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arranging no around a circle such 2 neighbours of 1,2,..,13 have prime sum

Source: Greece JBMO TST 2006 p1

June 16, 2019
number theoryprime numbersCircular arrayprime

Problem Statement

a) Is it possible to arrange numbers 1,2,...,131,2,...,13 in a circumference such that the sum of any two neighbouring numbers to be a prime number? b) Is the same problem possible for the numbers 1,2,...,161,2,...,16?
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