Problem #35
Difficulty: 5%
Circular Primes
Solution Language: Java
Problem Statement
The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.
There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.
How many circular primes are there below one million?
Approach
The solution involves:
- Generating all prime numbers below one million using Sieve of Eratosthenes
- For each prime, generating all rotations of its digits
- Checking if all rotations are also prime
- Counting all numbers that satisfy the circular prime property