Tritet Jr. is equal to \(4 \uparrow\uparrow 4\) in up-arrow notation[1], or \( \lbrace 4,4,2 \rbrace \) in BEAF.[2] The number used to be called tritet, a much larger number named and renamed by Jonathan Bowers. Sbiis Saibian coined the new name. Using Alistair Cockburn's megafuga- prefix, Tritet Jr. can be named "megafugafour".[3] It can also be named "boogafour" using the booga- prefix, or "troogatwo" using the trooga- prefix.
It is approximately \(10^{8.0723 \times 10^{153}}\), meaning that it's somewhat larger than a googolplex. The decimal expansion of Tritet Jr. is: 23,610,226,714,597,313,206............36,860,456,095,261,392,896. The leading digits are computed using logarithms and the terminating digits are computed using modular exponentiation.
Its exact value can be computed using basic laws of algebra: \(4\uparrow\uparrow4 = 4^{4^{4^{4}}} = 4^{4^{256}} = 4^{2^{512}} = 2^{2^{513}}\).
It is currently unknown, whether its successor, which is the 513th Fermat number, is composite or prime.[4]
Wiki user Hyp cos calls this number a tetbo, and it's equal to s(4,4,2), s(4,2,3), s(4,2,1,2), or s(4,2{2}2) in strong array notation. [5]
Googology wiki user HaydenTheGoogologist2009 calls this number Hayden's Tritet, and it's equal to 4(4)4 in Hayden's Array Notation.[6]
-illion name[]
Using Jonathan Bower's -illions series, some -illion name terms for Tritet Jr. are:
| 23 | Twenty-three
duo-mepentaconto- nonagintisescenti-pentaconto- octosexagintiseptingenti-ennetetraconto- duoquadragintiducenti-octetetraconto- novem-heptetetraconto- octoquadringenti-hexetetraconto- novemquinquagintiquadringenti-pentetetraconto- quattuornonagintiseptingenti-tetretetraconto- deciducenti-tretetraconto- doetriginticenti-duetetraconto- unsexagintitrecenti-metetraconto- novemnonagintiseptingenti-tetraconto- sexseptuagintisescenti-ennetriaconto- nonagintisescenti-octetriaconto- quinquinquagintiquadringenti-heptetriaconto- treseptuagintinongenti-hexetriaconto- doedecinongenti-pentetriaconto- quattuordecinongenti-tetretriaconto- trequadragintitrecenti-tretriaconto- quinquinquagintinongenti-duetriaconto- quattuornonagintisescenti-metriaconto- sexseptuagintiducenti-triaconto- novemtriginticenti-enneicoso- unseptuagintiquadringenti-octeicoso- trenonagintiquadringenti-hepteicoso- sexquinquagintioctingenti-hexeicoso- centreti-penteicoso- novemquadraginti-tetreicoso- doetrigintiseptingenti-trioicoso- septuagintinongenti-dueicoso- quattuorsescenti-meiocoso- nongenti-icoso- novemquadringenti-enneco- septenvigintioctingenti-octeco- septendecioctingenti-hepteco- septenvigintitrecenti-hexeco- quinoctoginticenti-penteco- octoquinquagintioctingenti-treteco- septenquinquagintiducenti-treco- doequinquaginti-dueco- quinsexaginticenti-meco- quinoctogintiquadringenti-veco- sexquadragintiseptingenti-xono- octoseptuaginticenti-yocto- tretrigintiquadringenti-zepto- novemviginti-atto- sexaginticenti-femto- quattuordeciquadringenti-pico- sexnonagintinongenti-nano- trequinquagintiseptingenti-micro- treoctogintiseptingenti-milli- quinseptingentillion |
|---|---|
| 610 | Six hundred ten
