Hyperos

View full site to see MathJax equation

Hyperos is equal to 2²⁰⁴⁸. The term was coined by Oganso. It is approximately equal to 32.317 quattuorducentillion in short scale. It is 617 digits long.

Its full decimal expansion is

32,317,006,071,311,007,300,714,876,688,669,951,960,444,102,669,715,484,032,130,345,427,524,655,138,867,890,893,197,201,411,522,913,463,688,717,960,921,898,019,494,119,559,150,490,921,095,088,152,386,448,283,120,630,877,367,300,996,091,750,197,750,389,652,106,796,057,638,384,067,568,276,792,218,642,619,756,161,838,094,338,476,170,470,581,645,852,036,305,042,887,575,891,541,065,808,607,552,399,123,930,385,521,914,333,389,668,342,420,684,974,786,564,569,494,856,176,035,326,322,058,077,805,659,331,026,192,708,460,314,150,258,592,864,177,116,725,943,603,718,461,857,357,598,351,152,301,645,904,403,697,613,233,287,231,227,125,684,710,820,209,725,157,101,726,931,323,469,678,542,580,656,697,935,045,997,268,352,998,638,215,525,166,389,437,335,543,602,135,433,229,604,645,318,478,604,952,148,193,555,853,611,059,596,230,656

Ruble calls it Foreroverlong as it's the four first (fifth in decimal) -long.

Approximations

Notation	Approximation
Arrow notation	\(2 \uparrow 2048\) (exact)
Bowers' Exploding Array Function	{2,2048} (exact)
Chained arrow notation	\(2 \rightarrow 2048\) (exact)
Scientific notation	\(3.2317 \times 10^{616}\)
Steinhaus-Moser Notation	256[3] (exact)
Fast-growing hierarchy	\(f_2(2037)\)
Hardy hierarchy	\(H_{\omega^2}(2037)\)

Sources

Oganso's googology

Penku stage: Two · Four · Nybble · Byte · Short · Int · Long · Overos · Überos · Yfiros · Superos · Hyperos · Ultralos · Hellos · Terolos · Plenolos · Penku

The -long suffix numbers

1-15: Long · Overlong · Tooerlong · Freerlong · Forerlong · Foreroverlong · Forertooerlong · Forerfreerlong · Tooerforerlong · Tooerforeroverlong · Tooerforertooerlong · Tooerforerfreerlong · Freerforerlong · Freerforeroverlong · Freerforertooerlong · Freerforerfreerlong
16-31: Hexer- ( -over- · -tooer- · -freer- · -forer- · -forerover- · -forertooer- · -forerfreer- · -tooerforer- · -tooerforerover- · -tooerforertooer- · -tooerforerfreer- · -freerforer- · -freerforerover- · -freerforertooer- · -freerforerfreer- ) long
32-47: Tooerhexer- ( -over- · -tooer- · -freer- · -forer- · -forerover- · -forertooer- · -forerfreer- · -tooerforer- · -tooerforerover- · -tooerforertooer- · -tooerforerfreer- · -freerforer- · -freerforerover- · -freerforertooer- · -freerforerfreer- ) long
48-63: Freerhexer- ( -over- · -tooer- · -freer- · -forer- · -forerover- · -forertooer- · -forerfreer- · -tooerforer- · -tooerforerover- · -tooerforertooer- · -tooerforerfreer- · -freerforer- · -freerforerover- · -freerforertooer- · -freerforerfreer- ) long
64-79: Forerhexer- ( -over- · -tooer- · -freer- · -forer- · -forerover- · -forertooer- · -forerfreer- · -tooerforer- · -tooerforerover- · -tooerforertooer- · -tooerforerfreer- · -freerforer- · -freerforerover- · -freerforertooer- · -freerforerfreer- ) long
80-95: Foreroverhexer- ( -over- · -tooer- · -freer- · -forer- · -forerover- · -forertooer- · -forerfreer- · -tooerforer- · -tooerforerover- · -tooerforertooer- · -tooerforerfreer- · -freerforer- · -freerforerover- · -freerforertooer- · -freerforerfreer- ) long
96-111: Forertooerhexer- ( -over- · -tooer- · -freer- · -forer- · -forerover- · -forertooer- · -forerfreer- · -tooerforer- · -tooerforerover- · -tooerforertooer- · -tooerforerfreer- · -freerforer- · -freerforerover- · -freerforertooer- · -freerforerfreer- ) long
112-127: Forerfreerhexer- ( -over- · -tooer- · -freer- · -forer- · -forerover- · -forertooer- · -forerfreer- · -tooerforer- · -tooerforerover- · -tooerforertooer- · -tooerforerfreer- · -freerforer- · -freerforerover- · -freerforertooer- · -freerforerfreer- ) long
128-143: Tooerforerhexer- ( -over- · -tooer- · -freer- · -forer- · -forerover- · -forertooer- · -forerfreer- · -tooerforer- · -tooerforerover- · -tooerforertooer- · -tooerforerfreer- · -freerforer- · -freerforerover- · -freerforertooer- · -freerforerfreer- ) long
144-159: Tooerforeroverhexer- ( -over- · -tooer- · -freer- · -forer- · -forerover- · -forertooer- · -forerfreer- · -tooerforer- · -tooerforerover- · -tooerforertooer- · -tooerforerfreer- · -freerforer- · -freerforerover- · -freerforertooer- · -freerforerfreer- ) long
160-175: Tooerforertooerhexer- ( -over- · -tooer- · -freer- · -forer- · -forerover- · -forertooer- · -forerfreer- · -tooerforer- · -tooerforerover- · -tooerforertooer- · -tooerforerfreer- · -freerforer- · -freerforerover- · -freerforertooer- · -freerforerfreer- ) long
176-191: Tooerforerfreerhexer- ( -over- · -tooer- · -freer- · -forer- · -forerover- · -forertooer- · -forerfreer- · -tooerforer- · -tooerforerover- · -tooerforertooer- · -tooerforerfreer- · -freerforer- · -freerforerover- · -freerforertooer- · -freerforerfreer- ) long
192-207: Freerforerhexer- ( -over- · -tooer- · -freer- · -forer- · -forerover- · -forertooer- · -forerfreer- · -tooerforer- · -tooerforerover- · -tooerforertooer- · -tooerforerfreer- · -freerforer- · -freerforerover- · -freerforertooer- · -freerforerfreer- ) long
208-223: Freerforeroverhexer- ( -over- · -tooer- · -freer- · -forer- · -forerover- · -forertooer- · -forerfreer- · -tooerforer- · -tooerforerover- · -tooerforertooer- · -tooerforerfreer- · -freerforer- · -freerforerover- · -freerforertooer- · -freerforerfreer- ) long
224-239: Freerforertooerhexer- ( -over- · -tooer- · -freer- · -forer- · -forerover- · -forertooer- · -forerfreer- · -tooerforer- · -tooerforerover- · -tooerforertooer- · -tooerforerfreer- · -freerforer- · -freerforerover- · -freerforertooer- · -freerforerfreer- ) long
240-255: Freerforerfreerhexer- ( -over- · -tooer- · -freer- · -forer- · -forerover- · -forertooer- · -forerfreer- · -tooerforer- · -tooerforerover- · -tooerforertooer- · -tooerforerfreer- · -freerforer- · -freerforerover- · -freerforertooer- · -freerforerfreer- ) long
256-2⁶⁴:Byterlong, Interlong, Shorterlong, Titlongertotlong