Question

What is an example of a twin prime number ?
A. $3,8$
B. $11,13$
C. $23,24$
D.$75,79$

Answer 1

Hint- To get to grips with this problem first we have to define the term twin prime numbers further we will discuss its properties and will decide the appropriate prime pair accordingly.

Complete step-by-step solution -
Two prime numbers are considered twin primes, if only one composite number is present between them. Or we can also call twin primes as two prime numbers whose difference is two. For instance, $(3,5)$ are twin primes because the difference between the two numbers is $5 - 3 = 2$. The alternate names given to twin primes are twin or prime pair twins.
Prime pair key properties:
• $(2,3)$ are not known to be twin primes, because there is no composite number between them, and the difference between the two primes is not $2$.
• $5$ is a prime number only available in two separate pairs
Any other prime pair$(3,5)$ is in the form of $(6n - 1,6n + 1),$where n is any natural number.
• The sum of each prime pair is divisible by $12$, apart from $(3,5)$.
The given option $(11,13)$ is correct by taking the help of the above properties
Owing to the discrepancy between the two prime numbers being equal to $2$ and the sum of both prime numbers being divisible by $12$.
Therefore option B is the correct one.

Note- A twin prime is a prime number that is either $2$ less or $2$ more than another prime number — either member of the twin prime pair, for example. In other words, a twin prime is a prime with a prime difference of two.