## FANDOM

10,385 Pages

For the SI prefix, see Mega-.

Mega is equal to Circle(2) or ② in circle notation or Pentagon(2) in Steinhaus-Moser notation.[1] It was defined by Hugo Steinhaus along with the megiston in the book Mathematical Snapshots. Mega can also be defined recursively as $$m_{256}$$ in the sequence defined by $$m_0 = 256$$ and $$m_{n + 1} = m_n^{m_n}$$.

Steinhaus showed that it is equal to Square(256)

Pentagon(2) = Square(Square(2)) = Square(Triangle(Triangle(2))) = Square(Triangle(4)) = Square(256) = Triangle256(256)

Using the general notation proposed by Susan Stepney, mega is:

$2[5] = 2[4][4] = 2[3]_2[4] = 2^{2}[3][4] = 4[3][4] = 4^{4}[4] = 256[4] = 256[3]_{256}$

The last 14 digits computed by Sbiis Saibian are ...93,539,660,742,656.[2] More digits can be calculated quite easily using modular exponentiation.

It is the last number listed on Robert Munafo's Notable Properties of Specific Numbers.[3]

## Values and approximations in other notations

Matt Hudelson calls the number zelda.[4] In his version of Steinhaus-Moser notation, it is denoted Triangle(2).

Mega can be expressed as M(2,3) in Hyper-Moser notation[5] or $$2 \downarrow\downarrow\downarrow 259$$ in down-arrow notation.

Mega can be bounded in arrow notation as:

$10\uparrow\uparrow 257 < \text{Mega} < 10\uparrow\uparrow 258\ \text{or}\ 2\uparrow\uparrow 259 < \text{Mega} < 2\uparrow\uparrow 260$

It can be bounded more precisely in Hyper-E notation:[2]

$E19,923,739,028,520,154,087,706,422,945,147,014,652,916,223,529,059,455,829,739,546,236,75\\ 7,445,592,829,019,852,096,549,871,643,037,231,579,555,867,729,029,727,837,739,722,687,243,\\ 833,688,041,650,758,866,703,047,684,995,147,926,044,802,500,789,969,233,229,482,277,620,4\\ 28,871,361,665,114,606,086,501,621,360,310,636,409,247,822,506,979,293,012,834,235,605,89\\ 2,457,887,360,583,787,492,777,424,798,206,285,182,369,042,469,497,447,438,158,240,050,711,\\ 323,245,053,205,431,372,163,355,524,614,258,748,270,064,178,183,600,550,138,767,745,559,3\\ 15,784,832,858,638,844,869,498,054,620,521,042,914,198,455,705,585,134,437,206,064,557,32\\ 3,165,937,735,931,605,786,380,378,378,018,264,857,422,432,758,696,743,477,636,091,751,483,\\ 267,310,595,348,292,927,018,011,128,165,226,311,150,554,708,199,087,683,524,760,666,293,6\\ 93,562,405,279,021,537\#255\\ < \text{Mega} <$ $E19,923,739,028,520,154,087,706,422,945,147,014,652,916,223,529,059,455,829,739,546,236,75\\ 7,445,592,829,019,852,096,549,871,643,037,231,579,555,867,729,029,727,837,739,722,687,243,\\ 833,688,041,650,758,866,703,047,684,995,147,926,044,802,500,789,969,233,229,482,277,620,4\\ 28,871,361,665,114,606,086,501,621,360,310,636,409,247,822,506,979,293,012,834,235,605,89\\ 2,457,887,360,583,787,492,777,424,798,206,285,182,369,042,469,497,447,438,158,240,050,711,\\ 323,245,053,205,431,372,163,355,524,614,258,748,270,064,178,183,600,550,138,767,745,559,3\\ 15,784,832,858,638,844,869,498,054,620,521,042,914,198,455,705,585,134,437,206,064,557,32\\ 3,165,937,735,931,605,786,380,378,378,018,264,857,422,432,758,696,743,477,636,091,751,483,\\ 267,310,595,348,292,927,018,011,128,165,226,311,150,554,708,199,087,683,524,760,666,293,6\\ 93,562,405,279,021,538\#255$

It is therefore between giggol and giggolplex.

