Number Pyramids

A number pyramid is created such that the number in the pink triangle is equal to the sum of pairwise products of the 3 neighboring numbers in yellow triangles. For instance, in the left pyramid above, \(11 = 1\cdot 2 + 2\cdot 3 + 3\cdot 1\).

The right pyramid has number \(4\) on top and \(1,3,5,7,9\) in the remaining 5 yellow triangles.

If each of \(a, b, c\) in the pink triangles is a composite number, compute \(a+b+c\).

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