PART 2 (1,000,000,000,000 ~ 1010^1,000,000,000,000)
The Astronomical Range (1,000,000,000,000 ~ 1080)
1,000,000,000,000
1,004,278,425,000
The coordinate when travelling along one axis where the humidity layer of Minecraft's original implementation of biomes would break down, causing only four distinct biomes to generate after this point.
1,099,511,627,776
240. The binary approximation of the tera- (1012) multiplier.
2,199,023,255,552
241
4,761,024,936,107
The coordinate when travelling along one axis where Minecraft's original implementation of biomes would break down. The exact expected distance is 2^39*5*sqrt(3)*(2^29)/(2^29 + 8) ~ 4,761,024,936,107.
7,625,597,484,987
327. Can also be expressed as 279, 196833, 3^3^3, 3^^3, or 3^^^2. It is a number that appears frequently when evaluating hyperoperators with the base of 3 (for example, 3^^^3, seen later in part 3, is a power tower of this many threes). Also its digits sum to 81, which is 34.
8,916,100,448,256
1212.
20,000,000,000,000
29,996,224,275,833
The trillionth prime number. It is also very close to SpongeBob's Number (see the entry below).
29,998,559,671,349
The number that Cookie Fonster dubbed SpongeBob's Number. It appears in the SpongeBob episode "Have You Seen This Snail?".
100,000,000,000,000
281,474,976,710,656
248. Can also be expressed as 424, 816, 82^4, 82^2^2, 84^2 1612, 648, 2566, 40964, or 167772162.
302,875,106,592,253
1313.
562,949,953,421,312
1,000,000,000,000,000
A quadrillion, or alternatively small fry.
1,125,899,906,842,624
250.
2,251,799,813,685,248
251, the first power of two that is a zeroless pandigital number.
9,007,199,254,740,991
The largest odd integer that can be exactly represented in the commonly-used IEEE double-precision floating point format. Also another case of 2^prime - 1 being composite; its smallest prime factor is 6,361.
11,112,006,825,558,016
1414. Can also be expressed as 1967, or 14^^2. Particularly notable because the first 4 digits are all ones (see 5^5^5^5 )
12,345,678,987,654,321
1111111112, the largest square of a repunit that is palindromic.
52,631,578,947,368,421
r(19), the integral-exaundevigintile.
53,905,378,846,979,747
The coordinate in a Minecraft world where the "Fartherer Lands" were purported to appear, however, they are just an artifact of how certain mods reintroduce the Far Lands to later versions of the game.
53,905,378,859,432,512
After the Far Lands were "patched" in Minecraft Beta 1.8, the Far Lands were actually moved to this coordinate, which we couldn't actually view in-game until the original 64-bit mod for 1.2.5 was released in mid-early 2021.
1,000,000,000,000,000,000
1,111,111,111,111,111,111
The next repunit prime after 11.
4,312,430,307,758,379,832
The coordinate in Minecraft where the "Farthest Lands" were similarly purported to generate.
6,428,888,932,339,941,376
7610.
9,223,372,036,854,775,807
The maximum 64-bit signed integer.
12,157,692,622,039,623,539
The largest number that is the sum of the consecutive powers of its digits.
12,345,678,910,987,654,321
A prime number that is easy to remember because it has all the numbers from 1 to 10 in its digits, followed by the digits backwards.
44,211,790,234,832,169,331
The quintillionth prime number.
1,000,000,000,000,000,000,000
1,322,314,049,613,223,140,496
The square of 36363636364, which is equal to 826446281*11*4. The square of that is 826446281*826446281*11*11*4*4 or 826446281*100000000001*16 or 13223140496*100000000001.
11,111,111,111,111,111,111,111
Another repunit prime. This is the last repunit prime we'll see for a while -- the next is not until (10^317 - 1)/9.
1,000,000,000,000,000,000,000,000
4,115,226,337,448,559,670,781,893
(10^27-1)/243, or r(3, 5) in the reptend function.
45,000,000,000,000,000,000,000,000
58,310,039,994,836,584,070,534,263
The 1,000,000,000,000,000,000,000,000th prime. So far this is the largest number whose index in the primes sequence is a power of 10 that we have been able to calculate.
1,000,000,000,000,000,000,000,000,000
1,267,650,600,228,229,401,496,703,205,376
2100. Can also be expressed as 450, 1625, or 335544324.
91,409,924,241,424,243,424,241,924,242,500
The sum of the 10th powers of the first 1000 integers.
99,999,999,999,999,999,999,999,999,999,999
The largest number that can be directly entered into the Windows calculator in Scientific mode (the largest number that it can calculate, however, is much larger).
340,282,366,920,938,463,463,374,607,431,768,211,456
2128. Can also be expressed as 464, 44^3, 22^7, and, using the weak hyperoperators, 4vv4, 4vvv2, or 2vvvv3.
443,426,488,243,037,769,948,249,630,619,149,892,803
323,257,909,929,174,534,292,273,980,721,360,271,853,387
387, starts in 3 and ends in 87.
8,175,100,408,620,645,429,587,604,206,419,312,153,467,715,321,856
The Far Lands in Minecraft would eventually begin to dissipate into what I refer to as the "Fringe Lands", beginning at this coordinate on the X axis when the other axis is within 12,550,824 of 0. The next three entries are all related to this phenomenon.
8,576,620,983,668,390,695,654,176,953,195,873,545,661,439,803,392
The coordinate of the second stage of the X Fringe Lands, where the terrain thins out further but still resembles the Edge Far Lands.
9,176,239,949,795,123,308,594,625,193,335,189,314,391,974,608,896
The coordinate of the third stage of the X Fringe Lands and initiation of the Z Fringe Lands in Minecraft when the other axis is within 12,550,824 of 0. This is where the X Fringe Lands really thin out. In the mobile version of the game, this would occur at only 12,561,029.
10,299,981,089,825,331,303,027,420,223,646,772,450,634,036,674,560
The coordinate of the fourth stage of the X Fringe Lands in Minecraft, where only one-block lines will generate (or, in some versions, almost nothing).
2,359,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
The farthest distance where any material in the Z Fringe Lands other than the ocean down to bedrock is known to generate.
182,833,274,602,320,380,000,000,000,000,000,000,000,000,000,000,000,000,000,000
80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000
52!, the number of ways a deck of playing cards can be arranged.
115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936
2^256. Can also be expressed as 2^(2^8) or 2^(2^(2^3)).
1,371,742,112,482,853,223,593,964,334,705,075,445,816,186,556,927,297,668,038,408,779,149,519,890,260,631
The sixth reptend in a reciprocal of a power of 3 (multiplying this number by 729 and adding 1 gives 1081). Can be expressed as r(3, 6) using the reptend function.
