Question

What are twin-primes ?

Answer 1

Hint: In order to answer the question, to know about the twin-primes, we will explain the term twin-primes with the perfect example related to it. We will also explain the properties of the twin-primes.

Complete answer:
Twin prime numbers are called twin primes if there is present only one composite number between them. Twin primes are twin prime numbers with a twin-digit disparity between them. Since the discrepancy between the twin numbers \[\left( {5-3 = 2} \right),{\text{ }}\left( {3,5} \right)\] is a twin prime. Prime twin or prime pair are some of the other names given to twin primes.

Properties of Twin-primes:-
-Since there is no composite number between them and the difference between the twin primes is not equal to 2, properties of twin primes \[\left( {2,3} \right)\] are not called twin primes. 5 is a single prime number that comes in twin distinct pairs.
-Except for \[\left( {3,5} \right)\] , every prime pair is in the form \[\left( {6n - 1,{\text{ }}6n + 1} \right)\] , where $n$ is any natural number. Except for \[\left( {3,5} \right)\], the number of each prime pair is divisible.

Note:The pair \[\left( {2,3} \right)\] is usually not considered a pair of twin primes. Since 2 is the only even prime, this pair is the only pair of prime numbers that differ by one; like all other twin primes, twin primes are as similar together as possible.