If you want to know the largest named number, maybe Googolplex would be a start. See related link.
There isn't a largest number. If you think you find it, then just add 1 to it, and you have a new 'largest number'. Or if, say the number you have is a gazillion. Well why not just multiply by 2 and have 2 gazillion or how about 100 gazillion, etc.
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It has been proven that there is no largest prime number, and therefore there exists a prime number, in fact, infinitely many, greater than 10^999999999 (having a billion digits); however, no humans have actually found a specific number of that size and identified it as prime.
M84 is the largest even number.
The largest number of squares that can be uncovered is 710.
9797 is the largest two digit prime number.
The largest whole number that rounds to 900 is 949.