Question

A number greater than a thousand whos prime factorization contains one prime number that does not repeat, one prime number that repeats 3 times,and one prime number that repeats twice

Answer 1

You can build as many numbers as you like: just pick three primes and repeat them as required.

The only caution is that you have to pick large enough primes to make sure that the result is larger than 1000.

Since $10^3 = 1000$, it is enough that the prime repeating three times is larger than 10.

So, for example, we can pick

• 2, not repeating
• 3, repeating twice
• 11, repeating 3 times

The result is

$2 \times 3^2 \times 11^3 = 23958$