Meaning of twin prime numbers 

What is a Twin Prime Number?

A twin prime is a prime number that is either 2 less or 2 more than another prime number. In other words, the consecutive prime numbers with a difference of two are known as twin prime numbers. For example, (5, 7) are twin primes as 5 and 7 are prime numbers and the difference between them is 2.

Twin Prime Numbers from 1 to 100

The twin prime numbers starting from 1 and ending up to 100 are: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61) and (71, 73). 

Properties of Twin Prime Numbers

  • 2 and 3 are prime numbers yet (2, 3) is not considered a twin prime number because the difference between the two numbers is one. It should also be kept in mind that 2 is the only even prime number that is the difference coming out to be one.
  • Five is the only prime number that is seen in two pairs of the twin primes, (3, 5) and (5,7). Other pairs greater than (3,5) are of the form (6n-1, 6n+1), where n is a natural number. It is clear that the number between two primes is a multiple of 6. Hence, we can say that the sum of any twin primes, except (3, 5), is divisible by 12. 
  • Brun’s theorem has historical importance. It was the first use of the Brun sieve which led to the introduction of modern sieve theory. This theorem was proved by Viggo Brun in 1919. This theorem states that the sum of the reciprocals of the twin primes converges to a finite value known as Brun’s constant, usually denoted by B2.  

What is Twin Prime Conjecture?

As we know that there are infinite numbers. So it is a big question that whether there are infinite pairs of twin primes or there is the biggest pair? This thought that there are infinite pairs of twin prime numbers is known as the twin prime conjecture. It is also known as Polignac’s conjecture in number theory and was introduced by de Polignac in 1849. However, this conjecture remains unsettled till date.

Conclusion 

Prime numbers that differ by two are known as twin prime numbers. The pair (2, 3) is not considered as a twin prime because the difference between the numbers is 1. The sum of any twin primes, except (3, 5), is divisible by 12. Brun’s theorem states that the sum of the reciprocals of the twin primes converges to a finite value known as Brun’s constant. The prime conjecture remains unsolved. Scientists are yet to work on it.