Question

Give three pairs of prime numbers whose difference is $2$ . [Remark: Two prime numbers whose difference is $2$ are called twin primes].

Answer 1

Hint: Write all prime numbers and select the prime numbers whose difference is $2$ .Try it.

Complete step by step answer:
So first of all prime numbers, In simple language prime numbers are those numbers which do not come in tables example $2$,$3$,$5$ etc. which does not come in table.
So first we know about factors, numbers which multiply together to get another number is called a factor.
Multiplying two whole numbers gives a product. The numbers that we multiply are the factors of the product.
Example: $2$ and $3$ are factors of $6$ , because $2\times 3=6$ .
The number $1$ is the smallest factor of every number.
Every number will have a minimum of two factors, $1$ and the number itself.
A number that has only two factors, $1$ and the number itself, is called a prime number.
So prime numbers do not have any factors.
But a prime number can be a factor such as $2\times 3=6$ Where $3$ is a prime number.
So prime numbers do not have a factor but prime numbers can be a factor.
So here we have to find three pairs of prime numbers which have a difference of $2$ . That is we want to find Twin primes.
So let us draw a table $1$ to $100$ so that we can find the Twin primes.

$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$11$	$12$	$13$	$14$	$15$	$16$	$17$	$18$	$19$	$20$
$21$	$22$	$23$	$24$	$25$	$26$	$27$	$28$	$29$	$30$
$31$	$32$	$33$	$34$	$35$	$36$	$37$	$38$	$39$	$40$
$41$	$42$	$43$	$44$	$45$	$46$	$47$	$48$	$49$	$50$
$51$	$52$	$53$	$54$	$55$	$56$	$57$	$58$	$59$	$60$
$61$	$62$	$63$	$64$	$65$	$66$	$67$	$68$	$69$	$70$
$71$	$72$	$73$	$74$	$75$	$76$	$77$	$78$	$79$	$80$
$81$	$82$	$83$	$84$	$85$	$86$	$87$	$88$	$89$	$90$
$91$	$92$	$93$	$94$	$95$	$96$	$97$	$98$	$99$	$100$

So let us select the conjugate prime numbers so that we can make a difference $2$ .
We can see the numbers are,
$3$ and $5$
$5$ and $7$
$11$ and $13$
$17$ and $19$
$41$ and $43$
$71$ and $73$
So these are the twin primes whose difference is $2$ .
As mentioned in question we can select any three pairs,
Let us select first three pairs
$3$ and $5$
$5$ and $7$
$11$ and $13$

So the above are the three pairs whose difference is $2$ .

Note: So here we have drawn a table because it gets easy to find the twin primes. These are the basic things you must know. Here you can take any of the pair. It does not mean that the first three pairs are given as an answer, you can select any of them.