Yes, if you take the range to be inclusive, it even works for 1, since 2 is prime.
The theorem related to this question is called Bertrand's Postulate, or Chebyshev's Theorem, or the Bertrand-Chebyshev theorem.
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Take any counting number greater than one. 2, 3, 4, 5 and so on. Double it. Between the number and twice the number, there will be at least one prime number. 3, a prime number, is in between 2 and 4.
Yes.
No, the sum of a prime number and a composite number is not always even.
It is 97. it is largest, because it is the largest double digit prime number.
No, and you do not even if you reverse them.