duo-mepentaconto- nonagintisescenti-pentaconto- octosexagintiseptingenti-ennetetraconto- duoquadragintiducenti-octetetraconto- novem-heptetetraconto- octoquadringenti-hexetetraconto- novemquinquagintiquadringenti-pentetetraconto- quattuornonagintiseptingenti-tetretetraconto- deciducenti-tretetraconto- doetriginticenti-duetetraconto- unsexagintitrecenti-metetraconto- novemnonagintiseptingenti-tetraconto- sexseptuagintisescenti-ennetriaconto- nonagintisescenti-octetriaconto- quinquinquagintiquadringenti-heptetriaconto- treseptuagintinongenti-hexetriaconto- doedecinongenti-pentetriaconto- quattuordecinongenti-tetretriaconto- trequadragintitrecenti-tretriaconto- quinquinquagintinongenti-duetriaconto- quattuornonagintisescenti-metriaconto- sexseptuagintiducenti-triaconto- novemtriginticenti-enneicoso- unseptuagintiquadringenti-octeicoso- trenonagintiquadringenti-hepteicoso- sexquinquagintioctingenti-hexeicoso- centreti-penteicoso- novemquadraginti-tetreicoso- doetrigintiseptingenti-trioicoso- septuagintinongenti-dueicoso- quattuorsescenti-meiocoso- nongenti-icoso- novemquadringenti-enneco- septenvigintioctingenti-octeco- septendecioctingenti-hepteco- septenvigintitrecenti-hexeco- quinoctoginticenti-penteco- octoquinquagintioctingenti-treteco- septenquinquagintiducenti-treco- doequinquaginti-dueco- quinsexaginticenti-meco- quinoctogintiquadringenti-veco- sexquadragintiseptingenti-xono- octoseptuaginticenti-yocto- tretrigintiquadringenti-zepto- novemviginti-atto- sexaginticenti-femto- quattuordeciquadringenti-pico- sexnonagintinongenti-nano- trequinquagintiseptingenti-micro- treoctogintiseptingenti-milli- quattuorseptingentillion |
| 226 | Two hundred twenty-six
duo-mepentaconto- nonagintisescenti-pentaconto- octosexagintiseptingenti-ennetetraconto- duoquadragintiducenti-octetetraconto- novem-heptetetraconto- octoquadringenti-hexetetraconto- novemquinquagintiquadringenti-pentetetraconto- quattuornonagintiseptingenti-tetretetraconto- deciducenti-tretetraconto- doetriginticenti-duetetraconto- unsexagintitrecenti-metetraconto- novemnonagintiseptingenti-tetraconto- sexseptuagintisescenti-ennetriaconto- nonagintisescenti-octetriaconto- quinquinquagintiquadringenti-heptetriaconto- treseptuagintinongenti-hexetriaconto- doedecinongenti-pentetriaconto- quattuordecinongenti-tetretriaconto- trequadragintitrecenti-tretriaconto- quinquinquagintinongenti-duetriaconto- quattuornonagintisescenti-metriaconto- sexseptuagintiducenti-triaconto- novemtriginticenti-enneicoso- unseptuagintiquadringenti-octeicoso- trenonagintiquadringenti-hepteicoso- sexquinquagintioctingenti-hexeicoso- centreti-penteicoso- novemquadraginti-tetreicoso- doetrigintiseptingenti-trioicoso- septuagintinongenti-dueicoso- quattuorsescenti-meiocoso- nongenti-icoso- novemquadringenti-enneco- septenvigintioctingenti-octeco- septendecioctingenti-hepteco- septenvigintitrecenti-hexeco- quinoctoginticenti-penteco- octoquinquagintioctingenti-treteco- septenquinquagintiducenti-treco- doequinquaginti-dueco- quinsexaginticenti-meco- quinoctogintiquadringenti-veco- sexquadragintiseptingenti-xono- octoseptuaginticenti-yocto- tretrigintiquadringenti-zepto- novemviginti-atto- sexaginticenti-femto- quattuordeciquadringenti-pico- sexnonagintinongenti-nano- trequinquagintiseptingenti-micro- treoctogintiseptingenti-milli- treseptingentillion |
