Question 423102: what is the largest four-digit number whose cube root is a prime number?
answer: 6859
but I don't understand how you get that answer?
thx!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 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:  , which is indeed prime (because we set it up that way)
If you need more help, email me at jim_thompson5910@hotmail.com
Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you
Jim
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