Near Goldbach Alphametics II (Posted on 2011-01-07)

(A) In this alphametic, each small letter in bold represents a different base x digit from 0 to x-1. None of the numbers can contain any leading zero.

prime + prime = number, whenever each of prime and number – 1 is a prime number.

Determine the minimum value of x for which this is possible. What is the next smallest value of x?

(B) Keeping all the other conditions in (A) unaltered, if number + 1 is a prime number (rather than number – 1), then what is the minimum value of x for which this is possible? What is the next smallest value of x?