Can every odd number be represented as $2pq-rs$ where $p$,$q$,$r$, and $s$ are distinct odd primes?

Question

A quick check shows this to be true for all odd numbers less than 4495, can it be shown for all odd numbers? Is this a known result?

Here is the PARI program I used to check:

x=[]; forprime(p=3, 100, forprime(q=3, 100, forprime(r=3, 100, forprime(s=3, 100, if(2*p*q-r*s>0 && p!=q && p!=r && p!=s && q!=r && q!=s && r!=s, x=setunion(x, [2*p*q-r*s])) ))));for(i=1, length(x), if(x[i]<5000,print(x[i])))

The first odd number that fails in this check is $4495$.