Conjecture on the ninth primary pseudoperfect number

A primary pseudoperfect number is a positive integer $K$ with the defining property that, for every prime divisor $p$ of $K$, one has $1/K+1/p$ equal to an integer. Let $K_r$ denote a primary pseudoperfect number with $r$ prime factors. The known values through $K_8$ suggest the following prediction. Ninth primary pseudoperfect number conjecture. There exists exactly one primary pseudoperfect number $K_9$ with nine prime factors, and

$$K_9\pmod{6^2\cdot 8}=258.$$

There are no further primary pseudoperfect numbers. This is explicitly presented as a prediction motivated by the observed remainder progression; its computational verification would require searching below a 106-digit upper bound for $K_9$, and the existence of $K_9$ and the nonexistence of all later examples remain open.