Is 3163 a Prime Number?

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, which is 1.

As 3163 has exactly two factors, it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 3163 has exactly 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 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 3163 is prime or composite.

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

Step 2: Divide 3163 by numbers starting from 2 up to the square root of 3163 (approximately 56.2).

Step 3: Check divisibility by 2, 3, 5, 7, and other primes up to 56. None of these numbers divide 3163 evenly.

Since 3163 is not divisible by any number other than 1 and itself, 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: The number in the ones' place value is 3. Since 3 is odd, 3163 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 3163 is 13. Since 13 is not divisible by 3, 3163 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 3. Therefore, 3163 is not divisible by 5.

Divisibility by 7, 11, 13, and other primes up to 56: Testing divisibility by these primes, none divide 3163 without a remainder.

Since 3163 is not divisible by any primes 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 range (for example, 1 to 1000).

Step 2: Leave 1 without coloring or crossing, 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 until you reach the table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers up to 1000.

3163 is not within this range but can be checked similarly, confirming it as a prime number.

Prime factorization is a process of breaking down a number into prime factors. Then multiply those factors to obtain the original number.

Step 1: Attempt to divide 3163 by the smallest prime, 2. It is not divisible as it is odd.

Step 2: Continue trying to divide by the next smallest primes like 3, 5, 7, etc., up to the square root of 3163.

Step 3: Since no division results in a whole number other than 1 and 3163 itself, 3163 cannot be factored further.

Therefore, 3163 is a prime number.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves.
  
   
• Composite numbers: Natural numbers greater than 1 that are not prime because they have more than two factors.
  
   
• Divisibility rules: Guidelines to determine if a number can be divided by another number without a remainder.
  
   
• Co-prime numbers: Two numbers having no common factors other than 1.
  
   
• Sieve of Eratosthenes: An ancient algorithm to find all prime numbers up to any given limit.