As the site words it, the classes are not disjoint and the second question is trivial. The prime $2$ is in class $2$, since $2+1=3$ and $3$ is in class $1$ ($3+1=4$); by induction on $r$, every prime of class $1$ is in every class, since $2$ and $3$ lie in class $r-1$, $p+1$ is even for odd $p$, and $2+1=3$. So the least prime of every class is $2$ and $p_r^{1/r}\to1$; a computation over the primes below $20000$ confirms that each of the classes $1$ to $6$, so read, has least element $2$ and contains class $1$. The corrected Statement inserts "it is in no class $\leq r-1$ and", so that each prime has exactly one class, the least $r$ for which the condition holds. The defect is already in Guy's A18 [Gu04, p. 66], "The Erdős–Selfridge classification of primes", which gives the definition in the site's words but states it as Erdős and Selfridge's classification of the primes, tables classes $1$ to $8$ as disjoint sets (class $1$ begins $2, 3, 5, 7, 11$ and class $2$ begins $13, 19, 29$), and gives the least primes of classes $1$ to $5$ as $2, 13, 37, 73, 1021$. The site's commentary gives the same sequence of least primes (A005113 in the OEIS). The same computation gives these least primes under the corrected Statement, followed by $2917$ and $15013$ for classes $6$ and $7$, the first entries of Guy's tables. The site also cites [Er77], which the corpus has not read. The formal-conjectures statement adopts the corrected definition, excluding the lower classes since its revision of 2026-08-16. Class $1$ is the same set in both forms, and no result about the site's wording is recorded.