Hi,
it seems like the meaning of 'hundreds of times' depends on context:
In math context:
I have run this experiment hundreds of times. =>implies > 100 times (a minimum of a hundred times) Because 'hundreds' is plural, I would understand 'hundreds of times' to mean 'at least two hundred'.
I have run this experiment thousands of times => implies > 1000 times (a minimum of a thousand times)
Similarly, at least 2000.
In non-math context:
You have asked me this same question hundreds of times. => implies many times yes
You have asked me this same question thousands of times => implies many times and, therefore, has no whatsoever difference from 'hundreds of times'? Well, thousands of times sounds a bit more than hundreds of times. But ther's really not much difference.
Best wishes, Clive
Please correct me if I'm wrong