# What is the largest possible number you can write using only 2 digits? **URL:** \ **Category:** Factual Questions\ **Created:** [August 19, 2000, 1:22pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961 "2000-08-19T13:22:18Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![MadHatter](https://avatars.discourse-cdn.com/v4/letter/m/f6c823/32.png) [@MadHatter](https://boards.straightdope.com/u/MadHatter)\ **Post date:** [August 19, 2000, 1:22pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/1 "2000-08-19T13:22:18Z")
This trivia question was thrown at me tonight, so I responded with the obvious remark of “99”. Wrong. I got this question in a trivia chat room, so the answer was never revealed. Does anyone here know the answer? ---
**Author:** ![Una\_Persson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/una_persson/32/346_2.png) [@Una\_Persson](https://boards.straightdope.com/u/Una_Persson)\ **Post date:** [August 19, 2000, 1:23pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/2 "2000-08-19T13:23:53Z")
FF? (Hexadecimal) ---
**Author:** ![GKittridge](https://avatars.discourse-cdn.com/v4/letter/g/e274bd/32.png) [@GKittridge](https://boards.straightdope.com/u/GKittridge)\ **Post date:** [August 19, 2000, 1:27pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/3 "2000-08-19T13:27:56Z")
9 raised to the 9th power (which is written with a regular 9 followed by a superscript 9). This is the number 9 multiplied by itself 9 times, which is 387,420,489. ---
**Author:** ![Joe\_Cool](https://avatars.discourse-cdn.com/v4/letter/j/ecb155/32.png) [@Joe\_Cool](https://boards.straightdope.com/u/Joe_Cool)\ **Post date:** [August 19, 2000, 2:09pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/4 "2000-08-19T14:09:35Z")
> [@](#): > > \*Originally posted by GKittridge \* > \*\*9 raised to the 9th power (which is written with a regular 9 followed by a superscript 9). This is the number 9 multiplied by itself 9 times, which is 387,420,489. \*\* I can beat it (provided you can use other symbols): 9![sup]9![/sup] 9! is the same as writing 1_2_3_4_5_6_7_8_9, which is 362880. So 9![sup]9![/sup] is the same as 362880[sup]362880[/sup], which is some huge number I don’t even want to think about. It should have something close to 2 million digits. If my computer ever gets done running the calculation I’ll give you the answer to 10 sigfigs or so. ---
**Author:** ![whitetho](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whitetho/32/1059_2.png) [@whitetho](https://boards.straightdope.com/u/whitetho)\ **Post date:** [August 19, 2000, 2:45pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/5 "2000-08-19T14:45:47Z")
How about 1/0 (one divided by zero), which is infinity? ---
**Author:** ![Scarlett67](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/scarlett67/32/7387_2.png) [@Scarlett67](https://boards.straightdope.com/u/Scarlett67)\ **Post date:** [August 19, 2000, 2:50pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/6 "2000-08-19T14:50:30Z")
> [@](#): > > \*Originally posted by whitetho \* > \*\*How about 1/0 (one divided by zero), which is infinity? \*\* 1/0 is undefined, because there is no number you can multiply by 0 to get 1. (BTW, 0/0 is called indeterminate, because you can multiply any number by 0 to get 0.) ---
**Author:** ![MysteryFellow63427](https://avatars.discourse-cdn.com/v4/letter/m/a88e4f/32.png) [@MysteryFellow63427](https://boards.straightdope.com/u/MysteryFellow63427)\ **Post date:** [August 19, 2000, 2:57pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/7 "2000-08-19T14:57:57Z")
> [@](#): > > \*Originally posted by Anthracite \* > \*\*FF? (Hexadecimal) \*\* I think the use of the term “digits” means only 0-9 (ie, two base 10 characters.) Otherwise you could use an arbitrarily large base. ---
**Author:** ![yabob](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/yabob/32/2821_2.png) [@yabob](https://boards.straightdope.com/u/yabob)\ **Post date:** [August 19, 2000, 3:32pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/8 "2000-08-19T15:32:38Z")
And you have to disallow other punctuation marks as well, or you can apply factorials to factorials: 99!!! would be quite large, indeed. If you limit to the same number of operator symbols as digits, 99!! beats Joe\_cool’s example - 99! should be in the vicinity of 10[sup]120[/sup] (very rough estimate). The factorial of that … My first thought was 9[sup]9[/sup]. I would guess that this was the “trick” the chat room was looking for - no punctuation marks involved. ---
**Author:** ![Joe\_Cool](https://avatars.discourse-cdn.com/v4/letter/j/ecb155/32.png) [@Joe\_Cool](https://boards.straightdope.com/u/Joe_Cool)\ **Post date:** [August 19, 2000, 3:49pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/9 "2000-08-19T15:49:59Z")
> [@](#): > > \*Originally posted by yabob \* > \*\*And you have to disallow other punctuation marks as well, or you can apply factorials to factorials: > > 99!!! > > would be quite large, indeed. If you limit to the same number of operator symbols as digits, 99!! beats Joe\_cool’s example - 99! should be in the vicinity of 10[sup]120[/sup] (very rough estimate). The factorial of that … > > My first thought was 9[sup]9[/sup]. I would guess that this was the “trick” the chat room was looking for - no punctuation marks involved. \*\* uh, good point. I didn’t think of that. haha ---