Mega is exactly equal to $$m(3)m(2)m(1)(2)$$ in m(n) map.

## Sources

Mega series: Mega · A-ooga (Megision) · Megisiduon · Megisitruon · Megisiquadruon
Grand Mega series: Grand Mega · Grand Megision · Grand Megisiduon (A-oogra) · Grand Megisitruon · Grand Megisiquadruon
Great Mega series: Great Mega · Great Megision · Great Megisiduon · Great Megisitruon (A-oogrea) · Great Megisiquadruon
Gong Mega series: Gong Mega · Gong Megision · Gong Megisiduon · Gong Megisitruon · Gong Megisiquadruon (A-oogonga)
Hexomega series: Hexomega · Hexomegision · Hexomegisiduon · Hexomegisitruon · Hexomegisiquadruon · Hexomegisiquinton (A-oohexa)
Heptomega series: Heptomega · A-oohepta (Heptomegisisexton) · Octomega · A-oocta · Nonomega · A-ooennea
Megistron series: Megiston (Megistron) · Megisiplextron · Megisiduplextron · Megisitriplextron · Megisiquadruplextron · A-oomega (Megisienneaplextron)
A-ooga series: A-ooga · Betomega (A-oogatiplex) · A-oogatiduplex · A-oogatitriplex · A-oogatiquadruplex · A-oogatiquintiplex
A-oogra series: A-oogra · A-oogratiplex · Betogiga (A-oogratiduplex) · A-oogratitriplex · A-oogratiquadruplex · A-oogratiquintiplex
A-oogrea series: A-oogrea · A-oogreatiplex · A-oogreatiduplex · Betotera (A-oogreatitriplex) · A-oogreatiquadruplex · A-oogreatiquintiplex
A-oogonga series: A-oogonga · A-oogongatiplex · A-oogongatiduplex · A-oogongatitriplex · Betopeta (A-oogongatiquadruplex) · A-oogongatiquintiplex
A-oohexa series: A-oohexa · A-oohexatiplex · A-oohexatiduplex · A-oohexatitriplex · A-oohexatiquadruplex · Betoexa (A-oohexatiquintiplex)
A-oohepta series: A-oohepta · Betozetta (A-ooheptatisextiplex) · A-oocta · Betoyotta · A-ooennea · Betoxota
A-oomega series: A-oomega · A-oomegatiplex · A-oomegatiduplex · A-oomegatitriplex · A-oomegatiquadruplex · Betodaka (A-oomegatienneaplex)
Betomega series: Betomega · Flexinega (Brantomega) · Breatomega · Bigiatomega · Biquadriatomega · Biquintiatomega
Betogiga series: Betogiga · Brantogiga · Flexitria (Breatogiga) · Bigiatogiga · Biquadriatogiga · Biquintiatogiga
Betotera series: Betotera · Brantotera · Breatotera · Flexitera (Bigiatotera) · Biquadriatotera · Biquintiatotera
Betopeta series: Betopeta · Brantopeta · Breatopeta · Bigatopeta · Flexipeta (Biquadriatopeta) · Biquintiatopeta
Betoexa series: Betoexa · Brantoexa · Breatoexa · Bigatoexa · Biquadriatoexa · Flexiexa (Biquintiatoexa)
Betozetta series: Betozetta · Flexizetta · Betoyotta · Betoxota · Betodaka
Flexinega series: Flexinega · Oktia (Fainega) · Funnynega · Ftetrinega · Fpentinega · Fhexinega
Flexitria series: Flexitria · Faitria · Oktria (Funnytria) · Ftetritria · Fpentitria · Fhexitria
Flexitera series: Flexitera · Faitera · Funnytera · Oktetra (Ftetritera)
Moser series: Moser · Grand Moser · Great Moser · Gong Moser
Maser series: Maser · Miser (Killaser) · Meser · Muser