1.  A device to check the primality of a number. (Using Arduino)

Idea: Suppose n is a given number. The idea is to check all the prime factors less than the square root of n.  (n < 2147483647)

Code:

 void setup() {

  Serial.begin(9600); // Initialize Serial communication at 9600 bps

  while (!Serial) {

    ; // Wait for serial port to connect (needed for native USB boards)

  }

  Serial.println("Enter a number to check if it is prime:");

}

void loop() {

  // Check if user has entered data in the Serial Monitor

  if (Serial.available() > 0) {

    // Read the incoming integer

    long number = Serial.parseInt();

    // Consume any leftover newline/carriage return characters

    while(Serial.available() > 0) {

      Serial.read();

    }

    // Print the number being evaluated

    Serial.print("Testing number: ");

    Serial.println(number);

    // Call the function and output the result

    if (isPrime(number)) {

      Serial.println("Result: It is a PRIME number.\n");

    } else {

      Serial.println("Result: It is NOT a prime number.\n");

    }

    Serial.println("Enter another number to check:");

  }

}

// Function to check if a number is prime

bool isPrime(long n) {

  // Corner cases

  if (n <= 1) return false; // 0 and 1 are not prime numbers

  if (n <= 3) return true;  // 2 and 3 are prime numbers

  // Exclude even numbers and multiples of 3

  if (n % 2 == 0 || n % 3 == 0) return false;

  // Optimized loop checking up to the square root of n

  // Every prime number can be expressed in the form (6k +/- 1)

  for (long i = 5; i * i <= n; i += 6) {

    if (n % i == 0 || n % (i + 2) == 0) {

      return false; // Found a factor, so it's not prime

    }

  }

  return true; // No factors found, it is prime

}