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
×

Problem Loading...

Note Loading...

Set Loading...