Big numbers

So I had dinner with some friends last night and was asked the riddle "How many zeroes are there at the end of 1 million factorial?". That is, 1,000,000 * 999,999 * 999,998...1 is some very big number- How many zeroes are at the end of it? Well, after some hints from my questioner and a day to think about it, I have today figured out that the answer is 249,998 - which might seem clever and make me proud except that the guy I was talking to was asked this as part of a maths competition and figured it out in his head!

So, 1,000,000 factorial might seem like a very large number, but it's peanuts really. I already knew about a Googol (a 1 with 100 zeroes after it) and a Googolplex (a 1 with a Googol of zeroes after it)... But how about Graham's number?

I laughed out loud when I read this:

"Although the solution to this problem is not yet known, Graham's number is the smallest known upper bound. This bound was found by Graham and B. L. Rotschild (see (GR), corollary 12). They also provided the lower bound 6, adding the qualified understatement: Clearly, there is some room for improvement here."

It is funny, when you start to try to get your head around just how incomprehensibly big this number is. I would argue that the "room for improvement " statement is the biggest understatement ever made!

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