Prime between n and 9 n divided by 8/Mistake
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Source Work
1986: David Wells: Curious and Interesting Numbers:
- The Dictionary
- $48$
1997: David Wells: Curious and Interesting Numbers (2nd ed.):
- The Dictionary
- $48$
Mistake
- If $n$ is greater than $48$, then there is a prime between $n$ and $9 n / 8$, inclusive.
Correction
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.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $48$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $48$