The Googol Range (1080 ~ 10500)
2,350,988,701,644,575,015,937,473,074,444,491,355,637,331,113,544,175,043,017,503,412,556,834,518,909,454,345,703,125
5125. Can also be expressed as 312525 or 5^(5^3).
2,135,987,035,920,910,082,395,021,706,169,552,114,602,704,522,356,652,769,947,041,607,822,219,725,780,640,550,022,962,086,936,576
2320, the "alphabetically last" power of two, and the number of possible 40-character strings of characters (such as passwords) if one character is represented by a byte. Can also be expressed as 4160, 1680, 3264, 25640, 102432, 6553620, 104857616, or 429496729610.
102,031,721,744,360,038,361,307,651,658,858,356,866,468,570,628,663,681,575,984,106,139,568,929,924,796,430,583,285,082,737,858,224
The first number x such that xx is greater than a googolplex.
10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
10100, a googol. This number is thought of as the quintessential large number. Can also be expressed as 10050, 1000025, or 10000020. Rather fittingly, most handheld calculators max out at a googol.
10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,267
The first prime number greater than 10100. It has been named gooprol.
11,072,956,794,213,997,867,135,792,524,782,958,162,100,420,243,896,887,959,405,463,694,950,387,058,446,840,611,319,035,458,679,209,984
f2(324). It is the first fast-growing hierarchy number to be greater than a googol.
17,498,005,798,264,095,394,980,017,816,940,970,922,825,355,447,145,699,491,406,164,851,279,623,993,595,007,385,788,105,416,184,430,592
2333, the first power of 2 to be greater than a googol.
255,895,648,634,818,208,370,064,452,304,769,558,261,700,170,817,472,823,398,081,655,524,438,021,806,620,809,813,295,008,281,436,789,493,636,144
Gijswit’s sequence is a slow-growing integer sequence named after Dion Gijswit. The sequence is defined as follows: Define b(1) = 1. To find the next term, b(n+1), expressed the string b(1), b(2), b(3), …, b(n) as XYk = XYYY…(k)…YYY, where X can be any string, Y is a non-empty string, and k is an arbitrary nonnegative integer. Then b(n+1) = k.
The first terms of Gijswit’s sequence are 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, … The first 4 does not occur until the 220th term, and the first run of 2 consecutive 4s does not occur until this many terms. The term at this position in the sequence is the first of two consecutive 4s.
13,407,807,929,942,597,099,574,024,998,205,846,127,479,365,820,592,393,377,723,561,443,721,764,030,073,546,976,801,874,298,166,903,427,690,031,858,186,486,050,853,753,882,811,946,569,946,433,649,006,084,096
44^4. Can also be expressed as 4256, 2512, or 4^^3.
111,035,955,729,697,564,867,052,472,991,659,265,008,498,270,260,836,147,884,134,648,785,275,850,530,870,579,456,318,461,683,861,207,229,750,350,262,470,951,399,008,247,186,575,943,346,298,133,067,315,141,536,151,233,617,126,670,896,649,530,882,460
The great triangrol, the first iterated triangle of 10 to be greater than googol.
457,247,370,827,617,741,197,988,111,568,358,481,938,728,852,309,099,222,679,469,593,049,839,963,420,210,333,790,580,704,160,951,074,531,321,444,901,691,815,272,062,185,642,432,556,012,802,926,383,173,296,753,543,667,123,914,037,494,284,407,864,654,778,235,025,148,605,395,518,975,765,889,346,136,259,716,506,630,086,877
r(3, 7), or (10243 - 1)/2187. It has 240 digits, meaning it is the first number of the form r(3, n) to be greater than googol.
3,728,363,792,258,191,548,993,633,728,836,738,827,663,827,363,737,273,636,545,667,788,929,274,772,736,448,477,372,847,929,010,928,777,666,382,822,777,266,626,166,362,626,262,712,828,287,374,747,489,929,182,837,774,737,727,771,882,919,383,748,474,772,919,273,773,747,446,952,945,950,469,309,285,928,394,919,107,499,377,482,993,748,839,238,391,638,474,682,948,492,917,389, 326,728,462,738,363,819,916,383,847
179,769,313,486,231,570,814,527,423,731,704,356,798,070,567,525,844,996,598,917,476,803,157,260,780,028,538,760,589,558,632,766,878,171,540,458,953,514,382,464,234,321,326,889,464,182,768,467,546,703,537,516,986,049,910,576,551,282,076,245,490,090,389,328,944,075,868,508,455,133,942,304,583,236,903,222,948,165,808,559,332,123,348,274,797,826,204,144,723,168,738,177,180,919,299,881,250,404,026,184,124,858,368
This number is equal to ((253-1)/252)*21023, or 2971(253 - 1). It is the largest number that can be represented in the commonly-used IEEE double-precision floating point format, and thus the largest number that many programs can represent.
788,657,867,364,790,503,552,363,213,932,185,062,295,135,977,687,173,263,294,742,533,244,359,449,963,403,342,920,304,284,011,984,623,904,177,212,138,919,638,830,257,642,790,242,637,105,061,926,624,952,829,931,113,462,857,270,763,317,237,396,988,943,922,445,621,451,664,240,254,033,291,864,131,227,428,294,853,277,524,242,407,573,903,240,321,257,405,579,568,660,226,031,904,170,324,062,351,700,858,796,178,922,222,789,623,703,897,374,720,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
The factorial of 200. This number is called the faxul.
The Bell-Gong Range (10500 ~ 101,000,000)
4858450636189713423582095962494202044581400587983244549483093085061934704708809928450644769865524364849997247024915119110411605739177407856919754326571855442057210445735883681829823754139634338225199452191651284348332905131193199953502413758765239264874613394906870130562295813219481113685339535565290850023875092856892694555974281546386510730049106723058933586052544096664351265349363643957125565695936815184334857605266940161251266951421550539554519153785457525756590740540157929001765967965480064427829131488548259914721248506352686630476300
The number that makes Tupper's self-referential formula, 1/2 < [mod([y/17]2-17[x]-mod([y],17), 2)], work. The formula is not truly self-referential, as the formula can actually graph any image possible with only two colors, so this is actually more similar to the decimal expansions of most extremely large numbers.
