bigger numbers!

on the nomenclature page, I only list numbers up to binilexian. naturally, that’s not the limit of how big -exian numbers can get. the -exian series is designed to be infinitely extendable. since a decent amount of my traffic comes from the Googology Wiki (hello!), I figured I might as well talk about how this system can be used to make some real googologisms. (like always, all numbers here are in seximal unless otherwise specified!)

“practically sized” powers of six

one
1

the loneliest number, one is a fundamental part of counting itself.

six
10, DEC6

six is, unsurprisingly, the basis of the base six numbering system. it’s got lots of fun properties! it’s a perfect number, a superior highly composite number, and it’s the only number where a 2D regular shape and a 3D regular shape with that many sides will tile space! what a great number.

nif
100, DEC36

the word nif comes from the Ndom language, which is spoken by about a thousand people on Yos Sudarso Island in Indonesia. languages that natively use seximal are rather rare, and the ones with the best-documented numbering systems are all spoken in the same part of the world. of all of these languages, Ndom’s numbering system is the most well documented, which is why the Misalian seximal system uses their word for nif.

other languages that use seximal natively include the Yam languages. speakers of Yam languages use seximal so they can count how many yams they have. the most well documented numbering system of these is that of Kómnzo, spoken in the village of Rouku in Papua New Guinea. since this system is used for counting food, there are words for large powers of six. Kómnzo speakers call nif “féta” or “fta”.

six nif / tarumba
1000, DEC216

even though six nif is indeed written with three zeros, it wouldn’t be fair to call it the seximal equivalent of one thousand. six is much smaller than ten, so 1000 is closer to DEC100 than it is to DEC1000. Kómnzo speakers call six nif “tarumba” or “taruba”. if you eat a yam every day, tarumba yams is enough to last you a bit under a week into August.

unexian
1 0000, DEC1,296

unexian is the actual seximal equivalent of one thousand. I came up with the -exian suffix as a thing that would sound kinda like -illion and also sound kinda like it means “six”. the direct inspiration was the number “googolplexian”, which suggests a fun puzzle of “how much is googolpl equal to?”. there’s a one in unexian chance of rolling a Yahtzee. Kómnzo speakers call unexian “ntamno” or “damno”. this is the recommended amount of yams to feed one family for a year.

six unexian
10 0000, DEC7,776

six unexian is the seximal equivalent of a myriad. there’s a one in six unexian chance of rolling all sixes in Yahtzee. Kómnzo speakers call it the very cool sounding name “wärämäkä”. six unexian yams will feed thirsy three (DEC21) people for a year.

nif unexian
100 0000, DEC46,656

nif unexian is a significant number in seximal because it’s six raised to the sixth power. it’s almost equal to the decimal number fifty thousand. Kómnzo speakers call it “wi”, though according to Christian Doehler, nobody in Rouku remembers a time when they actually had that many yams (as of July 2016). nif unexian yams will feed 332 (DEC128) people for a year.

six nif unexian / tarumba unexian
1000 0000, DEC279,936

six nif unexian is the seximal equivalent of a lakh. this many yams will feed 3315 (DEC767) people for a year, around the population of the Vatican.

biexian
1 0000 0000, DEC1,679,616

biexian is the seximal equivalent of a million. this many yams will feed 3 3150 (DEC4,602) people for a year, around the population of Dunn County, North Dakota.

six biexian
10 0000 0000, DEC10,077,696

six biexian is the seximal equivalent of a crore. this many yams will feed 33 1454 (DEC27,610) people for a year, around the population of Elmira, New York.

nif biexian
100 0000 0000, DEC60,466,176

nif biexian is between a crore and a myllion. this many yams will feed 331 4541 (DEC165,661) people for a year, around the population of Guam.

six nif biexian / tarumba biexian
1000 0000 0000, DEC362,797,056

six nif biexian is between a myllion and a billion. this many yams will feed 3314 5405 (DEC993,965) people for a year, around the population of Port-au-Prince.

triexian
1 0000 0000 0000, DEC2,176,782,336

triexian is the seximal equivalent of a billion. this many yams will feed 3 3145 4043 (DEC5,963,787) people for a year, around the population of Maryland. the current world population is about three and a half triexian.

six triexian
10 0000 0000 0000, DEC13,060,694,016

six triexian yams will feed 33 1454 0431 (DEC35,782,723) people for a year, around the population of Morocco.

nif triexian
100 0000 0000 0000, DEC78,364,164,096

nif triexian yams will feed 331 4540 4312 (DEC214,696,340) people for a year, around the population of Brazil.

six nif triexian / tarumba triexian
1000 0000 0000 0000, DEC470,184,984,576

six nif triexian yams will feed 3314 5404 3120 (DEC1,288,178,040) people for a year, around the population of China.

quadexian
1 0000 0000 0000 0000, DEC2,821,109,907,456

quadexian is the seximal equivalent of a trillion. this many yams is more than enough to feed everyone in the world for a year. the US national debt is about seven and a half quadexian dollars.

the -exian series

for everyday yam counting purposes, you can generally expect that you’ll never need any numbers larger than quadexian. however, not everyone exclusively deals with practically sized numbers. larger numbers in the -exian series can be used for counting more abundant things.

