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The Seven Primes (Posted on 20130426) 

Let a, b, c be positive integers such that
a, b, c, a+bc, a+cb, b+ca, a+b+c are 7 distinct primes.
The sum of two of a, b, c is 800.
If d be the difference of the largest prime and the least prime among those 7 primes, find the maximum value of d.
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