MathDB

Consider the set

E = \{5, 6, 7, 8, 9\}

. For any partition

{A, B}

E

, with both

A

and

B

non-empty, consider the number obtained by adding the product of elements of

A

to the product of elements of

B

. Let

N

be the largest prime number amonh these numbers. Find the sum of the digits of

N

Problem Statement