All strange numbers are prime. Every one digit prime number is
strange and a number of two or more digits is strange if and only
if so are the two numbers obtained from it by omitting either its
first or its last digit. Find all strange numbers.
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
Weekly Problem 45 - 2013
How many pairs of numbers of the form $x$, $2x+1$ are there in which both numbers are prime numbers less than $100$
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.