The fabulous Zillion bracelet is worth a fortune. It consists of eight exquisite diamonds each mounted on a bracelet segment. The segments are numbered from 1 to 8 starting from one end when the bracelet is undone.
Given the following, how much is the Zillion bracelet worth and what is the arrangement of segments by value?
1) Each segment is worth either two or three zillion dollars.
2) The Zillion bracelet is worth the total value of the segments: n zillion dollars.
3) n is prime.
4) Whether the bracelet is undone or done up (1 next to 8), no three consecutive segments are all of the same value.
5) The greater-value segments are all at prime-number locations.
Submit your answer to Gene Wirchenko <email@example.com>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, January 1, 2014 at noon Pacific Time. I will post the answer shortly after.