Prime and Composite Numbers are subsets of Natural Numbers based on divisibility. A prime number is divisible by only 1 and itself and a composite number is divisible by one or two more other
Every natural number, except 0 or 1, is either prime or composite.
Prime Numbers vs Composite Numbers
The following table lists five differences between a prime and composite number:
| Prime Numbers | Composite Numbers |
|---|---|
| All the natural numbers greater than 1 that have only two factors - one and the number itself are called prime numbers. | All natural numbers that can be expressed as a product of at least two smaller natural numbers are known as composite numbers. |
| Prime numbers have exactly two factors - 1 and the number itself. | Composite numbers have at least 3 or more factors. |
| All the prime numbers except 2 are odd numbers. | There is no such pattern for composite numbers. They can be odd or even both. |
| Their prime factorization has only one prime factor i.e., the number itself. | Their prime factorization has one or more other prime factors. For example, 49 has a prime factor of 7 and |
The product of two prime numbers is a composite number | The product of two composite numbers is also a composite number |
| Examples: 2, 3, 5, 7, ... | Examples: 4, 6, 8, 9, 10, ... |
Prime and Composite Numbers Chart
A prime and composite numbers chart is a table that lists all the numbers from 1 to 100 and identifies them as either prime or composite. Here is the prime and composite numbers chart
Tests for Prime and Composite numbers
We can use below quick steps.
- If the given number is 0 or 1, then it is neither prime not composite.
- If a number is even and not 2, then it is composite
- For other cases, a simple way is to find all divisors of a given number and check if the divisors are other than 1 and the number itself. If there are other, then the number is composite, else prime.
Also Check:
Important Facts about Prime and Compsite Numbers
- The number 2 is the only even prime number. All other even numbers can be divided by 2, making them composite. This uniqueness makes 2 particularly interesting in number theory​.
- Twin primes are pairs of prime numbers that differ by 2, such as (3, 5) and (11, 13). It is conjectured that there are infinitely many twin primes, although this has yet to be proven​
- The product of two prime numbers is always a composite number.
- All other prime numbers, with the exception of two and three, are either 6n+1 or 6n-1
- The smallest composite number is 4, as it can be divided by 1, 2, and 4. Every composite number can be factored into prime numbers
- All even numbers greater than 2 are composite, as they can be divided by 2. This property highlights a simple way to identify composite numbers within a specific range.
- Every composite number can be expressed as a product of prime numbers in a unique way (up to the order of factors), which is known as its prime factorization.
Read More:
Practice Questions on Prime and Composite Numbers
Here are some practice questions/problems based on prime and composite numbers:
1. Is 1 a composite number?
2. Check whether 23 is a prime number.
3. Check whether 56 is a prime number.
4. Check whether 2779 is a prime number. (Hint: Use Efficient Primarility Test)
5. Use Eratosthenes sieve to find all the prime numbers from 1 to 100.
6. Find the prime factors of 69.