It's Totally Totative!

Define a positive integer \(n\) to be totatively prime if the set of all positive integers less than \(n\) that are relatively prime to \(n\) contains no composite numbers. What is the largest totatively prime number?

For example, 9 is not totatively prime because 4 is less than 9 and is relatively prime to 9, but 4 is composite.

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