Java Programs›Numbers›Check Circular Prime

Check Circular Prime in Java

intermediate· Numbers · Number Theory

Problem

A circular prime is a prime number where every rotation of its digits — moving digits from the front to the back — produces another prime number.

Given a number, determine whether it is a circular prime.

Input

197

Output

Circular prime: true

Java Program

Java

public class CircularPrimeCheck {
    static boolean isPrime(int n) {
        if (n < 2) return false;
        for (int i = 2; (long) i * i <= n; i++) {
            if (n % i == 0) return false;
        }
        return true;
    }

    public static void main(String[] args) {
        int n = 197;
        String digits = String.valueOf(n);
        boolean isCircular = true;

        for (int i = 0; i < digits.length(); i++) {
            String rotated = digits.substring(i) + digits.substring(0, i); // moves the first i digits to the end
            if (!isPrime(Integer.parseInt(rotated))) {
                isCircular = false;
                break; // found a non-prime rotation, no need to check the rest
            }
        }

        System.out.println("Circular prime: " + isCircular);
    }
}

▶ Run Code

Output

Circular prime: true

Core Logic

Generating every rotation of the number's digits as a string, and checking that each one is prime, confirms the circular property directly.

How It Works

1digits holds the number's digits as a String, so they can be sliced and rearranged easily.
2For each rotation index i, digits.substring(i) + digits.substring(0, i) builds the digits moved i places, wrapping the front around to the back.
3Each rotated string is parsed back into an int and tested with the same square-root-bound isPrime() check.
4The first rotation that fails primality sets isCircular to false and exits the loop immediately with break.

For 197, the three rotations are 197, 971, and 719 — all three are prime, so isCircular stays true.

💡

Key Point: Every rotation of a number has the same digits, just reordered, so this only ever needs to check as many rotations as the number has digits — a 3-digit number needs exactly 3 checks.

Complexity

Time Complexity: O(d × √n)Space Complexity: O(d)

Why: Each of the d digit-rotations gets its own O(√n) primality check, and building each rotated string costs space proportional to the number of digits.

Key Concepts

digit rotationString.substring()early exit with break

Approach 2: Java 8

Java

import java.util.stream.IntStream;

public class CircularPrimeCheckStream {
    static boolean isPrime(int n) {
        if (n < 2) return false;
        return IntStream.rangeClosed(2, (int) Math.sqrt(n)).noneMatch(i -> n % i == 0);
    }

    public static void main(String[] args) {
        int n = 197;
        String digits = String.valueOf(n);

        // Every rotation of the digits must itself be prime
        boolean isCircular = IntStream.range(0, digits.length())
            .mapToObj(i -> digits.substring(i) + digits.substring(0, i))
            .allMatch(rotated -> isPrime(Integer.parseInt(rotated)));

        System.out.println("Circular prime: " + isCircular);
    }
}

▶ Run Code

Output

Circular prime: true

Core Logic

The same rotate-and-check idea can be expressed as a stream — map each rotation index to its rotated number, and require every one to be prime.

How It Works

1IntStream.range(0, digits.length()) generates every rotation index.
2.mapToObj(i -> digits.substring(i) + digits.substring(0, i)) maps each index to its rotated digit string, the same formula the loop version uses.
3.allMatch(rotated -> isPrime(Integer.parseInt(rotated))) parses and primality-checks every rotation, requiring all of them to pass.

For 197, the stream generates "197", "971", and "719", and allMatch() confirms all three are prime.

💡

Key Point: allMatch() short-circuits at the first non-prime rotation found, the same early-exit behavior as the loop's break.

Complexity

Time Complexity: O(d × √n)Space Complexity: O(d)

Why: The stream still builds and primality-checks each of the d rotated strings, the same total work as the manual loop.

Key Concepts

StreamIntStream.range()allMatch()

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