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\(abcdefghijklmnopqrstuvwxyz\) in base 36, when converted to base 10, is a large number with many digits that are prime. If these prime digits, when multiplied, form a number A, find the sum of all the prime factors of the sum of the digits of A.

Details and Assumptions

-If the number is 1234567654321 then we will proceed like this - \(2 \times 3 \times 5 \times 7 \times 5 \times 3 \times 2 = 6300\) (This is A in the question). Sum of digits=9. Prime factors=3 and 3. Their sum=3+3, so answer here is \(\boxed{6}\).

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