pentexian
1 0000 0000 0000 0000 0000
DEC3,656,158,440,062,976
about four quadrillion
the largest -exian number with a single “digit” name

unnilexian
1 0000 0000 0000 0000 0000 0000
DEC4,738,381,338,321,616,896
about five quintillion
notable for being the sixth -exian

ununexian
1 0000 0000 0000 0000 0000 0000 0000
DEC6,140,942,214,464,815,497,216
about six sextillion
there are about four nif ununexian stars in the observable universe

umbiexian
1 0000 0000 0000 0000 0000 0000 0000 0000
DEC7,958,661,109,946,400,884,391,936
about eight septillion

untriexian
1 0000 0000 0000 0000 0000 0000 0000 0000 0000
DEC10,314,424,798,490,535,546,171,949,056
about ten octillion
the seximal equivalent of googol; 1 followed by 100 zeros

unquadexian
1 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000
DEC13,367,494,538,843,734,067,838,845,976,576
about thirteen nonillion

umpentexian
1 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000
DEC17,324,272,922,341,479,351,919,144,385,642,496
about seventeen decillion

binilexian
1 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000
DEC22,452,257,707,354,557,240,087,211,123,792,674,816
about twenty two undecillion
the largest -exian number defined on the nomenclature page

biunexian
DEC29,098,125,988,731,506,183,153,025,616,435,306,561,536
about twenty nine duodecillion

bibiexian
DEC37,711,171,281,396,032,013,366,321,198,900,157,303,750,656
about thirty eight tredecillion

bitriexian
DEC48,873,677,980,689,257,489,322,752,273,774,603,865,660,850,176
about forty nine quattuordecillion

biquadexian
DEC63,340,286,662,973,277,706,162,286,946,811,886,609,896,461,828,096
about sixty three quindecillion

bipentexian
DEC82,089,011,515,213,367,907,186,323,883,068,205,046,425,814,529,212,416
about eighty two sedecillion

trinilexian
DEC106,387,358,923,716,524,807,713,475,752,456,393,740,167,855,629,859,291,136
about one hundred six septendecillion

quadanilexian
DEC504,103,876,157,462,118,901,767,181,449,118,688,686,067,677,834,070,116,931,382,690,099,920,633,856
about five hundred four trevigintillion

pentanilexian
DEC2,388,636,399,360,109,977,557,402,041,718,133,080,829,429,159,844,757,507,642,063,199,359,529,632,522,467,783,435,119,230,976
about two trigintillion

unnilnilexian
DEC11,318,270,138,763,686,083,720,407,615,440,940,552,884,061,160,572,696,063,187,703,399,142,305,408,416,300,319,167,091,236,629,993,190,344,408,170,496
about eleven sestrigintillion
notable for being the nifth -exian

binilnilexian
about one hundred twenty eight treseptuagintillion

trinilnilexian
about one undecicentillion

quadanilnilexian
about sixteen octoquadragintacentillion

pentanilnilexian
about one hundred eighty five quinquoctogintacentillion

unnilnilnilexian
about two tresvigintiducentillion
notable for being the six nifth -exian

unnilnilnilnilexian
about eighty six tresquadragintatrecentimillinillion
notable for being the unexianth -exian

can we go even bigger?

while the -exian series is fine and all, it’s not exactly the fastest growing number sequence. so, just for fun, here’s a completely different way of naming powers of six in the seximal system, based on Donald Knuth’s -yllion system. this is…

the -eciam series

it sounds kinda like -exian but it’s different! each number in the -eciam series is equal to the previous number squared.

six = 10
nif = 100
uneciam = unexian = 1 0000
bieciam = biexian = 1 0000 0000
uneciam bieciam = triexian = 1 0000 0000 0000
trieciam = quadexian = 1 0000 0000 0000 0000
uneciam trieciam = pentexian = 1 0000 0000 0000 0000 0000
bieciam trieciam = unnilexian = 1 0000 0000 0000 0000 0000 0000
uneciam bieciam trieciam = ununexian = 1 0000 0000 0000 0000 0000 0000 0000
quadeciam = umbiexian = 1 0000 0000 0000 0000 0000 0000 0000 0000
penteciam = biquadexian = 1 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000
unnileciam = pentabiexian = 1 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000
ununeciam = unquadaquadexian = 1 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000
umbieciam = tritribiexian = 1 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000
untrieciam = ununnilquadexian = 1 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000
unquadeciam = bibiunbiexian
umpenteciam = quadaquadabiquadexian
binileciam = untribipentabiexian
biuneciam = trinilpentaquadaquadexian
bibieciam = unnilunpentatribiexian
bitrieciam = biniltripentanilquadexian
biquadeciam = quadununquadumbiexian
bipenteciam = umbibitribibiquadexian
trinileciam = biquadapentanilquadapentabiexian
quadanileciam = quadapentapentaquadaquadaquadanilpentabiexian
pentanileciam = umbipentuntripentanilnilumbipentabiexian
unnilnileciam = bitriquadaquadumbipentabibitriquadaquadapentabiexian
unnilnilnileciam = 1210 4023 5035 5341 2122 2513 4151 0540 4231 5312 2335 2512 5405 4104 5340 3240 2010 1122 3512 4042 2452-exian

these are getting pretty big! just to make things a bit easier to say, let’s say that any repeated amount of nils can be replaced with number of nils represented in base six using the Germanic-based digits no, ain (or aim), twai, thri, fedru, and fimf(a), resulting in:

unnilnileciam → untwaieciam
unnilnilnileciam → unthrieciam

let’s say that this only applies for the -eciam series and not for the -exian series, since if you’re using numbers big enough that this makes a difference you’re probably going to prefer the faster growing -eciams anyway. okay, let’s get even bigger!

