5,000,000,000!

GNS · March 2005

Do it by hand? olo

0blique · March 2005

I can give you an approximation as follows:

Stirling's Formula for approximating Gamma(x+1) (which is also x! for integer x) is Gamma(x+1) = sqrt(2*pi*x)*X^X*e^-x

Since this converges for large x (large is more than 60), so we can get a close answer for 5e9!:

5_000_000_000! = Gamma (5_000_000_000 + 1)

= 1e5 sqrt (pi) * e ^ (5_e9 (ln (5e9) - 1))

which you can take to however many significant digits you like. If you want a base 10 number, you can convert as well:

= sqrt(pi)* 10 ^ (log e * 5e9 * (ln (5e9) - 1) + 5)
= 1.772453 e+46_323_424_672

The exponent is about 4.63*10^10, so it is far smaller than a googleplex, but still too big to fit on the board in expanded form.

[Edit: The estimation of 43,884,838,845 digits actually seems sort of good]

[Edit: I redid the caluclation using octave, and it is actualy close to
2.5844904e+46_323_377_617 because of rounding errors in my previous calculation. Also note that this is just an approximation]

Umbraed_Monkey · March 2005

</div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Black Mage @ Mar 4 2005, 12:45 AM)</td></tr><tr><td id='QUOTE'> </div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Mantrid @ Mar 4 2005, 12:30 AM)</td></tr><tr><td id='QUOTE'> Actually, it won't be anywhere near that many digits. For example: </td></tr></table><div class='postcolor'>
everytime you add one, you add the number of digits -1 in the number that you added to the answer: ie 1000! would be 3 digits longer than 999!, 1001! would be three digits longer than 1000! and 5 000 000 000 would be REALLY BLOODY LONG </td></tr></table><div class='postcolor'>
thus, I said, the answer will be at 10GB or bigger to store the answer. Youll need at least 9 digits * (5 billion - 1 billion) = 45 billion digits (and then some). 45 billion+ number of digits will need tens of gigabytes to store and display. If your answer is not approaching that amount of digits, its clearly wrong.

edit: Oblique pwnt.

Omega_Death · March 2005

I have no way of checking this so I'm going to say 0blique won. Congrats.

Omega_Death · March 2005

Just to be an A**hole now convert that number to binary. Then Hex. <img src='http://www.unknownworlds.com/forums/html/emoticons/biggrin-fix.gif' border='0' style='vertical-align:middle' alt='biggrin-fix.gif' />

Ambassador · March 2005

<a href='http://www.ticalc.org/archives/files/fileinfo/288/28844.html' target='_blank'>Here yah go</a>

Apparently this guy found a way to do it extemely high. If you have a TI-89 calculator it can do it for yah. Someone try it out.

Omega_Death · March 2005

</div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Ambassador @ Mar 4 2005, 01:28 AM)</td></tr><tr><td id='QUOTE'> <a href='http://www.ticalc.org/archives/files/fileinfo/288/28844.html' target='_blank'>Here yah go</a>

Apparently this guy found a way to do it extemely high. If you have a TI-89 calculator it can do it for yah. Someone try it out.  </td></tr></table><div class='postcolor'> 
I hate you, and the guy who wrote that program.

(side note: my head exploded when i tried to concieve the number that this program can handle up to.)
(side note2: I have a Ti-89 and am downloading.)

aonomus · March 2005

If you were a hardcore math nerd, you could probably break it up into smaller factorials to the power X, and then it'd be defined, but not simplified...

Omega_Death · March 2005

According to the Ti-89 program 5,000,000,000! is

2.5882191515e46323377617

Belgarion · March 2005

as far as i'm concerned you're all nerds. really really big mathy nerds. not that i don't have a great ammount of respect for math, but you're nerds all the same.

Ambassador · March 2005

</div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Omega Death @ Mar 4 2005, 01:39 AM)</td></tr><tr><td id='QUOTE'> According to the Ti-89 program 5,000,000,000! is

2.5882191515e46323377617 </td></tr></table><div class='postcolor'>
Gimme my damn cookie.

Edit: great guess on the 45 billion digits, yall were only off by 1 billion digits.

Transmission · March 2005

</div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Omega Death @ Mar 4 2005, 02:39 AM)</td></tr><tr><td id='QUOTE'> According to the Ti-89 program 5,000,000,000! is

2.5882191515e46323377617  </td></tr></table><div class='postcolor'> 
If that;s true, oblique was pretty far off. >>

UltimaGecko · March 2005

I haven't been in math for a really long time, but I'm pretty sure there was some pattern to figuring out really large factorials (although, even if you knew the pattern, I don't think it will help with writing out a number this large). Anyway, it wont end in a .5 or a .anything. Factorials only use whole numbers.

Anyway, here's a program I made, but it only goes to 170!...since I have no idea how to make it use more space (...but it's already a huge number...although maybe you'd rather scroll through that list of 1-999!).