**Author:** ![yabob](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/yabob/32/2821_2.png) [@yabob](https://boards.straightdope.com/u/yabob)\ **Post date:** [August 19, 2000, 4:05pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/10 "2000-08-19T16:05:03Z")
Sorry, that estimate’s way low … I meant to say 10[sup]140[/sup] the way I was thinking about it, and it’s still a very rough estimate. (my calculator shows 69! has an exponent of 98, and won’t show a higher factorial because the exponent exceeds 100. There’s 30 more factors all between 70 and 99. 100’s would add 60 to the exponent, so I just guess that I wind up adding about 40. I told you it was a rough estimate. Anybody that cares to can easily produce a better estimate with a bit of calculation.) ---
**Author:** ![The\_Ryan](https://avatars.discourse-cdn.com/v4/letter/t/7feea3/32.png) [@The\_Ryan](https://boards.straightdope.com/u/The_Ryan)\ **Post date:** [August 19, 2000, 4:32pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/11 "2000-08-19T16:32:43Z")
> [@](#): > > \*Originally posted by yabob \* > My first thought was 9[sup]9[/sup]. I would guess that this was the “trick” the chat room was looking for - no punctuation marks involved. Although in a chat room, it **would** require punctuation marks. Or at least, special coding. What about aleph 9? Or aleph aleph? 🙂 ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [August 19, 2000, 4:33pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/12 "2000-08-19T16:33:49Z")
The Windows calculator can handle up to 10[sup]499[/sup], I believe, and it says that 99! is 9.332621544394e+155 . After that, there’s some sort of formula for approximating large factorials (think we’re justified in calling that large?), but I can’t remember what it is… I know it has an x[sup]x[/sup] term in it, but other than that… Also, using conventional notation, if you want to apply multiple factorials, you need parentheses. A double exclamation point is usually interpreted as a symbol in itself, and signifies what’s known as the “double factorial”, where you skip every other factor. For instance, 99!! would be 99_97_95_93_…_5_3_1 . Of course, this is smaller than 9! . I think that using only two nines and two other characters, Joe\_Cool’s 9![sup]9![/sup], at 6.44_10[sup]2017526[/sup] (no programming required, just a little 8-digit scientific calculator and some algebra) is the best we can do. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [August 19, 2000, 4:37pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/13 "2000-08-19T16:37:32Z")
_slaps The Ryan with a transfinitely large trout_ Silly, Aleph isn’t a digit, and by Russel’s Paradox, Aleph[sub]Aleph[/sub] is undefined. ---
**Author:** ![yabob](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/yabob/32/2821_2.png) [@yabob](https://boards.straightdope.com/u/yabob)\ **Post date:** [August 19, 2000, 4:52pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/14 "2000-08-19T16:52:43Z")
OK. I’d never seen that convention before. Just out of curiosity - is there any combinatoric problem you know of where it turns out to be a useful construct? ---
**Author:** ![aseymayo](https://avatars.discourse-cdn.com/v4/letter/a/a88e57/32.png) [@aseymayo](https://boards.straightdope.com/u/aseymayo)\ **Post date:** [August 19, 2000, 5:12pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/15 "2000-08-19T17:12:20Z")
I can write any large number you like, if the two digits are my two fingers and I’m writing in dust (or sand - but dust is a lot more common at my house). ---
**Author:** ![black\_rabbit](https://avatars.discourse-cdn.com/v4/letter/b/f19dbf/32.png) [@black\_rabbit](https://boards.straightdope.com/u/black_rabbit)\ **Post date:** [August 19, 2000, 6:00pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/16 "2000-08-19T18:00:23Z")
damn. aseymayo got to it before me. ---
**Author:** ![Sofa\_King](https://avatars.discourse-cdn.com/v4/letter/s/58956e/32.png) [@Sofa\_King](https://boards.straightdope.com/u/Sofa_King)\ **Post date:** [August 19, 2000, 6:13pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/17 "2000-08-19T18:13:15Z")
2^n, where n represents any number proposed in this thread. ---
**Author:** ![Sofa\_King](https://avatars.discourse-cdn.com/v4/letter/s/58956e/32.png) [@Sofa\_King](https://boards.straightdope.com/u/Sofa_King)\ **Post date:** [August 19, 2000, 6:14pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/18 "2000-08-19T18:14:59Z")
I should have said, “the largest number”. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [August 19, 2000, 6:25pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/19 "2000-08-19T18:25:15Z")
The double factorial isn’t used much in combinatorials (I think), but it can be found in many infinite-series representations of functions. When I get to work I’ll see if I can look any up for you. ---
**Author:** ![lawoot](https://avatars.discourse-cdn.com/v4/letter/l/35a633/32.png) [@lawoot](https://boards.straightdope.com/u/lawoot)\ **Post date:** [August 19, 2000, 6:38pm UTC](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961/20 "2000-08-19T18:38:55Z")
> [@](#): > > \*Originally posted by aseymayo \* > \*\*I can write any large number you like, if the two digits are my two fingers and I’m writing in dust (or sand - but dust is a lot more common at my house). \*\* Knowing how alot of these trivia/brain teaser tings work, this probably IS the right answer [Next page](https://boards.straightdope.com/t/what-is-the-largest-possible-number-you-can-write-using-only-2-digits/29961.md?page=2)