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]

<!--QuoteBegin-Black Mage+Mar 4 2005, 12:45 AM--></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'><!--QuoteEBegin--> <!--QuoteBegin-Mantrid+Mar 4 2005, 12:30 AM--></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'><!--QuoteEBegin--> Actually, it won't be anywhere near that many digits. For example: <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd--> 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 <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd--> 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.

Omega_DeathSith apprentice to a box of CerealJoin Date: 2003-08-06Member: 19042Members

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

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. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> 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.)

aonomusDedicated NS Mastermind (no need for school)Join Date: 2003-11-26Member: 23605Members, Constellation

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...

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.

<!--QuoteBegin-Omega Death+Mar 4 2005, 01:39 AM--></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'><!--QuoteEBegin--> According to the Ti-89 program 5,000,000,000! is

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

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

<!--QuoteBegin-Omega Death+Mar 4 2005, 02:39 AM--></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'><!--QuoteEBegin--> According to the Ti-89 program 5,000,000,000! is

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

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 <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo--> ....plus, mine does negative number...even though you're not really supposed to have negative factorials, if I remember right.

<!--QuoteBegin-UltimaGecko+Mar 4 2005, 01:45 AM--></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'><!--QuoteEBegin--> Anyway, it wont end in a .5 or a .anything. Factorials only use whole numbers. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> Well, if you wanted to mutliply the 2.58...by that 46 billion exponent then you'd get your real answer.

<!--QuoteBegin-UltimaGecko+Mar 4 2005, 02:45 PM--></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'><!--QuoteEBegin--> 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 <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo--> ....plus, mine does negative number...even though you're not really supposed to have negative factorials, if I remember right. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> Just open up Excel, find a cell, and type in <b>=fact(<i>n</i>)</b>. Also goes up to 170. Rejects negative numbers. <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->

Well...my program is for people who ...don't have excel and stuff <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo--> . 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 <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo--> .

Omega_DeathSith apprentice to a box of CerealJoin Date: 2003-08-06Member: 19042Members

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.

<!--QuoteBegin-Omega Death+Mar 4 2005, 02:00 AM--></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'><!--QuoteEBegin--> 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. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> 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.

<!--QuoteBegin-Verthandi+Mar 4 2005, 01:27 PM--></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'><!--QuoteEBegin-->Yup, I think we reached a concensus that 5000000000! is "a really big number". <!--emo&;)--><img src='http://www.unknownworlds.com/forums/html/emoticons/wink-fix.gif' border='0' style='vertical-align:middle' alt='wink-fix.gif' /><!--endemo--><!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->

<!--QuoteBegin-UZi+Mar 4 2005, 04:42 AM--></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'><!--QuoteEBegin--> that number in feet is how long my whoohoo is! <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> So you have to drag it?

<!--QuoteBegin-Rellix+Mar 4 2005, 12:26 AM--></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'><!--QuoteEBegin--> I stuck it in the windows calculator...it says itl take a long time, so lets see how long a time that is! <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> 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.

UZiEight inches of C4 between the legs.Join Date: 2003-02-20Member: 13767Members

<!--QuoteBegin-InSaInE+Mar 4 2005, 04:51 AM--></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'><!--QuoteEBegin--> <!--QuoteBegin-UZi+Mar 4 2005, 04:42 AM--></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'><!--QuoteEBegin--> that number in feet is how long my whoohoo is! <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd--> So you have to drag it? <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> A a large army of midgets help....

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

## Comments

2005-02-02Member:39476Members2003-05-18Member:16477MembersStirling'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]

2002-11-25Member:9922Memberseverytime 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 <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->

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.

2003-08-06Member:19042Members2003-08-06Member:19042Members2003-02-24Member:13942MembersApparently 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.

2003-08-06Member:19042MembersApparently 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. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->

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.)

2003-11-26Member:23605Members, Constellation2003-08-06Member:19042Members2.5882191515e46323377617

2002-07-19Member:973Members2003-02-24Member:13942Members2.5882191515e46323377617 <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->

Gimme my damn cookie.

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

2003-03-12Member:14456Members2.5882191515e46323377617 <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->

If that;s true, oblique was pretty far off. >>

2003-05-14Member:16320MembersAnyway, 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 <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo--> ....plus, mine does negative number...even though you're not really supposed to have negative factorials, if I remember right.

2003-02-24Member:13942MembersWell, 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.

2002-12-12Member:10687Members, NS1 PlaytesterAnyway, 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 <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo--> ....plus, mine does negative number...even though you're not really supposed to have negative factorials, if I remember right. <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->

Just open up Excel, find a cell, and type in <b>=fact(<i>n</i>)</b>. Also goes up to 170. Rejects negative numbers. <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->

2003-05-14Member:16320MembersPffft, stupid variant data type, only supporting 10^306 <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo--> .

...Attack of the tongue.gifs.

2003-08-06Member:19042Members2002-11-07Member:7556MembersIf 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.

2002-04-12Member:423Members2003-02-15Member:13572Members, Constellation, Reinforced - Shadow2003-06-03Member:16972Members2002-12-12Member:10687Members, NS1 Playtester2003-02-20Member:13767Members2004-02-02Member:25954MembersSo you have to drag it?

2003-04-26Member:15861MembersI 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.

2003-10-29Member:22097MembersIt would outdo a 64 bit variable by a couple hundred billion didgets if I'm not mistaken...

2003-02-20Member:13767MembersSo you have to drag it? <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->

A a large army of midgets help....

2002-12-12Member:10687Members, NS1 Playtester2002-04-24Member:513Members, Constellation2003-09-08Member:20667MembersI 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