Peter's primes

Peter wrote a list of all the numbers that can be formed by changing one digit of the number 200. How many of Peter's numbers are prime?
Age
14 to 16
Challenge level
filled star empty star empty star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



Peter wrote a list of all the numbers that can be formed by changing one digit of the number $200$. How many of Peter's numbers are prime?

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