152,415,790,275,872,580,399,329,370,522,786,160,646,242,950,769,699,740,893,156,531,016,613,321,140,070,111,263,526,901,386,983,691,510,440,481,633,897,271,757,354,061,880,810,852,004,267,642,127,724,432,251,181,222,374,638,012,498,094,802,621,551,592,745,008,382,868,465,172,991,921,963,115,378,753,238,835,543,362,292,333,485,749,123,609,205,913,732,662,703,856,119,493,979,576,284,103,033,074,226,489,864,349,946,654,473,403,444,596,860,234,720,317,024,843,773,814,967,230,605,090,687,395,214,144,185,337,600,975,461,057,765,584,514,555,707,971,345,831,428,135,954,884,926,078,341,716,201,798,506,325,255,296,448,712,086,572,168,876,695,625,666,819,082,456,942,539,247,065,996,037,189,452,827,312,909,617,436,366,407,559,823,197,683,279,987,806,736,777,930,193,568,053,650,358,177,107,148,300,563,938,424,020,728,547,477,518,670,934,308,794,391,098,917,847,889,041,304,679,164,761,469,288,218,259,411,675,049,535,131,839,658,588,629,782,045,419,905,502,210,028,959
r(3, 8) using the reptend function (multiplying this number by 6561 gives 10729 - 1).
201,911,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,112,711,111,111,111,111,111,111,111,111,111,111,111,654,811,111,111,111,111,111,111,111,111,111,111,179,623,311,111,111,111,111,111,111,111,111,111,115,337,628,911,111,111,111,111,111,111,111,111,111,722,892,235,871,111,111,111,111,111,111,111,111,343,599,676,369,461,111,111,111,111,111,111,111,111,114,466,762,711,111,111,111,111,111,111,111,111,111,225,752,927,811,111,111,111,111,111,111,111,111,177,539,765,426,611,111,111,111,111,111,111,111,138,354,546,389,737,571,111,111,111,111,111,111,117,366,435,683,954,358,271,111,111,111,111,111,113,626,786,966,863,922,297,832,111,111,111,111,113,272,697,888,856,299,536,008,088,011,111,111,111,111,111,118,383,588,055,585,111,111,111,111,111,111,111,115,688,385,885,368,536,111,111,111,111,111,111,111,883,058,388,883,855,363,111,111,111,111,111,111,808,885,338,530,655,586,888,811,111,111,111,111,838,868,608,880,665,663,688,063,661,111,111,111,538,558,503,688,538,688,898,068,300,838,111,111,055,880,566,883,886,086,806,355,803,583,885,511,111,111,111,111,111,116,853,111,111,111,111,111,111,111,111,111,111,111,186,331,111,111,111,111,111,111,111,111,111,111,111,035,611,111,111,111,111,111
A prime number I found somewhere on the internet around Christmastime in 2019. The digits of this number, if arranged in rows of 38 digits, resemble an image of a Christmas tree.
10^1000
A thousandplex, googolchime, or great googol. It is a googol raised to the tenth power, which means that it is a googol googol googol googol googol googol googol googol googol googols, and also a googolding squared, making it also a googolding googoldings.
This number is Andre Joyce's great googol, but he provides no less than four conflicting definitions for the number.
Some larger handheld calculators max out at a googolchime.
10,511,037,747,648,833,807,375,964,227,980,446,845,001,219,312,136,414,557,971,919,721,403,348,752,281,897,905,455,737,919,462,735,423,546,944,182,536,662,064,704,153,963,607,829,519,415,690,865,021,054,297,158,034,984,496,960,855,220,033,307,686,824,006,744,542,373,596,082,351,395,082,670,864,979,654,840,526,871,217,991,174,385,901,000,026,186,534,720,385,698,212,884,526,220,757,201,760,703,768,364,064,444,890,514,400,566,289,413,011,031,384,676,455,588,231,817,225,085,081,648,372,921,391,558,969,490,469,623,984,717,870,371,500,785,398,918,855,203,982,990,908,713,337,748,372,185,704,423,627,770,322,341,926,717,704,953,978,353,709,764,138,110,298,836,991,429,855,395,534,504,549,203,880,045,057,969,334,956,068,971,917,319,701,594,253,915,185,300,634,899,019,949,084,540,490,744,582,619,572,287,847,459,842,271,273,802,947,547,147,891,821,693,243,011,474,805,144,249,820,197,686,520,329,327,396,563,323,889,755,557,605,560,252,815,946,013,003,290,512,302,837,187,859,201,905,176,985,994,113,336,495,692,075,035,559,367,679,630,402,918,224,167,105,142,189,275,149,510,738,812,480,892,407,752,924,918,306,914,500,472,886,833,917,554,875,031,580,462,499,864,906,544,959,472,704,484,493,903,721,569,536,328,770,398,541,866,504,305,277,184,641,095,297,703,354,693,522,344,642,060,637,206,460,029,232,533,992,047,394,275,463,266,304
2^3,322, the first power of 2 greater than a googolchime.
6.69092608710…*101,054
The number of ways to arrange a 17x17x17 Rubik's cube (a number with about 1055 digits), which is the record for the largest Rubik's cube. It is more than the number of Planck volumes in the universe raised to the fifth power! It is an example of the very large numbers that combinatorics can produce.
3.70299050082…*101,161
The astraexigol. It is a number with 1,162 digits, placing it between the 17x17x17 Rubik's cube number and 24096. It is equal to 110,486,247,050105 x 105.
285,582,352,639,284,585,877,883,951,619,467,722,053,564,898,109,387,750,941,281,441,454,233,825,176,870,078,186,811,426,536,266,861,532,376,562,723,428,374,790,025,086,172,668,260,686,379,490,742,753,664,125,712,696,394,736,044,363,145,019,512,609,533,842,595,746,908,394,073,306,892,915,306,959,446,920,306,633,335,276,251,008,340,608,514,692,606,029,200,459,277,123,359,692,240,505,083,775,297,449,602,858,230,164,887,658,671,442,178,006,058,268,942,965,846,794,860,351,030,996,096,138,085,617,724,007,298,896,518,096,401,894,330,339,787,111,149,522,191,295,031,038,519,612,608,731,236,106,937,117,869,470,607,182,426,238,430,640,410,357,634,968,902,284,203,509,168,375,054,151,291,381,753,286,153,108,422,700,588,456,034,782,707,033,704,875,118,269,274,695,850,182,123,964,332,024,357,463,939,832,587,826,030,408,304,659,558,897,933,837,861,571,207,602,709,842,836,087,636,128,991,870,732,100,541,958,676,023,785,599,756,317,966,109,598,779,113,079,591,465,089,810,036,446,824,450,852,489,278,995,102,128,182,376,351,161,855,246,343,414,863,405,914,892,059,350,681,579,164,188,968,878,441,348,266,947,843,390,238,823,034,797,642,209,314,532,117,291,556,856,308,834,174,479,768,964,626,316,076,492,278,794,341,783,753,213,171,018,555,574,529,832,630,104,577,791,697,457,516,132,745,672,643,089,264,594,262,670,212,859,129,374,222,128,344,971,405,742,361,545,526,339,564,230,337,229,299,700,767,261,631,943,847,230,407,141,752,026,369,866,800,719,403,951,819,378,890,142,755,935,620,811,228,760,152,467,835,232,636,425,957,744,569,129,378,289,667,630,827,956,075,826,249,824,673,986,255,582,709,786,366,930,477,525,657,484,230,610,056,330,917,966,464,432,484,283,230,067,206,006,192,889,698,725,469,570,122,775,638,307,348,365,188,166,492,407,190,150,575,300,455,640,035,350,487,371,078,345,081,147,273,937,244,964,311,002,800,932,118,945,429,216
Integer part of 1010^pi. This number has 1386 digits, placing it between 22^12 and Une See's Wall O'Nines.
