Odd Primes Problem Proof Given the odd prime numbers, 
Prove that if $x$ and $y$ are adjacent odd primes in this list, then $x + y$ has $3$ prime factors. The factors need not be distinct.
Here is an example I have provided:
$3 + 5 = 8 = 2 \cdot 2 \cdot 2$. Therefore, $8$ has $3$ repeated factors of $2$.

Suppose $x<y$ are adjacent odd primes. Then $x+y = 2a$, $a\in\mathbb{Z}$.
$x<y \Rightarrow 2x<x+y<2y \Rightarrow 2x<2a<2z \Rightarrow x<a<y$
How $x$ and $y$ are adjacent primes, then $a$ is not prime. Suppose $a=b\cdot c$, with $b, c>1$.
So $x+y = 2\cdot b\cdot c$. Therefore $x+y$ has at least 3 prime factors
