Find the largest number of the form which is the product of three distinct prime numbers and both the numbers of the form and are primes
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We want A A B B to be as big as possible, so we will start testing values that make A A B B as large as possible. The three requirements are: A A B is prime, A A B is prime, A A B B is product of three primes. (If one of the requirements is not met, I will skip the rest, because it won't matter). We can immediately skip all of the scenarios where B is even, because A A B or A B B will never be prime.
Therefore, the largest number that fits all three requirements is 9 9 1 1 .