101440 – 1 (999999…999999 w/ 1440 9s)
Une See's Wall O'Nines from the “My Number is Bigger!” thread.
Since the number of nines (1,440) is divisible by both 3 and 2, it is divisible by 7, 11, 13, and 37. 1,440 is also divisible by 9 and so 19 and 333667 also divide 10^1440 - 1. 1,440 is also equal to 16 x 90, so this number is also divisible by both 17 and 41 (90 is 18 x 5). 1,440 is definitely divisible by 8 and so this number is divisible by 73 and 137. 8 is 2 x 4 and so 101,440 - 1 is also divisible by 101.
As a result, it is possible to find many factors of Une See's Wall O'Nines, beginning with: 3(^4), 7, 11, 13, 17, 19, 31, 37, 41, 61, 73, 97, 101, 137....
33,644,764,876,431,783,266,621,612,005,107,543,310,302,148,460,680,063,906,564,769,974,680,081,442,166,662,368,155,595,513,633,734,025,582,065,332,680,836,159,373,734,790,483,865,268,263,040,892,463,056,431,887,354,544,369,559,827,491,606,602,099,884,183,933,864,652,731,300,088,830,269,235,673,613,135,117,579,297,437,854,413,752,130,520,504,347,701,602,264,758,318,906,527,890,855,154,366,159,582,987,279,682,987,510,631,200,575,428,783,453,215,515,103,870,818,298,969,791,613,127,856,265,033,195,487,140,214,287,532,698,187,962,046,936,097,879,900,350,962,302,291,026,368,131,493,195,275,630,227,837,628,441,540,360,584,402,572,114,334,961,180,023,091,208,287,046,088,923,962,328,835,461,505,776,583,271,252,546,093,591,128,203,925,285,393,434,620,904,245,248,929,403,901,706,233,888,991,085,841,065,183,173,360,437,470,737,908,552,631,764,325,733,993,712,871,937,587,746,897,479,926,305,837,065,742,830,161,637,408,969,178,426,378,624,212,835,258,112,820,516,370,298,089,332,099,905,707,920,064,367,426,202,389,783,111,470,054,074,998,459,250,360,633,560,933,883,831,923,386,783,056,136,435,351,892,133,279,732,908,133,732,642,652,633,989,763,922,723,407,882,928,177,953,580,570,993,691,049,175,470,808,931,841,056,146,322,338,217,465,637,321,248,226,383,092,103,297,701,648,054,726,243,842,374,862,411,453,093,812,206,564,914,032,751,086,643,394,517,512,161,526,545,361,333,111,314,042,436,854,805,106,765,843,493,523,836,959,653,428,071,768,775,328,348,234,345,557,366,719,731,392,746,273,629,108,210,679,280,784,718,035,329,131,176,778,924,659,089,938,635,459,327,894,523,777,674,406,192,240,337,638,674,004,021,330,343,297,496,902,028,328,145,933,418,826,817,683,893,072,003,634,795,623,117,103,101,291,953,169,794,607,632,737,589,253,530,772,552,375,943,788,434,504,067,715,555,779,056,450,443,016,640,119,462,580,972,216,729,758,615,026,968,443,146,952,034,614,932,291,105,970,676,243,268,515,992,834,709,891,284,706,740,862,008,587,135,016,260,312,071,903,172,086,094,081,298,321,581,077,282,076,353,186,624,611,278,245,537,208,532,365,305,775,956,430,072,517,744,315,051,539,600,905,168,603,220,349,163,222,640,885,248,852,433,158,051,534,849,622,434,848,299,380,905,070,483,482,449,327,453,732,624,567,755,879,089,187,190,803,662,058,009,594,743,150,052,402,532,709,746,995,318,770,724,376,825,907,419,939,632,265,984,147,498,193,609,285,223,945,039,707,165,443,156,421,328,157,688,908,058,783,183,404,917,434,556,270,520,223,564,846,495,196,112,460,268,313,970,975,069,382,648,706,613,264,507,665,074,611,512,677,522,748,621,598,642,530,711,298,441,182,622,661,057,163,515,069,260,029,861,704,945,425,047,491,378,115,154,139,941,550,671,256,271,197,133,252,763,631,939,606,902,895,650,288,268,608,362,241,082,050,562,430,701,794,976,171,121,233,066,073,310,059,947,366,875
10,000th term in the Fibonacci sequence. Since it ends with ...6875, it can be divided by 5 four times without leaving any remainder. It is about 3.366 novemvigintillion times a gargoogolchime.
