I don't know exactly, but it's in the high eight digits. Why, you ask?
Well, I searched a series of numbers, starting with 1 and roughly doubling. This gave the following data:
|Search string||Number of hits|
(Each number in the left column is either twice the previous one, or twice the previous one plus one.)
So here's what I'm thinking; numbers around 26 million, have, on average, 37 google hits. Since containing a given number is a Rare Event, I'm guessing that we can treat the number of hits of numbers around that magnitude as Poisson with parameter 37. The probability that a Poisson(37) random variable is equal to zero is exp(-37), or about one in 1016. So the first integer with no Google hits is probably larger than 26 million.
But by the same argument, numbers around 52 million have probability exp(-17), or about one in 25 million, of having no Google hits. So we expect one between, say, 52 million and 77 million.
And by the time we get up near 100 million, we should be seeing these numbers at a frequency of one in exp(12), or six in a million; they should become commonplace.
To get a better model, I'd take more samples. The number of Google hits for a number seems to follow a power law; the number of hits for n is a constant times n-α for some exponent α, somewhere between 1 and 1.5. (There are issues around saying that things follow power laws, though; it's easy to see them even when they're not there.) And there are various complications -- for example, powers of ten and powers of two are more common than the numbers around them. And how do we know that the occurrence of a number on various web pages is actually independent? To be honest, we don't; if a number exists on a web page, it's there for a reason, and if one person has something to say about it, why not someone else?