Let $a$, $b$, $c$, $d$ be distinct prime numbers such that:
- $a + b + c + 18 + d$,
- $a + b + c + 18 - d$,
- $b + c$,
- $c + d$

are also distinct prime numbers. Given that $a + b + c = 2010$, $a$, $b$, $c$, $d \neq 3$, and $d \leq 50$, find the maximum value of the difference between two of these prime numbers.

Let's think step by step and output the final answer within \boxed{}.
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