1,911,012,597,945,477,520,356,404,559,703,964,599,198,081,048,990,094,337,139,512,789,246,520,530,242,615,803,012,059,386,519,739,850,265,586,440,155,794,462,235,359,212,788,673,806,972,288,410,146,915,986,602,087,961,896,757,195,701,839,281,660,338,047,611,225,975,533,626,101,001,482,651,123,413,147,768,252,411,493,094,447,176,965,282,756,285,196,737,514,395,357,542,479,093,219,206,641,883,011,787,169,122,552,421,070,050,709,064,674,382,870,851,449,950,256,586,194,461,543,183,511,379,849,133,691,779,928,127,433,840,431,549,236,855,526,783,596,374,102,105,331,546,031,353,725,325,748,636,909,159,778,690,328,266,459,182,983,815,230,286,936,572,873,691,422,648,131,291,743,762,136,325,730,321,645,282,979,486,862,576,245,362,218,017,673,224,940,567,642,819,360,078,720,713,837,072,355,305,446,356,153,946,401,185,348,493,792,719,514,594,505,508,232,749,221,605,848,912,910,945,189,959,948,686,199,543,147,666,938,013,037,176,163,592,594,479,746,164,220,050,885,079,469,804,487,133,205,133,160,739,134,230,540,198,872,570,038,329,801,246,050,197,013,467,397,175,909,027,389,493,923,817,315,786,996,845,899,794,781,068,042,822,436,093,783,946,335,265,422,815,704,302,832,442,385,515,082,316,490,967,285,712,171,708,123,232,790,481,817,268,327,510,112,746,782,317,410,985,888,683,708,522,000,711,733,492,253,913,322,300,756,147,180,429,007,527,677,793,352,306,200,618,286,012,455,254,243,061,006,894,805,446,584,704,820,650,982,664,319,360,960,388,736,258,510,747,074,340,636,286,976,576,702,699,258,649,953,557,976,318,173,902,550,891,331,223,294,743,930,343,956,161,328,334,072,831,663,498,258,145,226,862,004,307,799,084,688,103,804,187,368,324,800,903,873,596,212,919,633,602,583,120,781,673,673,742,533,322,879,296,907,205,490,595,621,406,888,825,991,244,581,842,379,597,863,476,484,315,673,760,923,625,090,371,511,798,941,424,262,270,220,066,286,486,867,868,710,182,980,872,802,560,693,101,949,280,830,825,044,198,424,796,792,058,908,817,112,327,192,301,455,582,916,746,795,197,430,548,026,404,646,854,002,733,993,860,798,594,465,961,501,752,586,965,811,447,568,510,041,568,687,730,903,712,482,535,343,839,285,397,598,749,458,497,050,038,225,012,489,284,001,826,590,056,251,286,187,629,938,044,407,340,142,347,062,055,785,305,325,034,918,189,589,707,199,305,662,188,512,963,187,501,743,535,960,282,201,038,211,616,048,545,121,039,313,312,256,332,260,766,436,236,688,296,850,208,839,496,142,830,484,739,113,991,669,622,649,948,563,685,234,712,873,294,796,680,884,509,405,893,951,104,650,944,137,909,502,276,545,653,133,018,670,633,521,323,028,460,519,434,381,399,810,561,400,652,595,300,731,790,772,711,065,783,494,174,642,684,720,956,134,647,327,748,584,238,274,899,668,755,052,504,394,218,232,191,357,223,054,066,715,373,374,248,543,645,663,782,045,701,654,593,218,154,053,548,393,614,250,664,498,585,403,307,466,468,541,890,148,134,347,714,650,315,037,954,175,778,622,811,776,585,876,941,680,908,203,125
5^5^5. The first number of the form x^x^x that is greater than 101000.
103,003
A millinillion, the 1000th -illion (using the short scale).
1.99506311688… * 103,010
210,000, a binary googoltoll. It is the fourth 210^n number, and the first such number that is greater than a googolchime. It seems only slightly larger than a millinillion, but it is really 199.5 million times larger.
2.22225926304…*103,131
36,563. The smallest power of 3 where all the first 5 digits are the same. It has 3,132 digits, which places it between a binary-googoltoll (210,000) and a googolbell.
105,000
A googolbell.
1.6935087808430286711... x 106,556
(10^6561 - 1)/59049, or r(3, 10) using the reptend function. The last 10 digits are ...8023336551.
1.5054164145... x 109,391
The first triple exponential of 3. It starts with 15054164145220926243143..., and ends with ...686617859227. It has 9,392 digits, making it the largest double exponential of 3 that the Windows Calculator can calculate. It is also approximated to 4 digits of accuracy by the number of digits in the fifth power of 210^9,391.
8.23049512... x 109999
233,219, the largest power of 2 that the Windows Calculator can calculate.
9.64667... x 109999
320,959, the largest power of 3 that the Windows Calculator can calculate.
1010,000
A googoltoll. This value marks the limit of the built-in calculator on Windows, and attempting to calculate a number higher than this there results in a display of "Overflow" (or "Invalid input").
1.64609902... x 10^10,000
2^33220, the first power of 2 greater than googoltoll (click here for all the digits)
2.25573752222... x 1015,599
The largest known prime where all digits are prime (being either a 2, 3, 5, or 7). It consists of 1559 repetitions of 2255737522 followed by 2255737523. It was discovered in 2002.
3.515 x 1018,267
A lower bound for Σ(6), where Σ denotes the busy beaver function.
5.6450292694767... x 1019,677
r(3, 11) using the reptend function. The last 7 digits are ...4445517 (click here for all the digits)
2.0035299304... x 1019,728
265,536. Can also be expressed as 2^2^2^2^2, 2^2^2^4, 2^2^16, or 2^^5. It begins with 20035299304068464649790723515602... and ends with ...587895905719156736. The first non-trivial number of the form x^x^x^x^x, and the only one that we can know the leading digits as of yet, let alone full decimal expansion of (See 3^^5 on the next page). See the Hyperoperational Numbers page for all the digits.
This is also the record distance anyone has teleported in Minecraft using one of the new BigInteger mods.
9.9900209301... x 1030,102
2^100,000 (click here for all the digits).
2.659119772... x 1036,305
6^^3. Can also be expressed as 646,656.
1.8816764... x 1059,043
(10^59049 - 1)/531441. This number begins with 1881676423158... and ends with ...30891481839. Can be expressed as r(3, 12) using the reptend function (click here for all the digits)
10100000
A googolgong.
6.2060698... x 10183,230
Exponential factorial of 5. The last 21 digits are ...892256259918212890625. The last digits of 5^2^n converge to a leftward-infinite string ending in ...8212890625 that remains unchanged when raised to any power, with the number of stable digits being n+2. The same applies for 5^((any positive even integer)^n).
9.900656... x 10301,029
Millionth power of 2.
3.759... x 10695,974
7^^3.
The Double Exponential Range (101000000 ~ 10^10^80)
101,000,000
Ten to the power of a million. This number is called millionplex, or maximusmillion. In my very early days of being interested in large numbers (back in February of 2014) I tried to print out all zeroes of this number, not knowing that it would take 287 pages, and a lot of ink. This is the boundary between class 2 and class 3 numbers.
2.331504399... x 101,656,520
ee^e^e. The integer part is a 1656521-digit number beginning with 2331504399007195462289689911012137666332017428..., and ending with ...4009522025973862423782579139884667434294745087021, while the fractional part begins with .2212029997921176538924919342159917956853263194935148261438976714588239125037479438021479494946707473....
6.01452073... x 1015,151,335
8^^3. The last 10 digits are ...5421126656.
5.81887266... x 1017,425,169
(2013-2015 Mersenne prime record)
The largest known prime number at the time I first became interested in large numbers. The last 9 digits are ...724285951.
3.00376418... x 1022,338,618
(2016 Mersenne prime record)
The largest known prime number at the time this website was created. The last 4 digits are ...6351.
1.48894445... x 1024,862,047
(2018-2024 Mersenne prime record)
2^82,589,933 - 1. The largest known prime number as of 2023. The last 4 digits are ...2591.
8.81694327... x 1041,024,319
2^136,279,841 - 1. The largest known prime number as of October 2024. It can be shown that there are infinitely many primes, so this is certainly not the largest prime number. However, as the numbers get larger, it becomes more difficult to test if the number is prime.
