A number that cannot be expressed as the product of two smaller natural numbers and is greater than 1 is called a prime number.
What is Twin Prime Numbers
Composite numbers are defined as those natural numbers that do not fall under the category of primes. Even within prime numbers, we have different types, such as twin prime numbers and coprime numbers. We will study these in the upcoming sections. However, first, let us look at an example of prime numbers. Suppose we have the number 13. The only factors of 13 are 1 and the number itself. Thus, it is a prime number. On the other hand, a number such as 20 has the factors 1, 2, 4, 5, 10, 20. This implies that it is a composite number as it has more than two factors.
What is Twin Prime Numbers
Twin prime numbers are a set of two prime numbers that have only one composite number between them. In other words, if we subtract two prime numbers from each other, the modulus of the difference should be 2 for them to be twin prime numbers. Twin prime numbers are also called prime twins or prime pairs. Examples of twin prime numbers are as follows:
- (3, 5); There is only one composite number 4 between 3 and 5. Additionally, 5 – 3 = 2. Hence, according to the definition, these are twin primes.
- (11, 13); 12 is the composite number while the difference is 2.
- (29, 31); Similarly, 20 is the composite number between these two primes, and their difference is 2.
Properties of Twin Primes
- (2,3) cannot be considered as a twin prime number as they come one after another, and there is no composite number between them. Additionally, the difference between them is 1, not 2.
- The only prime number available in two different pairs is 5. Thus, we have (3, 5) and (5, 7) as twin prime numbers.
- The general form of twin prime numbers is given by (6n – 1, 6n + 1), where n is used to denote any natural number. The only prime pair that does not follow this rule is (3, 5).
- When we add the two numbers belonging to a prime pair, the sum is divisible by 12. However, (3, 5) is the exception to this rule.
What are Coprime Numbers
Coprime Numbers can be defined as a set of integers or numbers that have 1 as their only common factor. In other words, the value of the greatest common factor (GCF) is 1. They can also be termed as mutually prime or relatively prime numbers.
Properties of Coprime Numbers
- The only number that is coprime with all numbers is 1.
- Two prime numbers are always coprime with each other.
- Two successive numbers or integers are always coprime with each other.
- The product of two integers will always be coprime with the sum.
- As all even numbers have a common factor 2, they can never be coprime with one another.
- Any two numbers ending with 0 or 5 in their unit’s place cannot be coprime with one another as 5 will always be a common factor.
Conclusion
Prime numbers are a crucial subject that is used for mathematical research; hence, kids need to build a robust understanding of the foundations. They can do this by turning to an online educational service like Cuemath. Cuemath believes in guiding kids to develop crystal clear concepts so that they can solve the toughest problems within seconds. Children are sure to be successful with Cuemath, and good grades follow!
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