4000 of them.
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Not sure about the exact number but it is approx 1086.
If by "between" you mean "between but not including", then the answer is 9999 - 999 - 1 = 8999.If on the other hand, you mean to include both 9999 and 999, then the answer is 9999 - 999 + 1 = 9001.
3439
Well, honey, the even integers between 1000 and 9999 can be found by dividing the total range by 2, since every other number is even. So, 9999 - 1000 = 8999, and 8999 divided by 2 gives you 4499 even integers. But remember, I'm not your calculator, so don't come crying to me if you can't count 'em all yourself!
9*9*8*7 = 4536