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**roninpro** This is fine. If $\displaystyle e$ is even, then you are done. You can then factor 2 out of $\displaystyle e$ and write $\displaystyle 2\cdot 2\cdot e=d$. We have written $\displaystyle d$ as a product of at least 3 primes. ($\displaystyle e$ could be either prime or composite, but it doesn't matter.)

Fine. But if we want to conclude, we need to show that $\displaystyle e$ is not prime. If it is prime, then we fail, since $\displaystyle d$ will be written as a product of only two primes. For a contradiction, suppose that $\displaystyle e$ is prime. We can write $\displaystyle \frac{a+b}{2}=e$. How does this contradict the assumption that $\displaystyle a,b$ are adjacent odd primes?