1.175369... x 1041,077,011
The fuganine. The last 3 digits are ...209.
2.581174791713197181... x 1043,046,712
r(3, 18) using the reptend function. Can also be expressed as r(9, 9). The last 6 digits are ...819591.
10100,000,000
The googolbong, or alternatively googolmine.
6.89508080309... x 10121,210,694
f3(3) in the fast-growing hierarchy. Can also be expressed as fω(3). It contains over 121 million digits, making it larger than a googolbong. It begins with 6895080803092620165736389959..., and ends with ...928197722374144.
7.95231787455... x 10208,987,639
The billionth Fibonacci number. It starts with 795231787455468346782938519..., and ends with ...981560546875. It has been called fibonagygas by SuperJedi224.
4.612976... x 10301,029,995
Billionth power of 2.
4.281247... x 10369,693,099
99^9. Can also be expressed as 9387,420,489, 9^^3, or 3774,840,978. The last 10 digits are ...2627177289.
8.808065258... x 10646,456,992
M2147483647. It is one of the largest Mersenne numbers ever tested using the Lucas-Lehmer test, and was found to be composite. It starts with 880806525841981676603746574..., and ends with ...72323327.
101,000,000,000
A fugaten, billionplex, or maximusbillion.
4.4368382409... x 101,140,763,800
23,789,535,319. The last 33 digits are ...468088628828226888000862880268288. All of the last 33 digits are even, as well as 4 of the first 5 digits.
3.103280543... x 101,292,913,986
2^(2^32), the 32nd double exponential of 2, and the 5th triple exponential of 2. It starts with 31032805438632861402998911558..., and ends with ...464691982336.
2.198197017... x 101,663,618,948
33^20. The value of the tiny tritri (3 vvv 3 in down-arrow notation). The last 6 digits are ...704003.
9.630350133... x 102,585,827,972
22^33. Can also be expressed as 44^4^2. Also, the value of the googolpleiv, and the largest googolple- number that it is even feasible to compute the complete decimal expansion of (the next has over 200 quadrillion digits).
103,000,000,003
A nanillion, the billionth -illion. The name looks like that of a small number, but it is actually so large that storing all its zeroes would take a few gigabytes of space.
4.36326863455... x 103,010,299,956
210¹⁰. It starts with 43632686345562428988582910876713..., and ends with ...374549681787109376. A run of 5 consecutive zeroes appears 224 digits into its decimal expansion.
1.57262209439... x 104,771,212,547
310¹⁰. It has about 4.77 billion digits, and it begins with 15726220943978623535660666662765, and ends with ...63228442786552200000000001.
1010,000,000,000
10^^3, a trialogue.
3.70110361... x 10297,121,486,764
11^^3. The last 4 digits are ...6611.
1.31137265... x 10847,288,609,430
(10^847288609443 - 1)/7625597484987. Can be expressed as r(3, 27) using the reptend function. Its decimal expansion is: 13113726523970925.........159918811111111111124224837635082036.........271029922222222222235335948746193147.........382141033333333333346447059857304258.........49325214444444444445755817096841.........60436325555555555556866928207952.........71547436666666666667978039319063.........82658547777777777779089150430174......0488077
1.2580142906... x 103,638,334,640,024
3^(3^(3^3)). Can also be expressed as 37,625,597,484,987, 33^27, or 3^^4. It starts with 1258014290627491317... and ends with ...776100739387. This may in fact be the last entry whose complete decimal expansion can possibly be computed.
4.969981598... x 109,622,088,391,634
12^^3. The last 3 digits are ...016.
5.95311951612318355925717768203975499... x 10208,309,294,085,508,228
5^5^5^2.
1.322449... x 1022,212,093,154,093,428,529
(2^^3)^^3. Can also be expressed as 22^66.
279,641,170,620,168,673,833 ≈ 5.076025219... x 1023,974,381,246,463,762,439
This power of 2 has the same first 19 digits (and the same number of digits) as 350,247,984,153,525,417,450, the next entry. It starts with 5076025219062843177372568120346456..., and ends with ...8587147886872589316067950592. Below are more digits of this number.
5076025219062843177372568120346456935927492816254654790984064653519938602128051975679885879975580541765574009637650907195596863497405792871315669251518673955865859512297940530749576085592457044498319667847360873771617172575569546181956948620082218406839134172134693415904915620058635829457233050366816215795145160356036600669738183752476667835026594201793412520565721382905112556892172505685126763004615266903861759421465538732484357686815457863036097023385824203326083136963426241031811……………………………………………………………………………………………………………………………………………………………………………………... 45075036760278939992059369280492581033539282763085950607445348716061055760775692009947406394696219320249399727251506224600004884515946140322274051574741421945480649779256858587147886872589316067950592
In this and the next entry, the few digits after the identical leading digits are in red to highlight the difference.
350,247,984,153,525,417,450 ≈ 5.076025219... x 1023,974,381,246,463,762,439
This power of 3 is almost exactly equal to 279,641,170,620,168,673,833. It starts with 5076025219062843177406..., and ends with ...9374942249. It is approximately 1.00000000000000000000672 times 279,641,170,620,168.673,833. Below are more digits of this number.
5076025219062843177406678353203677516510936923793095250465635995537448249966593136547270101630625423591430098651531611516103466445594026633219245202613498464614072402169354219580023311818978334013780534100551003014183407203012909503849649838923286250988840786548498574052336990423486584341459428948834186492934637453987073004396864203641527965474985189240010730722635747810694534949057140074651216553506718140181098034508072067759722909472555062941561978392340682747108103736383786459278……………………………………………………………………………………………………………………………………………………………………………………….9374942249
2.285367... x 10381,600,854,690,147,056,244,358,827,360
2^2^100, the googolplexibit. The last 10 digits of this number are ...3335387136.
5.454312... x 1051,217,599,719,369,681,875,006,054,625,051,616,349
The fifth term in the Catalan-Mersenne sequence. Being greater than 1010^37, this number is far too large to even compute its complete decimal expansion, let alone plug it into any currently known primality test. The last 10 digits are ...7493833727.
1.1899811685... x 10102,435,199,438,739,363,750,012,109,250,103,232,700
2^2^2^7. It starts with 118998116852966565343067... and ends with ...53903192091641511936.
The Googolplex Range (10^10^80 ~ 10^10^500)
2.5517890642... x 103010299956639811952137388947244930267681898814621085413104274611271081892744245094869272521181861720
The googolth power of 2. It begins with 2551789064200187957632800640620918466171..., and ends with ...3890995893380022607743740081787109376. I actually have 74,000 digits of this number on a wall somewhere in my house.
