Alex, Max, Primes and whatnot

Logic Level 3

Alex and Max are given two different prime numbers, and the following dialogue ensues:

Alex: I don't know which of our numbers is greater.

Max: Then my number is not the greater one for sure.

What is the largest possible sum of their numbers, provided both the numbers are below 100 (but Alex and Max don't know that 100 is the upper bound)?


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