Infinitely many rational numbers and even more irrational numbers.
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34 is the midpoint between 12 and 56.
No.
The difference is 12.
The integers between 4 and 12 are 5, 6, 7, 8, 9, 10, and 11. Other numbers between 4 and 12 are √19, 6 1/2, and 11.987654321. There are infinitely many numbers between 4 and 12.
13 is the only prime number between 12 and 16.