Googolplex - How big is big?

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A googol

Think about an average sized room, say a lounge. Fill it with grains of sand. That's a lot of grains, in fact we are talking about 70 trillion grains, or 70,000,000,000,000.

Now scale this up and think about how many grains of sand we could tightly pack into the whole universe, with no gaps. That's a lot bigger. In fact it's

100,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000

That's the number 10, followed by 80 zeros, or 1080.

Now, step this up a notch. How many protons can fit into the universe, tightly packed, with no gaps? A proton is a subatomic particle that makes up atoms. You would fit about 10140 protons in the universe. 

Somewhere in between 1080 and 10140 is a googol. A googol is 10100, big right? 

 

Not that big though it turns out!

 

 The largest Perfect Number

A googol is 101 digits long. It dwarfs a billion, which is only 10 digits long.

Think about this:

The largest prime number known to this day has 23 million digits

The largest perfect number known to this day has 47 million digits

These are not numbers in the millions, No No NO! Numbers in the millions have 7 or 8 digits. We are talking tens of millions of digits just for the biggest prime and biggest perfect number. Pretty big right?!

Put it this way, if you started a word document, and held your finger down on say the number 4 so it just kept repeating and repeating, do you know how long it would take to get to a number that was as large as the largest perfect number...one of which that's 47 million digits long?

A minute, or 10, or an hour, a day, a week, longer? It would take about 18 days of sitting there, without a break, holding the number 4 down, to get to a number the size of 47 million digits long.

Furthermore, in a size 11 font, there would be 12240 pages of digits. 

THAT is how big the largest perfect number is.

 

A Googolplex

There exists a number that is so much more though, a googolplex

A googol is a number with a 101 digits, not much compared to the largest perfect number, but still pretty big. You wouldn't say no to that many pennies! Anyway, a googolplex is a 1 followed by a googol digits. Think about that for a second. A 1....followed by not 101 digits (no that's a googol, which has 3 digits), not 47 million digits (the largest perfect number, which has 8 digits), but the number that has 101 digits in it. That's a bit baffling, here is a breakdown:

1,000,000 is a million - it has 7 digits

47,000,000 is 47 million - it has 8 digits

1,000,000,000,000 is a trillion, it has 13 digits

47,000,000,000,000...…..(plus 47 million more zeros) is the size of the largest perfect number

A googolplex has a number of digits that is so large, that we have to think about it in terms of how many digits it has actually got, rather than the value of the number. Even then, it is too big to think about. 

 

Put it this way, a googolplex is so large, the universe is not big enough to write the number down. Let me expand. If we were to write 1 digit on 1 particle, and lined all the particles up, to represent the googolplex, there would not be enough particles of matter in the universe to do such a thing. 

 

Even a googolplex is not big

Ok, so it might be the largest number that we might be able to just about think of normally, and it certainly is big. But..... a googolplex is still just a tiny fraction, if at all, of infinity.