umfedrueciam (un-fedru-eciam) = 2⁵⁵⁵⁵-exian
umfimfeciam (un-fimf-eciam) = 2⁵ ⁵⁵⁵⁵-exian
unainnoeciam (un-ain-no-eciam) = 2⁵⁵ ⁵⁵⁵⁵-exian
unainaineciam (un-ain-ain-eciam) = 2⁵⁵⁵ ⁵⁵⁵⁵-exian
unaintwaieciam (un-ain-twai-eciam) = 2⁵⁵⁵⁵ ⁵⁵⁵⁵-exian
unainthrieciam (un-ain-tri-eciam) = 2⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵-exian
unaimfedrueciam (un-ain-fedru-eciam) = 2⁵⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵-exian
unaimfimfeciam (un-ain-fimf-eciam) = 2⁵⁵⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵-exian
untwainoeciam (un-twi-no-eciam) = 2⁵⁵⁵⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵-exian
unthrinoeciam (un-thri-no-eciam) = 2⁵⁵⁵⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵-exian
umfedrunoeciam (un-fedru-no-eciam) = 2⁵⁵⁵⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵-exian
umfimfanoeciam (un-fimf-no-eciam) = 2⁵⁵⁵⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵-exian
unainnonoeciam (un-ain-no-no-eciam) = 2⁵⁵⁵⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵ ⁵⁵⁵⁵-exian

okay, this is getting rather silly, but let’s go one level deeper. let’s say that any repeated amount of nos with the number of nos represented in base six using the Sanskrit-based digits shuny(a), ek(a), dvi, trey(a) (we already used tri), chatur, and panch(a), so “unainnonoeciam” can become “unaindvieciam”. we can continue this with unaintreyeciam, unainchatureciam, unaimpancheciam, unainekashunyeciam, and so on.

hey, what exactly does “unainekashunyeciam” mean anyway? well,

yes, we sure are getting well into the “far too big to be useful” category now I’d say. it’s only fitting to take this to its logical conclusion!

FIRST LAYER: main digits (Greek and Latin based): nil, un, bi, tri, quad(a), pent(a)
SECOND LAYER: repeated nils (Germanic based): no, ain, twai, thri, fedru, fimf(a)
THIRD LATER: repeated nos (Sanskrit based): shuny(a), ek(a), dvi, trey(a), chatur, panch(a)
FOURTH LAYER: repeated shunyas (Mandarin based): ling, yi, er, san, si, wu
FIFTH LAYER: repeated lings (Ndom based): mer, sas, thef, ithin, thonith, meregh(abo)
SIXTH LAYER: repeated mers (Kómnzo based): nibo, nabi, ed(a), eth(a), asar, tabru

this means we can introduce the massive numbers unainekayilingeciam, unainekayisasmereciam, unainekayisasnabiniboeciam, and even unainekayisasnabiniboniboeciam! real quick, how big is that last one?

that’s a bit hard to see so here it is again but bigger:

that’s probably big enough for now, I’d say.

list of numbers named here

nif
tarumba
unexian / uneciam
biexian / bieciam
triexian
quadexian / trieciam
pentexian
unnilexian
umbiexian / quadeciam
untriexian
unquadexian
umpentexian
binilexian
biunexian
bibiexian
bitriexian
biquadexian / penteciam
bipentexian
trinilexian
quadanilexian
pentanilexian
pentabiexian / unnileciam
unnilnilexian
unquadaquadexian / ununeciam
binilnilexian
trinilnilexian
tritribiexian / umbieciam
quadanilnilexian
pentanilnilexian
unnilnilnilexian
ununnilquadexian / untrieciam
unquadeciam
umpenteciam
binileciam
biuneciam
bibieciam
bitrieciam
biquadeciam
bipenteciam
trinileciam
quadanileciam
pentanileciam
unnilnileciam / untwaieciam
unnilnilnileciam / unthrieciam
umfedrueciam
umfimfeciam
unainnoeciam
unainaineciam
unaintwaieciam
unainthrieciam
unaimfedrueciam
unaimfimfeciam
untwainoeciam
unthrinoeciam
umfedrunoeciam
umfimfanoeciam
unainnonoeciam / unaindvieciam
unaintreyeciam
unainchatureciam
unaimpancheciam
unainekashunyeciam
unainekayilingeciam
unainekayisasmereciam
unainekayisasnabiniboeciam
unainekayisasnabiniboniboeciam