Question

What are twin-primes? Write all pairs of twin prime between $50$ and $100$.

Answer 1

Hint: According to the question we have to determine the twin-primes and explain the twin prime and then we have to write all the twin prime numbers in between $50$ and $100$ as given in the question. So, first of all we have to understand about the twin-primes which is as explained below:
Twin-primes: A twin prime is a prime number which can be either $2$ more or $2$ less than the another prime number and if we take an example so, if $41$ is a given prime number and if we add $2$ more to the given prime number which is $41$ we will get the another prime number which is $43$ or we can say that $41$ and $43$ are twin prime numbers because $43$ is $2$ more than the prime number $41$.
In other words we can also say that the twin prime number is a prime number that has a prime gap of two and it can be more than $2$ or less than $2$. Some-times the twin prime is used for a pair of twin primes; an alternate name for this is prime pair or twin prime.
Now, as we have understood about the twin prime numbers we have to check for those pairs one by one.

Complete step-by-step solution:
Step 1: First of all we have to check for the twin-primes in between $50$ to $60$ and the prime numbers in between are $53$, and $59$ , so there are no such pairs.
Step 2: Now, we have to check for the twin-primes in between $50$ to $70$ and the prime numbers in between are $53,59,61$ and $67$. Hence, there is only one such twin-pair which is $59,61$
Step 3: Now, we have to check for the twin-primes in between $50$ to $80$ and the prime numbers in between are $53,59,61,71,73$ and $79$. Hence, there is only one such twin-pair which is $71,73$
Step 4: Now, we have to check for the twin-primes in between $50$ to $100$ and the prime numbers in between are $53,59,61,71,73,79,83,89$ and $97$. Hence, there is no such twin-pair.

Hence, we have obtained all the twin-primes pairs in between $50$ and $100$ which are $59,61$ and $71,73$.

Note: Two primes become increasingly rare as one examines larger ranges, in keeping with the general tendency of gaps between adjacent primes to become larger as the numbers themselves get larger.
A twin prime is a prime number which can be either $2$ more or $2$ less than the other prime number.