Consider summing the digits of the number 141. We have 1 + 4 + 1 = 6. You might remember the rule that if the "sum of the digits" of some integer N is divisible by 3, then the original integer is also divisible by 3 (in the case 141 = 47 x 3).......

Now instead of determining divisibility by 3, consider the problem of determining the primality of the "sum of the digits" of some integer N that is written in base B.

In particular, consider base B = 7. Under this base, the integer 7 will be represented as 10. The sum of its digits will be 1 + 0 = 1.

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Prove that if an integer N is prime and is written in base 7, then the sum of its digits is always prime (excluding the example 7 above). If it is not true, find a counter-example......