Problem 1. How many three-digit prime numbers can be transformed into perfect cubes by changing the order of their digits?

Mathematical Gazette
Problem 1. How many three-digit prime numbers can be transformed into perfect cubes by changing the order of their digits? Solution

The perfect cubes of three digits are: $125, 216, 343, 512$ and $729 . \ldots \ldots \ldots .1$ p Prime numbers of three digits must end with an odd digit, different from 5, and must not be divisible by 3. Therefore, the sought numbers are among the numbers 251, 521, 433. $3 p$

They are checked and it is found that all three of these numbers are prime. $3 p$

Each incorrect result (false prime number found or prime number omitted) is penalized.