The Great Mega is equal to Circle(4) or ④ or Pentagon(4) in Steinhaus-Moser notation, or M(4,3) using Hyper-Moser notation. The term was coined by Aarex Tiaokhiao.[1]

In up-arrow notation, Great Mega is between \(4 \uparrow\uparrow\uparrow 5\) and \(4 \uparrow\uparrow\uparrow 6\). It is approximately 10↑↑10↑↑10↑↑101010617 in decimal.

The last 10 digits of the Great Mega are ...8,726,598,656.[2]

Using the general notation proposed by Susan Stepney, Great Mega can be bounded more precisely in Hyper-E notation:

\[\textrm E19,923,739,028,520,154,087,706,422,945,147,014,652,916,223,529,059,455,829,739,546,236,75\\ 7,445,592,829,019,852,096,549,871,643,037,231,579,555,867,729,029,727,837,739,722,687,243,\\ 833,688,041,650,758,866,703,047,684,995,147,926,044,802,500,789,969,233,229,482,277,620,4\\ 28,871,361,665,114,606,086,501,621,360,310,636,409,247,822,506,979,293,012,834,235,605,89\\ 2,457,887,360,583,787,492,777,424,798,206,285,182,369,042,469,497,447,438,158,240,050,711,\\ 323,245,053,205,431,372,163,355,524,614,258,748,270,064,178,183,600,550,138,767,745,559,3\\ 15,784,832,858,638,844,869,498,054,620,521,042,914,198,455,705,585,134,437,206,064,557,32\\ 3,165,937,735,931,605,786,380,378,378,018,264,857,422,432,758,696,743,477,636,091,751,483,\\ 267,310,595,348,292,927,018,011,128,165,226,311,150,554,708,199,087,683,524,760,666,293,6\\ 93,562,405,279,021,537\#(4[4]_{3}+4[4]_{2}+4[4]_{1}+2)\\ < \text{Great Mega} <\] \[E19,923,739,028,520,154,087,706,422,945,147,014,652,916,223,529,059,455,829,739,546,236,75\\ 7,445,592,829,019,852,096,549,871,643,037,231,579,555,867,729,029,727,837,739,722,687,243,\\ 833,688,041,650,758,866,703,047,684,995,147,926,044,802,500,789,969,233,229,482,277,620,4\\ 28,871,361,665,114,606,086,501,621,360,310,636,409,247,822,506,979,293,012,834,235,605,89\\ 2,457,887,360,583,787,492,777,424,798,206,285,182,369,042,469,497,447,438,158,240,050,711,\\ 323,245,053,205,431,372,163,355,524,614,258,748,270,064,178,183,600,550,138,767,745,559,3\\ 15,784,832,858,638,844,869,498,054,620,521,042,914,198,455,705,585,134,437,206,064,557,32\\ 3,165,937,735,931,605,786,380,378,378,018,264,857,422,432,758,696,743,477,636,091,751,483,\\ 267,310,595,348,292,927,018,011,128,165,226,311,150,554,708,199,087,683,524,760,666,293,6\\ 93,562,405,279,021,538\#(4[4]_{3}+4[4]_{2}+4[4]_{1}+2)\]

where

\[\textrm E19,923,739,028,520,154,087,706,422,945,147,014,652,916,223,529,059,455,829,739,546,236,75\\ 7,445,592,829,019,852,096,549,871,643,037,231,579,555,867,729,029,727,837,739,722,687,243,\\ 833,688,041,650,758,866,703,047,684,995,147,926,044,802,500,789,969,233,229,482,277,620,4\\ 28,871,361,665,114,606,086,501,621,360,310,636,409,247,822,506,979,293,012,834,235,605,89\\ 2,457,887,360,583,787,492,777,424,798,206,285,182,369,042,469,497,447,438,158,240,050,711,\\ 323,245,053,205,431,372,163,355,524,614,258,748,270,064,178,183,600,550,138,767,745,559,3\\ 15,784,832,858,638,844,869,498,054,620,521,042,914,198,455,705,585,134,437,206,064,557,32\\ 3,165,937,735,931,605,786,380,378,378,018,264,857,422,432,758,696,743,477,636,091,751,483,\\ 267,310,595,348,292,927,018,011,128,165,226,311,150,554,708,199,087,683,524,760,666,293,6\\ 93,562,405,279,021,537\#(4[4]_{2}+4[4]_{1}+2)\\ < 4[4]_{3} <\] \[E19,923,739,028,520,154,087,706,422,945,147,014,652,916,223,529,059,455,829,739,546,236,75\\ 7,445,592,829,019,852,096,549,871,643,037,231,579,555,867,729,029,727,837,739,722,687,243,\\ 833,688,041,650,758,866,703,047,684,995,147,926,044,802,500,789,969,233,229,482,277,620,4\\ 28,871,361,665,114,606,086,501,621,360,310,636,409,247,822,506,979,293,012,834,235,605,89\\ 2,457,887,360,583,787,492,777,424,798,206,285,182,369,042,469,497,447,438,158,240,050,711,\\ 323,245,053,205,431,372,163,355,524,614,258,748,270,064,178,183,600,550,138,767,745,559,3\\ 15,784,832,858,638,844,869,498,054,620,521,042,914,198,455,705,585,134,437,206,064,557,32\\ 3,165,937,735,931,605,786,380,378,378,018,264,857,422,432,758,696,743,477,636,091,751,483,\\ 267,310,595,348,292,927,018,011,128,165,226,311,150,554,708,199,087,683,524,760,666,293,6\\ 93,562,405,279,021,538\#(4[4]_{2}+4[4]_{1}+2),\]

