A book called The Penguin Dictionary of Curious and Interesting Numbers by David Wells (1986) contains fascinating numbers and their properties. One of which is the only 3-digit numbers that are prime and all rearrangements of their digit are also prime are 113,119, and 337. Find the 2-digit numbers that also have this property.

11 - 11

13 - 31
17 - 71
19 - 91
37 - 73
I am getting bored, you keep going

To find the two-digit numbers that have the property of being prime and having all rearrangements of their digits also being prime, we can follow these steps:

1. Generate a list of all two-digit numbers.
2. Check if each number in the list is prime.
3. For each prime number found, generate all possible rearrangements of its digits.
4. Check if each rearrangement is also prime.
5. Compile a list of prime numbers where all rearrangements are also prime.

Let's go through the steps to find the two-digit numbers that satisfy these conditions:

Step 1: Generate a list of all two-digit numbers.
We consider numbers from 10 to 99.

Step 2: Check if each number in the list is prime.
To determine if a number is prime, we need to check if it is divisible by any number less than its square root. We can use a simple algorithm such as the trial division algorithm.

Step 3: Generate all possible rearrangements of each prime number.
For a two-digit number, we have only two possible rearrangements: switching the order of the digits.

Step 4: Check if each rearrangement is also prime.
Apply the same prime-checking algorithm to each rearrangement.

Step 5: Compile a list of prime numbers where all rearrangements are also prime.
Collect all the two-digit prime numbers that satisfy the condition mentioned above.

Now, let me perform these steps and provide you with the list of two-digit numbers that have the property of being prime and having all rearrangements of their digits also being prime.