# Did Writing This Make Sense?

A Quora question asks: Why does it not make sense to say that 5 is a prime number and 8 is composite in this scenario: ‘There are 5 gallons of water in container A and 8 gallons of milk in container B”?

It depends on what you mean by “make sense” – and also to some extent on the context.

We often say that an action doesn’t make sense if we can see no good reason for taking it, and so a statement can make sense in the sense of having a well-defined meaning – but it may not make sense to say it if it is not in any way useful.

In general the number of gallons in a container is a real number with zero probability of ever being an exact integer of any kind, so the question of primality of the exact value almost never has any well-defined mathematical meaning.

But if we are only looking at the volumes rounded to the nearest integer, then statements about the factorization properties of those integers make mathematical sense (in the sense of having a well defined meaning) even though we might usually say that it doesn’t make sense to be talking about those properties because we can’t see why one would care.

Most of the time that would probably be right, but there may be particular contexts in which the factorizability does matter.

For example, if we wanted to transfer the water in our containers into a number of full one gallon jugs, and then to cut planks to make a rectangular box holding those jugs in more than one row with no empty spaces, then that would be possible (with acceptable wastage) if the number of gallons in the container is (close enough to) an integer that is composite but not if it is prime. And so in that unlikely context it would make sense (in both senses of making sense) to say that 8 is composite but 5 is prime.

Of course it may not make sense to want that, or even to have written this answer; but I hope that, once written, it does make at least some kind of sense.

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### 2 Responses to Did Writing This Make Sense?

1. bob worcester says:

Does it matter at all that the 5 litre can be poured into 2 rows of 3 containers even if the container rows are not completely full? A container of liquid should be infinitely divisible into other containers making its ‘prime’ quality meaningless.

2. alan says:

The requirement that all the jugs be full “makes sense” in the sense of having a well-defined meaning but probably does not “make sense” in the sense of being a reasonable thing to require.