| 714 | Seven hundred fourteen
duo-mepentaconto- nonagintisescenti-pentaconto- octosexagintiseptingenti-ennetetraconto- duoquadragintiducenti-octetetraconto- novem-heptetetraconto- octoquadringenti-hexetetraconto- novemquinquagintiquadringenti-pentetetraconto- quattuornonagintiseptingenti-tetretetraconto- deciducenti-tretetraconto- doetriginticenti-duetetraconto- unsexagintitrecenti-metetraconto- novemnonagintiseptingenti-tetraconto- sexseptuagintisescenti-ennetriaconto- nonagintisescenti-octetriaconto- quinquinquagintiquadringenti-heptetriaconto- treseptuagintinongenti-hexetriaconto- doedecinongenti-pentetriaconto- quattuordecinongenti-tetretriaconto- trequadragintitrecenti-tretriaconto- quinquinquagintinongenti-duetriaconto- quattuornonagintisescenti-metriaconto- sexseptuagintiducenti-triaconto- novemtriginticenti-enneicoso- unseptuagintiquadringenti-octeicoso- trenonagintiquadringenti-hepteicoso- sexquinquagintioctingenti-hexeicoso- centreti-penteicoso- novemquadraginti-tetreicoso- doetrigintiseptingenti-trioicoso- septuagintinongenti-dueicoso- quattuorsescenti-meiocoso- nongenti-icoso- novemquadringenti-enneco- septenvigintioctingenti-octeco- septendecioctingenti-hepteco- septenvigintitrecenti-hexeco- quinoctoginticenti-penteco- octoquinquagintioctingenti-treteco- septenquinquagintiducenti-treco- doequinquaginti-dueco- quinsexaginticenti-meco- quinoctogintiquadringenti-veco- sexquadragintiseptingenti-xono- octoseptuaginticenti-yocto- tretrigintiquadringenti-zepto- novemviginti-atto- sexaginticenti-femto- quattuordeciquadringenti-pico- sexnonagintinongenti-nano- trequinquagintiseptingenti-micro- treoctogintiseptingenti-milli- duoseptingentillion |
| 597 | Five hundred ninety-seven
duo-mepentaconto- nonagintisescenti-pentaconto- octosexagintiseptingenti-ennetetraconto- duoquadragintiducenti-octetetraconto- novem-heptetetraconto- octoquadringenti-hexetetraconto- novemquinquagintiquadringenti-pentetetraconto- quattuornonagintiseptingenti-tetretetraconto- deciducenti-tretetraconto- doetriginticenti-duetetraconto- unsexagintitrecenti-metetraconto- novemnonagintiseptingenti-tetraconto- sexseptuagintisescenti-ennetriaconto- nonagintisescenti-octetriaconto- quinquinquagintiquadringenti-heptetriaconto- treseptuagintinongenti-hexetriaconto- doedecinongenti-pentetriaconto- quattuordecinongenti-tetretriaconto- trequadragintitrecenti-tretriaconto- quinquinquagintinongenti-duetriaconto- quattuornonagintisescenti-metriaconto- sexseptuagintiducenti-triaconto- novemtriginticenti-enneicoso- unseptuagintiquadringenti-octeicoso- trenonagintiquadringenti-hepteicoso- sexquinquagintioctingenti-hexeicoso- centreti-penteicoso- novemquadraginti-tetreicoso- doetrigintiseptingenti-trioicoso- septuagintinongenti-dueicoso- quattuorsescenti-meiocoso- nongenti-icoso- novemquadringenti-enneco- septenvigintioctingenti-octeco- septendecioctingenti-hepteco- septenvigintitrecenti-hexeco- quinoctoginticenti-penteco- octoquinquagintioctingenti-treteco- septenquinquagintiducenti-treco- doequinquaginti-dueco- quinsexaginticenti-meco- quinoctogintiquadringenti-veco- sexquadragintiseptingenti-xono- octoseptuaginticenti-yocto- tretrigintiquadringenti-zepto- novemviginti-atto- sexaginticenti-femto- quattuordeciquadringenti-pico- sexnonagintinongenti-nano- trequinquagintiseptingenti-micro- treoctogintiseptingenti-milli- unseptingentillion |
