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There are infinitely many of them.

Some of them are given by:

  • All numbers of the form 3n+1/n for n ∈ the prime numbers are rational numbers between 3 & 4, and as there are an infinite number of prime numbers, there are an infinite number of these.
  • All numbers of the form 4n+1/n for n ∈ the prime numbers are rational numbers between 4 & 5, and as there are an infinite number of prime numbers, there are an infinite number of these.

There are still more than the infinitely many given above.

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Q: Rational numbers between 3 and 5?
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They are 4, 3 and 2 which are rational numbers because they can be expressed as fractions as for example 3 as a fraction is 3/1.


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