\[E19,923,739,028,520,154,087,706,422,945,147,014,652,916,223,529,059,455,829,739,546,236,75\\ 7,445,592,829,019,852,096,549,871,643,037,231,579,555,867,729,029,727,837,739,722,687,243,\\ 833,688,041,650,758,866,703,047,684,995,147,926,044,802,500,789,969,233,229,482,277,620,4\\ 28,871,361,665,114,606,086,501,621,360,310,636,409,247,822,506,979,293,012,834,235,605,89\\ 2,457,887,360,583,787,492,777,424,798,206,285,182,369,042,469,497,447,438,158,240,050,711,\\ 323,245,053,205,431,372,163,355,524,614,258,748,270,064,178,183,600,550,138,767,745,559,3\\ 15,784,832,858,638,844,869,498,054,620,521,042,914,198,455,705,585,134,437,206,064,557,32\\ 3,165,937,735,931,605,786,380,378,378,018,264,857,422,432,758,696,743,477,636,091,751,483,\\ 267,310,595,348,292,927,018,011,128,165,226,311,150,554,708,199,087,683,524,760,666,293,6\\ 93,562,405,279,021,537\#(4[4]_{1}+2)\\ < 4[4]_{2} <\] \[E19,923,739,028,520,154,087,706,422,945,147,014,652,916,223,529,059,455,829,739,546,236,75\\ 7,445,592,829,019,852,096,549,871,643,037,231,579,555,867,729,029,727,837,739,722,687,243,\\ 833,688,041,650,758,866,703,047,684,995,147,926,044,802,500,789,969,233,229,482,277,620,4\\ 28,871,361,665,114,606,086,501,621,360,310,636,409,247,822,506,979,293,012,834,235,605,89\\ 2,457,887,360,583,787,492,777,424,798,206,285,182,369,042,469,497,447,438,158,240,050,711,\\ 323,245,053,205,431,372,163,355,524,614,258,748,270,064,178,183,600,550,138,767,745,559,3\\ 15,784,832,858,638,844,869,498,054,620,521,042,914,198,455,705,585,134,437,206,064,557,32\\ 3,165,937,735,931,605,786,380,378,378,018,264,857,422,432,758,696,743,477,636,091,751,483,\\ 267,310,595,348,292,927,018,011,128,165,226,311,150,554,708,199,087,683,524,760,666,293,6\\ 93,562,405,279,021,538\#(4[4]_{1}+2),\]

\[E19,923,739,028,520,154,087,706,422,945,147,014,652,916,223,529,059,455,829,739,546,236,75\\ 7,445,592,829,019,852,096,549,871,643,037,231,579,555,867,729,029,727,837,739,722,687,243,\\ 833,688,041,650,758,866,703,047,684,995,147,926,044,802,500,789,969,233,229,482,277,620,4\\ 28,871,361,665,114,606,086,501,621,360,310,636,409,247,822,506,979,293,012,834,235,605,89\\ 2,457,887,360,583,787,492,777,424,798,206,285,182,369,042,469,497,447,438,158,240,050,711,\\ 323,245,053,205,431,372,163,355,524,614,258,748,270,064,178,183,600,550,138,767,745,559,3\\ 15,784,832,858,638,844,869,498,054,620,521,042,914,198,455,705,585,134,437,206,064,557,32\\ 3,165,937,735,931,605,786,380,378,378,018,264,857,422,432,758,696,743,477,636,091,751,483,\\ 267,310,595,348,292,927,018,011,128,165,226,311,150,554,708,199,087,683,524,760,666,293,6\\ 93,562,405,279,021,537\#2\\ < 4[4]_{1} <\] \[E19,923,739,028,520,154,087,706,422,945,147,014,652,916,223,529,059,455,829,739,546,236,75\\ 7,445,592,829,019,852,096,549,871,643,037,231,579,555,867,729,029,727,837,739,722,687,243,\\ 833,688,041,650,758,866,703,047,684,995,147,926,044,802,500,789,969,233,229,482,277,620,4\\ 28,871,361,665,114,606,086,501,621,360,310,636,409,247,822,506,979,293,012,834,235,605,89\\ 2,457,887,360,583,787,492,777,424,798,206,285,182,369,042,469,497,447,438,158,240,050,711,\\ 323,245,053,205,431,372,163,355,524,614,258,748,270,064,178,183,600,550,138,767,745,559,3\\ 15,784,832,858,638,844,869,498,054,620,521,042,914,198,455,705,585,134,437,206,064,557,32\\ 3,165,937,735,931,605,786,380,378,378,018,264,857,422,432,758,696,743,477,636,091,751,483,\\ 267,310,595,348,292,927,018,011,128,165,226,311,150,554,708,199,087,683,524,760,666,293,6\\ 93,562,405,279,021,538\#2,\]

\[4[4]_{1} = 4[3]_{4} = 4[3][3][3][3],\]

\[4[4]_{n} = 4[4]_{n-1}[4]_{1} = 4[4]_{n-1}[3]...[3], \text{with \(4[4]_{n-1}\) [3]'s and \(n \geq {2}\)}.\]

Etymology

The name of this number is based on the word "great" and the number "mega".

Sources

See also

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

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