I tend to teach 5th graders math ever so often just so they can be "friendly" with math in a playful manner, instead of being afraid.
However, one question that I constantly struggle with is this: Why should we care if a number is prime or not?
Coming from a computing background I try my best to explain to them the use of prime numbers in cryptography and how primes are related to factorization (as kid friendly an explanation as possible). However, they "sigh" and move on with the belief that I'm telling the truth. But, they still don't seem to get excited about it.
Answers for questions like these: Real-world applications of prime numbers? don't seem to be well suited for 5th graders.
What are some interesting ways/examples that one can use to help 5th graders understand why the study/knowledge of primes is useful? Bonus if they can "see the use" sooner in their 10 year old lifespan instead of waiting till college.
I'm okay even conjuring "games" to help them learn/understand. For example, currently I'm trying to use something like Diffie Hellman Key Exchange to make a game for them to encode messages and see if "eavesdroppers" (i.e., other students) can guess the message. Something on the lines of Alice wants to send Bob a number that she's thinking about. Other students have to guess what that number is. The number can be 'encoded' (loosely speaking) as a manipulation of numbers similar to the key exchange protocol, but that 5th graders can play around with. Hopefully the 'decoding' process shows them why it's better to choose primes. However, this could be rather abstract. That's the best I've got for now.
Any other ideas?