Input a number to check if it is a Permutable Prime or enter a start and end range to generate all Permutable Primes within that range.
A Permutable Prime, also known as a rearrangeable prime, is a unique type of prime number. It is defined as a prime number that remains a prime no matter how its digits are rearranged. For example: The number 13 is a prime. Rearranging its digits gives 13 and 31, both of which are also prime. Therefore, 13 is a Permutable Prime.
Some common Permutable Primes include: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 199, 311, 337, 373, 733, 919, and 991.
To check if a number is a Permutable Prime or generate all Permutable Primes within a range, follow these steps:
Solution:
1. Initial prime check:
Verify that 113 is a prime number.
2. Generate permutations:
The permutations of 113 are: 113, 131, and 311.
3. Check primality of permutations:
All permutations (113, 131, 311) are prime.
Result: 113 is a Permutable Prime.
Solution:
1. Initial prime check:
Verify that 197 is a prime number.
2. Generate permutations:
The permutations of 197 are: 197, 179, 971, 917, 719, and 791.
3. Check primality of permutations:
Among these, 917 and 791 are not prime.
Result: 197 is not a Permutable Prime.