No, a prime number cannot be given between 2 consecutive natural numbers as consecutive means continuous. Like if the numbers are 18 and 19,then how can we find any number between them. The numbers are consecutive,thus no prime number can exist between 2 consecutive natural numbers.
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Perhaps it is not properly formed.  this question.

prime numbers are supposed to be integers.

two consecutive natural numbers are consecutive integers.  So there is no possibility of another integer in between two consecutive integers.

we can think of a prime number between squares of two consecutive integers...

like:    2 and 3  are consecutive natural numbers..  5,7 are prime numbers between the squares 4 and 9 of 2 and 3.

example:    17, 19, 23 are prime numbers between  squares of 4 and 5.

229 is a prime number between 15 square and 16 square.

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