Anumber greater than 1000 whose prime factorization contains one prime number that does not repeat one prime number that repeats three times and one prime number that repeats twice

Consider the prime factorization of 1000:



We see that the prime factorization of 1000 contains 5 repeating three times and 2 repeating three times.

We can keep 5 repeating 3 times, 

We can write a prime whose square is larger than , for example: 

Then we can write any prime which does not repeat, for example 2.

Thus the number we formed is 

12,250