Representing integers as difference of semi-primes

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Can every integer, $k$ (where $4 \le k < n$), be written as the difference of two semi-primes whose prime factors are at most $n$ ?

or put another way:

Given positive integers $k\ge 4$, $n > k$ , do there exist primes $a,b,c,d$ at most $n$ such that $ab−cd=k$ ?