The numbers '$13$‘ and ’$31$‘ are prime numbers. Both these numbers have the same digits ’$1$‘and ’$3$‘. Find such pairs of prime numbers up to ’$100$'.

Prime Numbers: Prime numbers are the positive integers having only two factors, $1$ and the number itself.

• $1$ is neither a prime number nor a composite number.
• The only even prime number is '$2$'.
• No prime number greater than '$5$‘ ends in a ’$5$'.

Pairs of prime numbers having the same digits are:

$17$ and $71$

$37$ and $73$

$79$ and $97$

Therefore, there are '$3$‘ such pairs under ’$100$'.