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Every day I go to the swimming pool and swim the same number of lengths. I like to count the number of lengths I've done as I go as a fraction of the total number of lengths I'm going to do that day.
If I swam ten lengths a day...
I don't swim ten lengths a day. In fact, the total number of lengths I swim each day is rather special...
Let's call the total number of lengths I swim $n$.
After the first length, for every length I swim, the total so far (let's call it $t$) is either a prime number, or the fraction $\frac{t}{n}$ will simplify (or both).
It is, in fact, the largest number for which this is true.
Can you work out how many lengths I swim each day?