Prime between n and 9 n divided by 8/Mistake

Source Work

The Dictionary

$48$

The Dictionary

$48$

If $n$ is greater than $48$, then there is a prime between $n$ and $9 n / 8$, inclusive.

While this is in fact true, the statement as it stands actually holds for $n = 32$.

What is more probably what is required here is the statement:

If $n$ is greater than or equal to $48$, then there is a prime between $n$ and $9 n / 8$, exclusive.

With this latter statement, when $n = 47$, $n$ itself is prime and so there exists such a prime.

Also note that if $9 n / 8$ is an integer, then it is not a prime as it has $9$ as a divisor.

Thus whether this upper bound is exclusive or inclusive is immaterial.