Problem Solution

it's less than $100$;

it's one more than a multiple of $3$;

exactly one of its digits, you get a prime;

if you reverse its digits, you get a prime;

it has exactly four factors;

the sum of its digits is prime;

if you multiply it by $5$, the answer is greater than $100$.

 

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.