There are two types of numbers, mostly —

Prime numbers and composite numbers, depending on the number of factors.

A prime number is a natural number that is divisible only by 1 and itself.

For example, 3 is a prime number because it is divisible by 1 and itself.

A composite number is a positive number that is divisible by more than two numbers.

For example, 6 is divisible by 1, 2, 3, and 6, making it a composite number.

Prime numbers follow a few properties like: 

• Prime numbers are positive numbers always greater than 1. 
   
• 2 is the only even prime number. 
   
• They have only two factors: 1 and the number itself.
   
• Any two distinct prime numbers are co-prime numbers because they have only one common factor that is 1.
   
• As 593 has only two factors, it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 593 has only two factors, it is a prime number. Few methods are used to distinguish between prime and composite numbers. A few methods are: 

• Counting Divisors Method 
   
• Divisibility Test 
   
• Prime Number Chart
   
• Prime Factorization

The method in which we count the number of divisors to categorize the numbers as prime or composite is called the counting divisors method. Based on the count of the divisors, we categorize prime and composite numbers. - If there is a total count of only 2 divisors, then the number would be prime.  If the count is more than 2, then the number is composite. Let’s check whether 593 is prime or composite.

Step 1: All numbers are divisible by 1 and itself.

Step 2: Divide 593 by 2. It is not divisible by 2, so 2 is not a factor of 593.

Step 3: Divide 593 by 3. The sum of the digits of 593 is 17, which is not divisible by 3, so 3 is not a factor.

Step 4: Continue checking divisibility with primes like 5, 7, 11, etc., up to the square root of 593 (approximately 24.35).

Since 593 is not divisible by any of these primes, it is concluded that 593 has only two factors: 1 and 593. Since 593 has only 2 divisors, it is a prime number.

We use a set of rules to check whether a number is divisible by another number completely or not. It is called the Divisibility Test Method. 

Divisibility by 2: 593 is not even, so it is not divisible by 2. 

Divisibility by 3: The sum of the digits of 593 is 17, which is not divisible by 3. 

Divisibility by 5: The unit digit of 593 is 3, so it is not divisible by 5. 

Divisibility by 7: By performing the divisibility check for 7, 593 is not divisible by 7. 

Divisibility by 11: The alternating sum of digits is not divisible by 11.

Since 593 is not divisible by any numbers other than 1 and itself, it is a prime number.

The prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.” In this method, we follow the following steps.

Step 1: Write numbers in a sequence up to a certain point.

Step 2: Leave 1 without marking, as it is neither prime nor composite.

Step 3: Mark 2 because it is a prime number and cross out all the multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all the multiples of 3.

Step 5: Repeat this process with subsequent numbers to identify primes.

Through this process, we will have a list of prime numbers. 593 appears in the list of prime numbers, confirming it is prime.

Prime factorization is the process of breaking down a number into its prime factors. Since 593 is not divisible by any prime number other than 1 and 593, it cannot be factored further into other primes. Therefore, 593 is a prime number.

•  Prime numbers: Natural numbers greater than 1 with no divisors other than 1 and itself, such as 593. 

• Composite numbers: Numbers greater than 1 with more than two factors, such as 12, which is divisible by 1, 2, 3, 4, 6, and 12. 

• Divisor: A number by which another number is divided exactly, leaving no remainder. For example, 1 and 593 are divisors of 593. 

• Divisibility: A property that determines whether one number can be exactly divided by another. 

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.