The numbers 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991 and 997 are prime.
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Including 100 and 999 themselves, 900. If you don't count 100 and 999, there are 898.
Oh, dude, there are like 899 numbers between 100 and 999. You just subtract the starting number from the ending number, but hey, who's counting? Oh wait, we are, literally.
One. 997 and 2
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.
The answer must have an even number and an odd number, because if you add two odd numbers, the sum would be even. Therefore, the first answer is the only prime even number: 2. 2 + 997 is 999, so the other answer would be 997. 997+2 (!?!) 997+2 (!?!) 2 and 997