# So many primes

We are given three integers $$a, b,$$ and $$c$$ such that $$a, b, c, a+b-c, a+c-b, b+c-a,$$ and $$a+b+c$$ are 7 distinct primes. Let $$d$$ be the difference between the largest and smallest of these 7 primes. Suppose that $$800∈{a+b, b+c, c+a}.$$ Determine the maximum possible value of $$d$$.

• From a reviewer
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