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Pairing off so that sum is a prime

Source: Pan African Olympiad 2010

October 1, 2011
number theoryprime numbersnumber theory proposed

Problem Statement

a) Show that it is possible to pair off the numbers 1,2,3,…,101,2,3,\ldots ,10 so that the sums of each of the five pairs are five different prime numbers. b) Is it possible to pair off the numbers 1,2,3,…,201,2,3,\ldots ,20 so that the sums of each of the ten pairs are ten different prime numbers?
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