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This is a list to compare the values of factorials and ackermann numbers and such. For ackermann numbers>5, only those with an m>3 are shown. Powers of 10 are highlighted. Only natural numbers are shown. Above 1000, the only powers shown are powers of 10.

Basically, this is a condensed, specialized version of the one on the googology wiki.

1

  • 1 - Loneliest number
  • 2=2!=ack(0,1)=ack(1,0)
  • 3=ack(0,2)=ack(1,1)=TREE(2)
  • 4=22=ack(0,3)=ack(1,2)=g0=2→2→2→...
  • 5=ack(0,4)=ack(1,3)=ack(3,0) - Age of this site, in years.
  • 6=3! - Number of popes per square mile in Vatican City.
  • 7±2 - Number of objects able to be held in human working memory.
  • 8=23
  • 9=32 - Number of planets

10

  • 12 - Number of playable years in HOI III
  • 13=ack(3,1)=ack(4,0)
  • 15 - Number of playable years in HOI IV
  • 16=24
  • 20 - God's number (Maximum number of moves required to solve any Rubik's cube position)
  • 24=4!
  • 25=52
  • 27=33
  • 29=ack(3,2)
  • 32=25
  • 36=62
  • 49=72
  • 61=ack(3,3)
  • 64=26
  • 81=34

100

  • 100 - Number of playable years in Victoria II.
  • 108 - Classes of animal.
  • 120=5!
  • 121=112
  • 125=53=ack(3,4)
  • 128=27
  • 144=122
  • 147±17 - Number of phonemes in Taa.
  • 169=132
  • 193 - UN Member states.
  • 196=142
  • 206 - Number of sovereign states.
  • 212 - Number of cardinals.
  • 216=63
  • 225=152
  • 243=35
  • 247 - Smallest natural number without a Wikipedia article.
  • 253=ack(3,5)
  • 256=28
  • 289=172
  • 324=182
  • 342 - My Reddit link karma, as of 05 Jun 2016.
  • 343=73
  • 361=192
  • 377 - Number of playable years in EU4.
  • 400=202
  • 441=212
  • 484=222
  • 509=ack(3,6)
  • 512=29
  • 529=232
  • 536 - Years since the death of Rome (At Epirus).
  • 576=242
  • 625=54
  • 675 - Number of playable years in CK2.
  • 676=262
  • 720=6!=3!!
  • 729=36 - Last shown non-ten power>2
  • 784=282
  • 841=292
  • 900=302
  • 961=312 - Last shown square.

≥1,000

  • 1,023=ack(3,7)
  • 1,760 - Number of yards in a mile.
  • ~1,800 - Number of orders of animals (Personal calculation, rough estimate).
  • ~2,000 - Number of characters in shakespeare's plays (Personal calculation, VERY rough estimate).
  • 2,045=ack(3,8)
  • 2,768 - Years since the birth of Rome.
  • 3,308 - Number of known exoplanets. (As of 10 May 2016)
  • 4,093=ack(3,9)
  • 5,040=7!
  • 5,280 - Number of feet in a mile.
  • 6,013=1 m/s in imperial units (furlongs per fortnight), rounded.
  • 6,174=Kaprekar's constant
  • 8,189=ack(3,10)
  • 16,381=ack(3,11)
  • 18,201 - My Reddit comment karma, as of 05 Jun 2016.
  • ~31,000 - Number of families of animals (Personal calculation, rough estimate).
  • 32,765=ack(3,12)
  • 40,320=8!
  • 65,533=ack(3,13)=ack(4,1)=ack(5,0)
  • 65,536=2↑↑4=2↑↑↑3=216

≥100,000

  • ~180,000 - Number of aircraft in the world. Source
  • ~235,000 - Years since death of Y-chromosomal Adam.
  • 362,880=9!
  • ~500,000 - Number of headwords in the Academic Dictionary of Lithuanian.
  • ~520,000 - Number of animal genera (Personal calculation, rough estimate).
  • ~570,000 - Number of words in *War and Peace* (Varies by translation, so give or take 10K)
  • 1,000,000 - Million
  • 3,628,800=10!
  • 5,117,648 - Number of articles on Wikipedia as of 31 Mar 2016
  • ~6,800,000 - Number of characters in Zettels Traum, the longest novel in one volume.
  • ~8,700,000 - Number of species.
  • ~20,000,000 - People who died in the Great War.
  • 39,916,800=11!
  • ~56,800,000 - Population of the Roman Empire at its height.
  • ~69,930,000 - Number of dogs in the United States.
  • ~70,000,000 - People who died in WWII.
  • ~74,060,000 - Number of cats in the United States.
  • 299,792,458 = c in m/s
  • 322,369,319 - Population of the United States as of 2016
  • ~380,000,000 - Native English speakers
  • 479,001,600=12!
  • ~650,000,000 - Speakers of English
  • ~659,500,000 - Number of vehicles.

