# Large numbers

 In one of the homeworks, you had to estimate how large eee10 is. We can compute with the calculator: ```e10 ~ 22026 ee10 ~ 109566 eee10 ≤ 10109566 and because 10x ≤ ex/3 one also has 10ee10 ≥ e109565 ``` So one can say that the number has between 109565 and 109566 digits. One could not even write down a number with 1090 digits because there are less elementary particles in the universe than that. The Eddington number is the number of protons in the observable universe. It is believed to be less than 1080. These numbers are astronomical, in the proper sense of the word. It is interesting that Archimedes (whose 2300th birthday we celebrate) has estimated the number of sand grains in the universe. The Sand reconer got about this number as an upper bound. He estimated that 8 * 1063 grains of sand would be needed to fill the universe. source.

## The graph of eee10

We can plot the graph from 0 to 1, but already from 0 to 2, Mathematica refuses to plot it. The online Mathematica version is more forgiving. Here is the graph in Wolfram Alpha.

## The integer digits of ee10

This can still be written down by typing "Floor[Exp[Exp[10]]]".
```
9387512218583594745539690918995541531009584046561616020605905299722770917
56643174045789642161542666221186248885109035770936484011458213525445995968952
70247574596016987708892173045619561154773552332646127879507727370720244156666
89717132346997543823972950588115027099471233278301685635826041260906156684599
60118464370026156340540512782031536399864955827898930228192861200154758465191
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61090641206302820519934880060121043197303921265539759574717306841145256598423
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21057029735207835371714634024819324045619273082891703376077311407879899701527
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25547177614055902219584094785214988781505088337257634920635362489979681584387
38932912323646807855228390505676831454576274354699273308660128568986008196832
66231194501080400462232955696145411127311954858278375762265340460852921456227
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40380828942703824737142205136944916615749488535096060173706149598542977566654
31994228440128874702953676303844744807656285831212984360940109051686265474987
86028591676495057944226320102114714256705877060558883127494842820187065077216
78332009781720649615433356208013886494947484990883131731493373260782697544005
85008742065093772217950386248701627128187737252584447050153677911791374061868
38999270660507990684216945707850002712159832205098105216679507189826185444478
85575951463619720926097358675086304302950713329793846219501530743707024059178
06452917124291184704293715612975429878700283114360378911152497575451374195073
42937124605548511058901401923472996435046697440475199665786644455962377624075
96543412794915218354390930683133468746288618050545813014681423560622989350409
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41333244710952855918489229283602220184033030300243697418918801752874208730003
46929873192869054502725378655908732398499773165181719523233495110938008695233
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02652687716829338746670971107634456331013950249009862946198731855543944052270
46060026336192154911469261083730629673759490986657831272704608083962361164417
02899512086846411923412208447340672713452206818245168896031096307620250340268
28407036053840225937209285485788708800932116965970491010037087592947667273329
4217057199083822060121

```