[sqrt17]

Most philosophers know the difference between "known" and "known to have property P".

If Clinton is a well-known ex-President, and he is a peanut farmer, he might be called a "well-known ex-President" in the "known" sense, but not necessarily in the "known to have property P".

"known N" in the second sense is thus non-intersectional and must be analyzed as "P(x) & known(P(x))" rather than "P(x) & known(x)". Non-intersectionality is not as weird as you may think, as superlatives such as "largest" are also non-intersectional in the sense that if someone has the smallest green t-shirt, it's the case that they have a green t-shirt, but it's not (necessarily) the case that they have the smallest t-shirt, (e.g. when the smallest t-shirt is actually red).

If you want to put it back in language, put it like this: As of 2011, the "largest number known to be prime", as reported by GIMPS (the Great Internet Mersenne Prime Search),15 is p := 243112609 − 1.

So, the "largest known prime number" is a way to describe our knowledge about numbers, rather than a property that you can attribute to numbers out of context.