What is a number greater than 1,000 whose prime factorization contains 1 prime number that does not repeat, 1 prime number that repeats three times, and 1 prime number that repeats twice

You could just fill in the spaces.

So for the prime number that doesn't repeat, you can just say a random prime number, say like 7.

For the prime number that repeats 3 times, say like 11.

And the prime number that repeats twice, you can just say something like 13.

Then it would be 7 * 11 * 11 * 11 * 13 * 13, which the solution would be 1,574,573, above 1000.