Back when I first got interested in large numbers, I used to do all my calculations on the Windows calculator. I erroneously obtained 1226771622962442794288155796038821007259530432563079... as the leading digits of this number when I first tried the calculation, but in early May of 2014, the result somehow changed to 3655853..., and I discovered that the Windows calculator was only accurate to about 38 digits (128 bits) with logarithms.
1.2724681704... x 104771212547196624372950279032551153092001288641906958648298656403052291527836611230429683556476163015
Googolth power of 3. The last digits are ...65522 followed by 100 zeros, and then a 1.
3.9188192081... x 106989700043360188047862611052755069732318101185378914586895725388728918107255754905130727478818138279
Googolth power of 5. Multiplying this number by the entry before the last results in a googolplex.
1010^100
A googolplex. Can also be expressed as 10^10^10^2. Along with the googol, it is one of the two quintessential large numbers. The most common description of the googolplex's size is that it would not be possible to write out all the zeros even if a digit could be written on a single atom.
Some factors of numbers just above googolplex have been found, such as:
googolplex + 1 = 316912650057057350374175801344000001 x 155409907106060194289411023528840396801 x 1467607904432329964944690923937202176001 x 11438565962996913740067907829760000000001 x 495176015714152109959649689600000000000001 x 7399415202816574979127045311692800000000001 x 9823157208340761024963422324575436800000001 x 153011449181500580269468675253...004467201
googolplex + 2 = 2 x 3 x 166666666666666666666666666666...666666666666666666666666666667 (10100 digits in the final factor)
googolplex + 3 = 7 x 1429 x 999700089973008097570728781365...8916325102469259222233330001 (10100 - 4 digits in the final factor)
googolplex + 4 = 22 x 1129 x 1181 x 18917 x 54917 x 14950993 x 2936848501 x 63822551333 x ...
googolplex + 5 = 3 x 5 x 29 x 666666667 x 344827...2069
10^10^100 + 37 is the first integer after 10^10^100 with no known prime factors. It could plausibly be the first prime greater than googolplex, although we may never know for sure. In fact, for n = 37, 111, 133, 183, 187, 193, 331, 499, 511, and 519, no factors of 10^10^100 + n are known.
1.0016338457... x 1010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
320959032742893846042965675220214012506075180067979301169235453386341774775719406287167658023089812370, the first power of 3 that is greater than a googolplex. It is very close to a googolplex in terms of ratio (in fact it is less than 1.002 times a googolplex). It starts with 1001633845720065037245058736407..., and ends with ...5287979849.
1.0023777406... x 1010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
233,219,280,948,873,623,478,703,194,294,893,901,758,648,313,930,245,806,120,547,563,958,159,347,766,086,252,158,501,397,433,593,701,551. It is the first power of 2 to be greater than a googolplex. Coincidentally, it is very close to a googolplex (in fact even closer in terms of ratio than 1024 is to 1000) It starts with 100237774068258191291356652609799417599067..., and it ends with ...215599182339992927666157787971954826805248. More digits are given below.
100237774068258191291356652609799417599067343177599679075853090406145885491297965766192391921808372207511666330351479842825690694045923065369420716156150106516721534771683438379710931765831859029500096278333967134504248458798713324431058768246620528030281025712858245475129072285125516670526408042732689668962555802951707932337674892866805183099975191984453558986140352179091036611149246971005741711...215599182339992927666157787971954826805248
7.0842519670... x 1015684240429131529254685698284890751184639406145730291592802676915731672495230992603635422093849214947
The reptend in the reciprocal of 3^212. Can be expressed as r(3, 212) using the reptend function. It is the first value of r(3, n) to be greater than a googolplex. It starts with 70842519670086169864263801438..., and ends with ...5839. About 3210 digits in to this number, we find these digits: ...6950111111111111...*101 1s total*...1111111118195363078119....
1.6294043324... x 10995657055180967481723488710810833949177056029941963334338855462168341353507911292252707750506615682567
The factorial of a googol, sometimes referred to as the googolbang. It starts with 162940433245933737..., and ends with ...5616 followed by exactly 2.5*1099 - 18 zeroes.
2.4759123324... x 102929392929325571200070163461348562945302629498978182062432072821815998238017214192638690235643150485962835182238406135226103499082417
The triangrolplex. It is the first iterated triangle of 2 to be greater than 10 to the power of triangrol, and it has about 2.929*10^132 digits beginning with 2475912332475733472364471024200423..., and ending with ...358932426146.
2.3610226714... x 108072304726028225379382630397085399030071367921738743031867082828418414481568309149198911814701229483451981557574771156496457238535299087481244990261351116
4^4^4^4. Can also be expressed as 4^4^256, 2^2^513, 4^^4, or 4^^^2. Bowers used to call this number tritet, but he later reassigned that name to the much larger 4^^^^4 (seen in part 3), hence the name Tritet Jr.
1010^303
An ecetonplex.
102.88143726501021051... x 10^436
295 719 274 042 928 204 424 865 040 058 775 542 505 814 054 438 541 885 854 149 030 735 229 109 523 951 584 103 470 215 627 747 553 797 463 635 129 121 836 969 199 786 005 635 947 291 219 432 249 974 804 994 912 958 522 358 749 039 882 132 482 089 698 627 890 927 242 238 394 036 253 560 129 178 156 977 985 035 837 611 338 125 082 186 620 901 965 139 876 889 799 294 204 083 600 450 928 306 589 731 842 380 857 398 374 764 175 466 159 268 112 616 959 965 220 874 514 966 744 994 952 198 799 891 188 036 626 702 635 888 708 426 354 717 521 502 687 896 981 315 387 158 640 463 040 000, (2 to the power of the weak factorial of 1000) and thus the first number that is a square, cube, 4th power, 5th power, ..., 998th power, 999th power, and 1000th power. It starts with 11765156730407309953860743389954009625..., and ends with ...5509376.
3.9098490222... x 101124021466074751860097567522104789648012545442387518261576295420518517444766080791595055342613832148848657928846792570107753324167422010021177933700772606989124114395556249
831380979217553830172695027125136140707494294575475485321118531096366377975795248722471714194063487219461564568491620652987627661309480232956516340085351404053765203720536942043185
5146383193275981445894731731211119067826441631620760954270094664304695825570332511004312335248637332796979930683278729227794366058973791
2^3^4^5. This is an example of a number that can be expressed using power towers. It has more than 1.12*10488 digits beginning with 390984902223805103367261..., and ending with ...3472100352. It is much larger than 5^4^3^2 which has "just" 183,231 digits.
The Triple Exponential Range (10^10^500 ~ 10^10^10^80)
~ 101.992373902852*10^619
The second step in the calculation of the Mega. This number begins with 39844342006... and ends with ...365056. Can be expressed as 2vvv5.
