How much time has passed between the events in Portal 1 and 2?

Assuming the announcer was reciting the number of days you had been in stasis, as with your earlier 50-day wake up call, "it has been 9 9 9 9 9..9 9...[static]", it has been at least 273 years, or 27,300 assuming the pause wasn't a broken-record effect.

In "The Final Hours of Portal 2" e-book, Keighley mentions that:

One way to further differentiate Portal and Half-Life was to set the game far in the future—at least 50,000 years.

It doesn't explicitly say that Portal 2 was set in 52,000 AD, but the general point was that the events between the two series are so distant from one another as to not interfere.

No exact number has been stated that I'm aware of. All we know is that "hundreds of years" have passed between the end of Portal 1 and the beginning of Portal 2.

In an unused GLaDOS voice line she states that:

Fifty thousand years is a lot of time to think. About me. About you. We were doing so well together. _Source

Referring respectively to herself and the protagonist Chell.