# Problem 518: Prime triples and geometric sequences
Let S(n) = Σ a+b+c over all triples (a,b,c) such that: a, b, and c are
prime numbers. a < b < c < n. a+1, b+1, and c+1 form a
geometric sequence. For example, S(100) = 1035 with the following
triples: (2, 5, 11), (2, 11, 47), (5, 11, 23), (5, 17, 53), (7, 11, 17),
(7, 23, 71), (11, 23, 47), (17, 23, 31), (17, 41, 97), (31, 47, 71),
(71, 83, 97) Find S(108).