
EXAMPLE

For any set of n elements, there are 2^n  1 nonempty subsets.
For n=3, consider the set {7, 19, 67}.
The averages of the 2^3  1 = 7 nonempty subsets are:
avg({7}) = 7
avg({19}) = 19
avg({67}) = 67
avg({7, 19}) = 13
avg({7, 67}) = 37
avg({19, 67}) = 43
avg({7, 19, 67}) = 31
All these averages are different primes, and no such set exists with the largest element < 67. Hence, a(3) = 67.
Sets which minimize the largest elements are:
n = 1 {2}
n = 2 {3, 7}
n = 3 {7, 19, 67}
n = 4 {5, 17, 89, 1277}
n = 5 {209173, 322573, 536773, 1217893, 2484733}
