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For 100! just use your computer:




It is not that simple, is it ?

Most computers can not store integer numbers larger then

(2^64 -1) = (18446744073709551616-1) = 18446744073709551615

as they are limited by 64 bits processors and memory slots.

The number 100! is substantially large then that.

So nearly all numerical software switches to floating point number presentation which shortens the number part of the storage space to at least 56 bit as the exponential needs to be stored as well.

This limit the total integer part of the floating point number to :

(2^56 -1) = (72057594037927936-1) = 72057594037927935

Which in turn only allowes floating point numbers to be accurate only to their 17th digit.

This is much much much smaller then the number 100! you give (about 8 times more digits) :

110! = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518
286253697920827223758251185210916864000000000000000000000000


So the comment "just use your computer" is misleading at best.

You have to have access to a supercomputer (very large computer bus sizes) or special analytical mathematical software packages to even be able to produce the above number in all its digits.

I dare say that the vast majority of the people out there don not have access to either or even understand the need for either in this situation.

Wouter

Last edited by Wouter; 01/15/08 10:35 AM.

Wouter Hijink
Formula 16 NED 243 (one-off; homebuild)
The Netherlands