Is 10003 a prime number?

The number 10003 has only two factors, which are 1 and 10003 itself. Therefore, the number 10003 is a prime number.

A number to be a prime number should follow the criteria that it should not have factors more than 2. Here, 10003 has exactly 2 factors, making it a prime number.

Given below are a few ways that can be used to find prime or composite numbers.

The different methods we can use to check if a number is a prime number are explained below.

1. Counting Divisors Method
2. Divisibility Test
3. Prime Number Chart
4. Prime Factorization
    

For the counting divisors method, it is to be checked whether the number is divisible by any numbers other than 1 and the number itself.

The counting divisors method for 10003 would simply be

Divisors of 10003 = 1, 10003
Number of divisors = 2

Since 10003 has only two divisors, it can be considered a prime number.
 

In the division test, we try to divide the number by any of the prime numbers. If we cannot, then it is considered a prime number.

In the divisibility method, the prime number only has 2 divisors, which are 1 and itself.

The divisors of 10003 are 1 and 10003.

Thus, 10003 consists of 2 factors that divide it completely without any remainder.
 

The prime number chart is the list of prime numbers starting from 2 to infinity.

The list of prime numbers under 100 is;

2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

10003 is not in this list, but it is still a prime number as it is greater than 100 and has no divisors other than 1 and itself.
 

This method is only used for a non-prime number/composite number. Since 10003 is a prime number, it does not have any prime factors other than 10003 itself.

Factors of 10003 = 1 × 10003
 

• Prime Number: A natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. For example, 2, 3, and 5 are prime numbers. 10003 is a prime number because it has no divisors other than 1 and 10003.

• Divisibility: A number is divisible by another if it can be divided by it without leaving a remainder. To check if a number is prime, divisibility tests are performed by dividing the number by smaller prime numbers.

• Divisors: The numbers that divide a given number exactly, without leaving a remainder. For 10003, the only divisors are 1 and 10003 itself, indicating it is prime.

• Prime Factorization: The process of breaking down a number into its prime factors. Since 10003 is a prime number, its prime factorization is just 1 × 10003.

• Composite Number: A natural number greater than 1 that has more than two divisors. Unlike prime numbers, composite numbers can be divided by numbers other than 1 and themselves. 10003 is not a composite number.