What are prime numbers?
Prime numbers are numbers that have exactly two positive factors. Factors of any prime number that you may come across will only be two numbers – 1 and the number itself. Some examples of numbers with only such factors, prime numbers, are 3, 5, 7 and 11.
What are composite numbers?
Composite numbers are numbers that have more than two positive factors. In other words, the numbers that don’t belong to the group of prime numbers are composite numbers — except 0 and 1. The numbers 0 and 1 are special numbers that neither belong to prime numbers nor composite numbers. Some examples of composite numbers are 4, 6, 8, 9 and 12.
What are twin prime numbers?
Twin prime numbers are pairs of prime numbers. These prime numbers are 2 less or 2 more than each other, such that there is exactly 1 composite number between them. In other words, the difference between the two prime numbers in a twin prime pair is 2. You can check this using the smallest twin prime pair, (3, 5). In this case, the difference between 5 and 3 is 2. Twin prime numbers are also known as prime twins and prime pairs.
Some examples of twin primes are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139), (149, 151), (179, 181), (191, 193) and (197, 199).
Solved Examples
Example 1: Are 9 and 11 twin prime numbers?
Solution:
9 and 11 are not twin prime numbers despite their difference being 2. This is because though 11 is a prime number, 9 is a composite number. Twin primes have both prime numbers.
Example 2: Does the pair (2, 3) form twin prime numbers?
Solution:
The pair (2 and 3) are not twin prime numbers despite being prime numbers. This is because the difference between 2 and 3 is not 2. Also, there is no composite number between 2 and 3.
Fun Facts
- 5 is the only number that is a part of two twin primes. 5 appears in the twin primes (3, 5) and (5, 7).
- Twin prime numbers are rarer among bigger numbers. It gets more difficult to check for twin primes among bigger numbers. This is because most big numbers are likely to have many factors.
- All twin prime numbers higher than 5, sandwich multiples of 6. So, we can generalize twin primes above 5 as (6n – 1, 6n + 1). This is true only for specific values of n.
- Mathematicians are yet to determine whether there are an infinite number of twin primes. Even though the chances of stumbling upon twin primes reduce with bigger numbers, mathematicians have not proved that there is an end to the list of twin prime numbers. This is known as the twin prime conjecture.
Prime numbers are numbers that have exactly two positive factors: 1 and the number itself. On the other hand, composite numbers have more than two positive factors.
Even though 2 is the smallest prime number, the prime number nearest to 2 is 3. Since the difference between 2 and 3 is not 2 and because they don’t have any composite numbers between them, they don’t form a twin prime. So, the smallest twin pair is (3, 5).
A twin prime is a pair of prime numbers that are 2 less or 2 more than each other. Whereas coprime numbers can be any pair of numbers whose greatest common factor is 1. That means two composite numbers can be coprime numbers if their GCF is 1.
Twin prime numbers are prime numbers that differ by 2. On the other hand, prime triplets are a set of 3 prime numbers in which the difference between the smallest prime number and the biggest prime number is