoltriduexitrex · Doogoltriplexitrex · Doogolquadriplexitrex · Toogolplex · Toogoltrex · Toonolplex · Tooqnolplex · Toodcolplex · Toomolplex · Toomyrolplex · Binary-Toogolplex · Octal-Toogolplex · Googoldutrex · Goodcoldutrex · Googolplexidutrex · Googolduplexidutrex · Doogoldutrex · Doodcoldutrex · Googolduexidutrex · Doogolplexidutrex · Toogolduplex · Toodcolduplex · Toomolduplex · Binary-Toogolduplex · Googoltritrex · Googolplexitritrex · Doogoltritrex · Googoldexidutrex · Doogolplexitritrex · Toogoltriplex · Googolquadritrex · Doogolquadritrex · Toogolquadriplex · Toogolquintiplex · Toogolsextiplex · Toogolseptiplex · Toogoloctiplex · Toogolnoniplex · Toogoldeciplex
2-entry series
Linear series
Megoogol · Meg-Googol · Meg-Doogol · Meg-Kiloogol · Meg-Kil-Googol · Meg-Dukiloogol · Meg-Trukiloogol · Dumegoogol · Dumeg-Googol · Dumeg-Kiloogol · Dumeg-Dukiloogol · Trumegoogol · Trumeg-Kiloogol · Tetrumegoogol · Pentumegoogol · Gigoogol · Gig-Googol · Gig-Kiloogol · Gig-Megoogol · Dugigoogol · Trugigoogol · Teroogol · Duteroogol · Truteroogol · Petoogol · Ectoogol · Zettoogol · Yottoogol · Xennoogol · Wekoogol
Two-row series
Linoogol · Lin-Googol · Lin-Doogol · Lin-Kiloogol · Lin-Megoogol · Lin-Gigoogol · Dulinoogol · Dulin-Googol · Trulinoogol · Kilulinoogol · Kilulin-Googol · Kilulin-Linoogol · Kilulin-Dulinoogol · Dukilulinoogol · Megulinoogol · Megulin-Kilulinoogol · Dumegulinoogol · Gigulinoogol · Terulinoogol · Petulinoogol · Ectulinoogol · Zettulinoogol · Yottulinoogol · Xennulinoogol · Wekulinoogol
Note: The readers should be careful that numbers defined by Username5243's Array Notation are ill-defined as explained in Username5243's Array Notation#Issues. So, when an article refers to a number defined by the notation, it actually refers to an intended value, not an actual value itself (for example, a[c]b = \(a \uparrow^c b\) in arrow notation). In addition, even if the notation is ill-defined, a class category should be based on an intended value when listed, not an actual value itself, as it is not hard to fix all the issues from the original definition, hence it should not be removed.