Bah, I have been pre-empted with high quality maths in my 15 minutes of writing this program <img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /> ....plus, mine does negative number...even though you're not really supposed to have negative factorials, if I remember right.

Ambassador · March 2005

</div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (UltimaGecko @ Mar 4 2005, 01:45 AM)</td></tr><tr><td id='QUOTE'> Anyway, it wont end in a .5 or a .anything. Factorials only use whole numbers.  </td></tr></table><div class='postcolor'> 
Well, if you wanted to mutliply the 2.58...by that 46 billion exponent then you'd get your real answer.

The decimal is just scientific notation.

Verthandi · March 2005

</div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (UltimaGecko @ Mar 4 2005, 02:45 PM)</td></tr><tr><td id='QUOTE'> I haven't been in math for a really long time, but I'm pretty sure there was some pattern to figuring out really large factorials (although, even if you knew the pattern, I don't think it will help with writing out a number this large). Anyway, it wont end in a .5 or a .anything. Factorials only use whole numbers.

Anyway, here's a program I made, but it only goes to 170!...since I have no idea how to make it use more space (...but it's already a huge number...although maybe you'd rather scroll through that list of 1-999!).

Bah, I have been pre-empted with high quality maths in my 15 minutes of writing this program <img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /> ....plus, mine does negative number...even though you're not really supposed to have negative factorials, if I remember right.  </td></tr></table><div class='postcolor'> 
Just open up Excel, find a cell, and type in <b>=fact(<i>n</i>)</b>. Also goes up to 170. Rejects negative numbers. <img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' />

UltimaGecko · March 2005

Well...my program is for people who ...don't have excel and stuff <img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /> . Plus if they're too lazy to take out their negative sign mine will still work for them.

Pffft, stupid variant data type, only supporting 10^306 <img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /> .

...Attack of the tongue.gifs.

Omega_Death · March 2005

I'm pretty impressed, I posted this question in a game forum and within an hour or two had an answer that while I have no way of proving is also satisfactory.

NumbersNotFound · March 2005

</div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Omega Death @ Mar 4 2005, 02:00 AM)</td></tr><tr><td id='QUOTE'> I'm pretty impressed, I posted this question in a game forum and within an hour or two had an answer that while I have no way of proving is also satisfactory.  </td></tr></table><div class='postcolor'> 
If i ever get a chance i'll write a class that uses linked arrays of unsigned long ints with manual multiplication. it'd probably be really expensive on the computer, but i think it'd work to a point.

SoulSkorpion · March 2005

This reeks of homework to me. Why are you asking these questions?

Rellix · March 2005

I stuck it in the windows calculator...it says itl take a long time, so lets see how long a time that is!

Monkfish · March 2005

I know what it is....it's a <i>really</i> big number!

Verthandi · March 2005

</div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Verthandi @ Mar 4 2005, 01:27 PM)</td></tr><tr><td id='QUOTE'>Yup, I think we reached a concensus that 5000000000! is "a really big number". <img src='http://www.unknownworlds.com/forums/html/emoticons/wink-fix.gif' border='0' style='vertical-align:middle' alt='wink-fix.gif' /></td></tr></table><div class='postcolor'>

UZi · March 2005

that number in feet is how long my whoohoo is!

InSaInE · March 2005

</div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (UZi @ Mar 4 2005, 04:42 AM)</td></tr><tr><td id='QUOTE'> that number in feet is how long my whoohoo is!  </td></tr></table><div class='postcolor'> 
So you have to drag it?

im_lost · March 2005

</div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (Rellix @ Mar 4 2005, 12:26 AM)</td></tr><tr><td id='QUOTE'> I stuck it in the windows calculator...it says itl take a long time, so lets see how long a time that is!  </td></tr></table><div class='postcolor'> 
I tried that, but after the fifth alert saying "This operation will take a long time. Do you want to continue?" (about once a minute), I decided it wasn't worth it.

Swiftspear · March 2005

Ok... so if your factorial # is... however many didgets you need to store it... what size variable would you need to store it in binary?

It would outdo a 64 bit variable by a couple hundred billion didgets if I'm not mistaken...

UZi · March 2005

</div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (InSaInE @ Mar 4 2005, 04:51 AM)</td></tr><tr><td id='QUOTE'> </div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (UZi @ Mar 4 2005, 04:42 AM)</td></tr><tr><td id='QUOTE'> that number in feet is how long my whoohoo is! </td></tr></table><div class='postcolor'>
So you have to drag it?  </td></tr></table><div class='postcolor'> 
A a large army of midgets help....

Verthandi · March 2005

Be reminded that the number in question has just over 46 billion digits. In comparison, a 64-bit variable would be nothing.

Gwahir · March 2005

the blood loss must kill you...

Geminosity · March 2005

ooh fun!

I was all like "that's not 5 billion, it's five thousand million" but when I looked it up it turns out you can call that a billion but also the definition I knew which is a million million = billion is also correct o.O

5,000,000,000!

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