Is 1013 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.

Since 1013 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 1013 meets this criterion, it is a prime number. Few methods are used to distinguish between prime and composite numbers. Some of these 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 1013 is prime or composite.

1. All numbers are divisible by 1 and itself.

2. Divide 1013 by numbers starting from 2 up to the square root of 1013.

3. None of these numbers divide 1013 exactly, which means 1013 has no divisors other than 1 and 1013. Since 1013 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. Here are some tests:

Divisibility by 2: 1013 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in 1013 is 5, which is not divisible by 3.

Divisibility by 5: 1013 does not end in 0 or 5, so it is not divisible by 5.

Divisibility by 7, 11, etc.: Further divisibility tests up to the square root of 1013 confirm that 1013 is not divisible by any of these numbers. Since 1013 is not divisible by any number 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 these steps:

1. Write numbers in range and apply the sieve method to filter primes.

2. Through this process, we identify prime numbers up to a certain limit.

3. Although 1013 is beyond the basic chart up to 100, further checking confirms its primality through divisibility tests as explained earlier. Since 1013 meets the criteria of having no divisors other than 1 and itself, it is 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. Here’s how it applies to 1013:

1. Attempt to divide 1013 by prime numbers starting from

2 up to its square root. 2. Since no prime number divides 1013 exactly, it has no factors other than 1 and itself.

Therefore, 1013 is a prime number.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and itself.

• Composite numbers: Natural numbers greater than 1 that have more than two divisors.

• Divisibility rules: A set of rules to determine if one number is divisible by another without performing division.

• Sieve of Eratosthenes: An ancient algorithm to find all prime numbers up to a certain limit.

• Prime factorization: The process of expressing a number as the product of its prime factors.