| ... ... |
2,690,768,242,009,408,459,794,210,132,361,799,676,690,455,973,912,914,343,955,694,276,139,471 |
| 456 | Four hundred fifty-six trillion |
| 095 | Ninety-five billion |
| 261 | Two hundred sixty-one million |
| 392 | Three hundred ninety-two thousand |
| 896 | Eight hundred ninety-six |
Approximations[]
| Notation | Lower bound | Upper bound |
|---|---|---|
| Down-arrow notation | \(4\downarrow\downarrow257\) | |
| Steinhaus-Moser Notation | 79[3][3] | 80[3][3] |
| Copy notation | 7[7[154]] | 8[8[154]] |
| H* function | H(2H(50)) | H(3H(50)) |
| Taro's multivariable Ackermann function | A(3,A(3,509)) | A(3,A(3,510)) |
| Pound-Star Notation | #*((1))*(2,8,7,10,3)*11 | #*((1))*(9,0,9,2,7,5)*8 |
| Hyper-E notation | E[4]1#4 | |
| Bashicu matrix system | (0)(1)[22] | (0)(1)[23] |
| Hyperfactorial array notation | (96!)! | (97!)! |
| Fast-growing hierarchy | \(f_2(f_2(504))\) | \(f_2(f_2(505))\) |
| Hardy hierarchy | \(H_{\omega^22}(504)\) | \(H_{\omega^22}(505)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^{\omega^\omega}}}(4)\) | |
Sources[]
- ↑ Ascending with Up Arrows
- ↑ Bowers, Jonathan. Infinity Scrapers. Retrieved January 2013.
- ↑ 3.2.2 - The Fz, The Fuga & The Megafuga
- ↑ http://www.prothsearch.com/fermat.html
- ↑ Numbers from linear array notation | Steps Toward Infinity!
- ↑ Hayden's Big Numbers. Retrieved 2022-04-18.
See also[]
3 entries: tritri · tritet · tripent · trisept · tridecal
4 entries: tetratri · supertet · general(plex) (tetradecal)
5-10 entries: pentatri · superpent · pentadecal(plex) · hexatri · superhex · hexadecal(plex) · heptatri · supersept · heptadecal · superoct · octadecal · superenn · ennadecal · iteral (superdecal)
Over 10 entries: ultatri · dupertri · duperdecal (iteralplex) · truperdecal · quadruperdecal
Gar-: garone · gartwo · garthree · garfour · garfive · garsix · garseven · gareight · garnine · garten · garhundred · garmillion · gargoogol · gareceton · gartrialogue · gargoogolplex · gargiggol
Fz-: fzone · fztwo · fzthree · fzfour · fzfive · fzsix · fzseven · fzeight · fznine · fzten · fztwenty · fzthirty · fzhundred · fzthousand · fzmillion · fzgoogol · fzmilliplexion · fzgoogolplex · fzgargoogolplex · fzgiggol
Fuga-: fugaone · fugatwo · fugathree · fugafour · fugafive · fugasix · fugaseven · fugaeight · fuganine · fugaten · fugahundred · fugagoogol · fugagoogolplex · fugagargoogolplex · fugagiggol
Megafuga-: megafugaone · megafugatwo · megafugathree · megafugafour · megafugafive · megafugasix · megafugaseven · megafugaeight · megafuganine · megafugaten · megafugahundred · megafugagoogol · megafugagoogolplex · megafugagargoogolplex · megafugagargantugoogolplex · megafugagrangol
Extensions:
Booga-:: boogaone · boogatwo · boogathree · boogafour · boogafive · boogasix · boogaten · boogahundred · boogagoogol · boogagoogolplex
Gag-:: gagone · gagtwo · gagthree · gagfour · gagfive · gagsix · gagseven · gageight · gagnine · gagten · gaggoogol · gaggoogolplex