Question 423102
Let's start off by listing the prime numbers:


Primes: 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, 33, ...



Now let's cube each prime in that list. So 2^3 = 8, 3^3 = 27, 5^3 = 125, etc. I'm going to list the cubes of each prime below


Cubes of each prime above: 


8, 27, 125, 343, 729, 1331, 2197, 4913, 6859, 12167, 24389, 29791, 35937, ...


Note: 33^3 = 35937



Now all we need to notice is that 6859 is the largest 4 digit number of this list. The next largest cube of a prime is 12167, but that is 5 digits.



So 6859 is the largest 4 digit number whose cube root is a prime number.



Note: {{{root(3,6859)=19}}}, which is indeed prime (because we set it up that way)



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