I finally got around to check GOG again yesterday. Added a few new releases to my wishlist and purchased a few, including Still Life 2. I really enjoyed SL1 so I thought I'd make a nice distraction from what's commonly referred to as 'life'. I kind of regretted it after adding it to the downloader, though - it's about 10GB and my internet connection isn't very good at the moment.

So, while wasting time watching the MB's slowly trickle in, I noticed that I'd been a member here for 799 days. Which, of course, that being yesterday, means that I've been a member here for 800 days today. Still in a kind of watching-the-washing-machine-going-round-and-round-with-mild-interest mood, I started thinking about the number 800. Factorise it and you get 2^5 times 5^2. That's a kind of symmetry I find mildly amusing. Most likely completely useless information, hence perfect for a small give-away:

There is a number N that is the product of A^B (that is, A to the power of B) times B^A, where both A and B are prime numbers and A is smaller than B. Given A=2 and B=5, N=800. The digital root of 800 is 8+0+0 = 8. The next larger N is 6272, which is 2^7 * 7^2. The digital root of 6272 is also 8. What is the next larger N that satisfies the above and also has a digital root of 8?

The first person to post the correct values for A, B and N gets a game of his/her choice (except TW2 - sorry).

In case of no correct answers before I've finished downloading SL2 (about 10 hours left right now, but I'll have to pause it now and then), the winner will be the first to 'explain' the topic subject.

You might ant to re-calculate, your second number doesn't go perfectly to 8

I would say: 42?

In any case: I found A=3, B=5, N = 640000. N squares down into 800, where the digital root is 8.

Edit: I think I'm getting confused. Give me a bit.

Your answer is, indeed, right. It's pH7's question that is wrong.

How is digital root of of 6272 also 8?

6+2+7+2 = 17
1+7 = 8

Oh, ok thanks. Apparently, I misunderstood what "digital root" was. :)

nvm, can't count ;)

I've just found it also.

But 5 and 13 seems to be better suited: 4+5+3+2+3+8+5+2+5+3+9+0+6+2+5 = 6+2 = 8

I have it figured out. 6+2+7+2 = 17, 1+7 = 8

And I have the answer too now.

N = 4437573632. A = 2, B = 23. The sum of N is 44, 4+4 is 8


It's not 2 and 13 because you get 28, sum that is 10

That's why I edited. :)

7^11 * 11^7 = 38532504363714053 digital route is 8.
Probably not the smallest N, but I think it's the smallest A & B.

Yeah. that's why I removed my answer. Found an error in the script ;)

Ah, didn't spot the edit. I'm not sure your new answer is right either though. I got different values in my calculator and it only goes up to 9 decimals. I tried to stay to only numbers that didn't have an exponential since it's freaking hard to get the other decimals.