1010^1000
~ 101.33574*10^2184
55^5^5. Can also be expressed as 55^3125 or 5^^4. It starts with 1111028808179974... and ends with ...368408203125.
1.1012... x 101.1108... x10^2995
323281636769528800926351835023715983973984323619326165910831413485929742700614215858942141292106552658655336465357914729285203965080715619199116722509946605105626673348798836006162294182458797474912197648530006955831576558130503183566407157106681376566223204801235020125399185687545703740505109962601951819661206114099497774415669249849517161138917502311677484261152258180196442417263225035593038585881444310942065035095950968920888389323498161935201957798922364631858060372284385450391159744978925581552135811733071466716275536403692138744273025655311079042801587771071317707818903385967587979484369185094844251637825100180602091701300876876190228712613086437184900891973008415413477696907113884570850828598860696626410481432832844094100826116232464208915607276696040687112832527101783824480669487635858647253383141631348791228260728473906203725598228752389342927138278256534360590147021443638153883341336753743557373740258664286769593494932066218257550633397824448019376123474957267951100839969601433169299011802011353423919188601748382783035482235824456588469271162860703563827825008650136982644347755800437593829155230334977038413602212482422463082770749404366756571246832044509274708873551740261609250013164948050664827712410682109581186226279073091600705128891179623377611491193784719075593155134132119861544862985298953157046231119522631684692927840673684947765672758179718968195051448247021997594897806066825356698023148924431034439929167486436751376851275352433970244209116321685994874937454240000970260852611972489931273452282717090545149603043675870441461036998276359955007513619787255451780489258954265537968233037891487070908863055478972572155885891645274813928635609562785170231395436547214234661500453445623786721029033022048541732944548871220992681820063964305385904603945604977842198581605651064946875779905090889766773832652744222938527719657149024753614748515839492031568782193565415664874200229968066648896335517186105578256402313241340793141213794104216695907548602642379918936430864016649088748010144419406946003624367011037506878788757303930909519203355274584690593124735832595663826689493522300529514552691741876929779941519694758215851991668880927292010743110148171242562857668987845128822912305866712251501413711230794404236391257037956703998180856038614384774057293203055643604999066282108259591994285239555727967337561031646570430581567298707606370652940711613268758400882221281054963146345346057708680256470043815221248551070611875638429848732503207978402391534054221372415220031260793282280644916666252483076216355242870777936484322692691549040582101278345987944082069717503507453838119958141448884209889781617662644198843131526286262397115741973216919572875864790560514151386183619100907525011160547039478029143804667958049904149586286817594229383815283374141230187361581095697722247182288230817929105078090385316593009410672378202095683482818921143088889368689129227674208706841139417708342562906431362802786311036654466474123009080163880092407685548424371828934100. Its leading digits are 110128396785490937431723239464422714....
The digits of this number end with a sort of countdown pattern: ...028027026025024023022021020019018017016015014013012011010009008007006005004003002001. The pattern occurs starting at the 2997th last digit. Indeed, multiplying this number by 998001 gives a number that ends with 2996 zeroes followed by a 1.
~ 10^(9*10^4815)
2^2^16000. This number has something cursed in its first digits: 9221944678184914343981123467894434901218173123046909204778796241870670206677654750679179975...658443227136 (notice how it misses the 5?)
~ 102.413825645*10^15,937
9 * 87 * 65*4^(3*(2^1)))) This number begins with 6613158771793989045471703473..., and ends with ...852084414770288001024.
~ 106.031226*10^19,727
2^^6. Can also be expressed as 2^2^2^2^4, 2^2^2^16, 2^2^65536. It begins with 2120038728808211984885164691662274630835654230675372483625951752354414565561161..., and ends with ...3010305614986891826277507437428736. Notable for being the first power tower of 2s greater than googolplex.
~ 102.06917*10^36,305
6^^4. Can also be expressed as 66^46656. The decimal expansion of this number starts with 4446235190... and ends with ...0138438656.
1010^100,000
A googolplexigong.
~ 109*10^125,073
23^4^3^2. An example of a number that can be expressed with a 5-height power tower. This number begins with 20881306227627455814962154903166664113427... and ends with ...805692076405844859168963428352.
~ 104.829*10^183,230
Exponential factorial of 6. This number begins with 110356... and ends with ...22607743740081787109376. More digits are given below.
1103560225917696632179145334475344911419051187213486921746877175936136651431714552864199276654776541...042803106285328198624380944537003185235736096046992680891830197061490109937833490419136188999442576576769103890995893380022607743740081787109376
~ 103.1*10^695,974
7^^4. Can also be expressed as 77^823543. This number begins with 7833005237480055565403854094754653082919... and ends with ...8511366058254036038182879357182733172343. Power towers of 7s actually have the cool property that each time you add a 7 to the tower, another two last digits become constant, not just one (this number has 6 convergent terminating digits).
~1010^1,011,229
2^4^6^8. The first and last digits are 91232625227963370860086......795948302336.
~105.4*10^15,151,335
8^^4. Can also be expressed as 88^16,777,216, or 23*250331648. This number begins with 64740329646697067997386625179... and ends with ...887920249826536946437619449856.
~ 1010^20,538,505
33^3^2^2^2. This number begins with 145717531... and ends with ...8027.
~ 101.041392685158*10^43,046,721
1110^9^8. The decimal expansion of this number starts 2373570079623504840997604286196... and ends ...8446 followed by 43,046,721 zeroes and then a 1. The first 6 digits are all prime.
1010^100,000,000
A googolplexibong.
~104.085*10^369,693,099
9^^4. The largest number that can be made with 4 digits and the basic mathematical operators. This number begins with 21419832947968056113333.... and ends with ...401045865289.
1010^1,000,000,000
A billiduplexion.
~ 109.3418*10^1,292,913,985
2^2^2^2^5. The largest number I have directly calculated the leading digits of. It starts with 315921269337233843004184822... and ends with ...78717272631317364736. I'm not even 100% sure if the result for this number's first digits is correct, as Mathematica may not be reliable to that many digits.
~ 105.78*10^2,585,827,972
44^4^4^2. Can also be expressed as 2^2^8589934593.
~ 108.038723426*10^3,327,237,905
3vvv4, or 33^6973568822. The last 4 digits are ...5683. Computing the first digits of this number is probably still possible.
1010^10,000,000,000
10^^4, a tetralogue. Notable for being about as far as we can currently go in calculating the leading digits of large powers (however, with more dedicated resources, the limit could be extended a bit further, perhaps putting 3^^5's first digits within reach, although no one has tried to put more computational effort into this as far as I know).
~ 1010^297,121,486,764
11^^4. The last 6 digits are ...066611.
>> PART 3