≥109

  • 109 - Billion
  • ~2.1*109 - 232
  • ~3*109 - Base pairs in the human genome.
  • ~3.4*109 - People who speak a descendant of PIE.
  • ~6.2*109=13!
  • ~7.3*109 - Population of Earth
  • ~9.0*109 - Coulomb's Constant (Rounded)
  • 1010=10↑↑2
  • ~1.07±.07*1010 - Number of people who have ever lived.
  • ~1.4*1010 - Age of the universe, in years.
  • ~4*1010 - Number of earthlike planets in the galaxy.
  • ~8.7*1010=14!
  • ~1.5*1011=1 AU in meters.
  • ~1.7*1011 - Number of galaxies in the universe.
  • ~2.5*1011 - Number of stars in the galaxy.
  • 1012 - Trillion.
  • ~3.04*1012 - Number of trees on Earth.
  • ~7.6*1012=3↑↑3=3↑↑↑2
  • ~3*1013 - Number of pages indexed by Google in 2014.
  • ~5.1*1014 - Area of Earth in m2, rounded.
  • ~3.6*1015 - Area of a Minecraft world in m2.
  • ~3.2*1017 - Number of ants.
  • ~9.2*1017 - Volume of a Minecraft world in m3.
  • ~1.8*1019=264
  • ~1.1*1021 - Volume of Earth in m3, rounded.
  • ~1022±2 - Grains of sand on earth.
  • ~3*1023 - Number of stars in the universe.
  • ~5*1023 - Number of exoplants in the universe. (Personal estimate)
  • ~6.0*1023 - Avogadro constant.
  • ~6.2*1023=4!!
  • ~6.0*1024 - Mass of Earth in kg, rounded.
  • ~1.9*1027 - Mass of Jupiter in kg, rounded.
  • ~1030 - Terran beings.
  • ~2.0*1030 - Mass of the sun in kg, rounded.
  • 1033 - Decillion
  • ~3.4*1038=2128
  • ~1042 - Mass of the galaxy in kg, rounded.

≥1050

  • ~1.3*1050 - Number of atoms on Earth.
  • ~1.2*1057 - Number of atoms in the solar system.
  • 1063 - Vigintillion
  • ~8.1*1067=52! - Number of arrangements of a deck of playing cards.
  • ~1068 - Number of atoms in our galaxy.
  • ~1.2*1077=2256
  • ~1080±2 - Number of atoms in the observable universe.
  • 10100 - Googol
  • 10140 - Asaṃkhyeya
  • 4↑↑3 ~ 10102.2
  • ~8*10184 - Volume of the universe in Planck volumes.
  • 5!! ~ 10102.3
  • ~6.4*10254 - Volume time of the universe in Planck units. Probably the largest number of use.
  • 10303 - Centillion
  • 3!!!=6!! ~ 10103.2
  • 7!! ~ 10104.2
  • 2↑↑5 ~ 10104.3
  • 8!! ~ 10105.2
  • ~10105.3 - Smallest solution to Archimedes' cattle problem
  • 7↑↑3 ~ 10105.8
  • 9!! ~ 10106.3
  • 257,885,161-1 - Largest known prime (2013-2016 Jan 6).
  • 8↑↑3 ~ 10107.2
  • 274,207,281-1 - Largest known prime (2016 Jan 6+).
  • 9↑↑3 ~ 10108.6

≥10↑↑3

  • 10↑↑3
  • 3↑↑4 ~ 1010101.1
  • 4!!! ~ 1010101.3
  • 1010100 - Googolplex
  • 4↑↑4 ~ 1010102.2
  • 5!!! ~ 1010102.3
  • 3!4 ~ 1010103.2
  • 2↑↑6 ~ 1010104.3
  • 7↑↑4 ~ 1010105.8
  • 8↑↑4 ~ 1010107.2
  • 9↑↑4 ~ 1010108.6
  • 10↑↑4
  • Skewes' Number (1st), rounded.
  • Skewes' Number (2nd), rounded.
  • 3!5 - May be more than 3↑↑5. Not sure.
  • 3↑↑5
  • 2↑↑7
  • 7↑↑5
  • 8↑↑5
  • 9↑↑5

≥10↑↑5

  • 10↑↑5
  • 3↑↑6
  • 2↑↑8
  • 7↑↑6
  • 8↑↑6
  • 9↑↑6
  • 10↑↑6
  • 3↑↑7
  • 2↑↑9
  • 7↑↑7
  • 8↑↑7
  • 9↑↑7
  • 10↑↑7
  • 3↑↑8
  • 2↑↑10
  • 7↑↑8
  • 8↑↑8
  • 9↑↑8
  • 10↑↑8
  • 3↑↑9
  • 2↑↑11
  • 7↑↑9
  • 8↑↑9
  • 9↑↑9
  • 10↑↑9

≥10↑↑10

  • 2→3→4=2↑↑↑4 - May be larger than 3↑↑↑3
  • 3↑↑↑3
  • 10↑↑↑3
  • 10↑↑↑10
  • 10↑↑↑10100
  • g1=3→3→4
  • 4→3→4
  • 10→3→4
  • 10→(10→100→3)→3
  • 4→4→3
  • 10→100→4
  • 10→(10→100→4)→4
  • 5→5→5
  • 10→100→5
  • 10→(10→100→5)→5
  • 10→100→6
  • 10→(10→100→6)→6
  • 7→7→7
  • 10→100→7
  • 10→(10→100→7)→7

≥10→10→10

  • 10→10→10
  • 10→10→100
  • 10→10→(10→10→100)
  • G=g64 - Graham's number
  • xkcd number - ack(G,G)
  • 10→10→100→2
  • TREE(3)
  • SSCG(3) - May be greater than the two below.
  • marxen.c
  • loader.c
  • Rayo's Number - Largest natural number with a Wikipedia entry.
  • BIG FOOT - Largest named number

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