Hundred googolplexian and one!
There is no end to the list of integers; we don't have names for very large numbers - practically, there are very approximately 1040 atoms in the universe - less than half a Google - so there isn't much call for very large numbers outside of mathematics.
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graham numbers
There are a bunch of them between googolplexian and infinity. Here are the first few: googolplexian + 1 googolplexian + 2 googolplexian + 3 googolplexian + 4 googolplexian + 5 googolplexian + 6 . . googolplexian + 3 million . . etc. There are an infinite number of those.
Yes. After googolplex.
To write a googolplexian, you would start with a 1 followed by a googolplex number of zeros. A googolplex is 10 raised to the power of a googol, which is 10^100. So a googolplex is 10^(10^100). Therefore, a googolplexian would be written as 10^(10^(10^100)).
One hundred million one hundred nineteen thousand in numbers is 100,119,000