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.
100,000,000,000,000,000
1,000,000,000,000,000,000
1,111,111,111,111,111,111
The next repunit prime after 11.
2,005,829,741,820,646,245
The largest known integer n such that the decimal expansion of 3^n starts with n.
2,305,843,009,213,693,951
2,360,165,090,985,064,742
The largest known integer such that the decimal expansion of 2^n starts with n.
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 (septillionth) 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
381. Can also be expressed as 2727, 33^4.
323,257,909,929,174,534,292,273,980,721,360,271,853,387
387, starts in 3 and ends in 87.
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
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.
A googol is also just above the maximum value for the trig functions in the Windows calculator; attempting to calculate any trig function with a larger number there results in the 'Invalid input' error.
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
~ 1.34*10^154
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
~ 4.5724737*10^239
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
~ 1.797693*10^308
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
~ 7.886579*10^374
The factorial of 200. This number is called the faxul.
1.0000009377765355041159521080236291875... * 10^431
7^510, very slightly larger than 10^431.
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
~1.5241579*10^725
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
~ 1.0511*10^1000
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
~ 2.85582*10^1,385
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 divisible by 8, making this number divisible by 73 and 137 as well. 8 is 2 x 4 and so 101,440 - 1 is also divisible by 101.
As a result, it is possible to find many prime 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, 271, ....
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
~ 3.364*10^2,089
10,000th term in the Fibonacci sequence.
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
~ 1.9110126*10^2,184
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.
1693508780843028671103659672.........67278023336551
~ 1.6935087808430286711... x 106,556
(10^6561 - 1)/59049, or r(3, 10) using the reptend function.
15054164145220926243143.........686617859227
1.5054164145... x 109,391
3^3^3^2. It is also approximated to 4 digits of accuracy by the number of digits in 3210^9,391.
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 larger than this there results in a display of "Overflow" (or "Invalid input" if you attempt to calculate an exponent larger than e^100,000, seen a little later on in this list).
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)
20035299304068464649790723515602............587895905719156736
~ 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. The first non-trivial number of the form x^x^x^x^x, and the only one whose complete decimal expansion can be calculated. See the Hyperoperational Numbers page for all the digits.
This is also the record distance anyone has teleported in Minecraft using one of the 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.
2.8066633604261231793183... x 1043,429
e^100,000. This was the largest exponential result that could be calculated on the Windows XP calculator, and this limit still exists in a form in the present Windows calculator. Attempting to calculate any exponential expression that would evaluate to a number larger than this on the Windows calculator results in an "Invalid input" error (see also 10^10,000).
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....
6,014,520,73.........,555,421,126,656
6.01452073... x 1015,151,335
8^^3.
581,887,266,...,724,285,951
~ 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.
300376418.........6351
~ 3.00376418... x 1022,338,618
(2016 Mersenne prime record)
The largest known prime number at the time this website was created.
148894445.........2591
~ 1.48894445... x 1024,862,047
(2018-2024 Mersenne prime record)
282,589,933 - 1. The largest known prime number as of 2023.
881694327.........551
~ 8.81694327... x 1041,024,319
2136,279,841 - 1. The largest known prime number as of this writing. It was found to be prime in 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 a given number is prime.
1.175369... x 1041,077,011
The fuganine. The last 3 digits are ...209.
2581174791713197181.........486819591
2.581174791713197181... x 1043,046,712
r(3, 18) using the reptend function. Can also be expressed as r(9, 9).
10100,000,000
A googolbong, or alternatively googolmine.
6895080803092620165736389959.........928197722374144
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.
795231787455468346782938519.........981560546875
7.95231787455... x 10208,987,639
The billionth Fibonacci number. SuperJedi224 coined the name fibonagygas for this number.
4.612976... x 10301,029,995
Billionth power of 2.
4281247......2627177289
~ 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.
880806525841981676603746574.........72323327
~ 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.
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.
310,328,054,386,328,614,029,989,115,58.........,464,691,982,336
~ 3.103280543... x 101,292,913,986
2^(2^32), the 32nd double exponential of 2, and the 5th triple exponential of 2.
2198197017.........704003
~ 2.198197017... x 101,663,618,948
33^20. The value of the tiny tritri (3 vvv 3 in down-arrow notation).
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 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.
43632686345562428988582910876713............374549681787109376
~ 4.36326863455... x 103,010,299,956
210¹⁰. A run of 5 consecutive zeroes appears 224 digits into its decimal expansion.
15726220943978623535660666662765.........63228442786552200000000001
~ 1.57262209439... x 104,771,212,547
310¹⁰.
>> PART 3