Hey folks,

So as part of my grad class we have a math question to answer every week. We can seek outside opinions from anywhere we choose (so I’m not cheating 😉 ) so I figured I’d throw it up on here in case anyone wants to geek out with me every week.

This week’s question:

Consider the set of even numbers = {2, 4, 6, 8, 10, 12,…}. If these were the only numbers in our world, which do you think should be the prime numbers?

Hopefully I’ll see you in the comments!

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Ooooh, that’s cool. I’ll bite. I think it would be only the numbers that are STRICTLY divisible by powers of 2 and itself: 2, 4, 8, 16, ….. all other even numbers would be “composite”: 6, 10, 12, 14, 18, …. but I’ll have to think about it some more.

That is interesting – I think I’m leaning towards numbers that are only divisible by 2 and themselves, but factors have to be numbers that exist in the even number set. Which makes 4, 6, 10, 12, 14, 18… prime.

But, I feel like I’m missing something.

I agree with your interpretation, except that 12=2*6 should not be prime. So it turns out every number 2*(odd primes to any power), with only a single factor of 2, will be prime (as well as 4).

12 is not prime, you’re right… Thanks Nick.

Ackh! Now that you mention it, that does sound more reasonable. I wasn’t thinking that 3,5,7,… were not even numbers in this new world order. I think I like your answer better.