Question

A list consists of the following pairs of numbers: $(41,43),(45,47),(49,51),(51,53),(55,57),(63,65),(67,69),(71,73)$Categorise them as pairs of co-prime or twin prime numbers.

Answer 1

Co-prime:-Two numbers are said to be co-prime if they do not have any common factor other than $1$.

Twin prime:-Pairs of prime numbers having a difference of 2 are called twin primes.

Co-prime	Twin prime
$\left(41,43\right)$	$\left(41,43\right)$
$\left(45,47\right)$	$\left(71,73\right)$
$(49,51)$
$\left(51,53\right)$
$\left(55,57\right)$
$\left(63,65\right)$
$\left(67,69\right)$
$\left(71,73\right)$

Hence, from all given pairs of number only $\left(41,43\right)$and $\left(71,73\right)$ are twin prime all pairs are co-prime.