[VladRussian]

>This is ultimately an epistemic issue - what do we mean by "known"? What property does the largest known prime have that the next largest prime lacks?

"known" is by "whom". Being "known" isn't an intrinsic property that one prime has and another lacks. "Knowing" some specific number as a prime is a property of the one who "knows". If some person (or alien race) knows p as the largest known [to them] prime and another person knows q as the largest known [to him] prime it has absolutely no bearing on the intrinsic properties of either p or q.

>These are the types of questions philosophy asks.

if it really so nowadays, then it would explain why there is no philosophers anymore

[bumbledraven]

p is "known" by the mathematical community. As of 2011, p is the largest natural number such that (a) we know p is prime and (b) we know a polynomial-time algorithm to enumerate the digits in the decimal expansion of p.