originally posted by Weedpacket
And there was much rejoicing.
And what exactly do we do now, eat the minstrels?
I almost burned up a CPU on this one. As you've more/less shown, expressed as a percentage, the probability increases several % for each power of 10 with a decrease in the increase as n is increased ... a 19% chance out of 100, 27.1% in 1000, 34.39% in 10,000, 40.951% out of 100,000, 46.856% (rounded) in 1,000,000, 52.17% in 10,000,000 and after that it got boring sitting around waiting for the 100 million computation to finish, as I don't have a Cray, or even a Beowulf cluster. I guess if I'd been downloading a big file, I could have waited ... might have been interesting to see what would happen when PHP got up to 90% or more of CPU.....
Based on this, I'd have to guess that for an infinitely large natural number nnn..., you're gonna have a repeating decimal nine, a la 99.99999...% chance....
I'm pretty sure that that's what your regexp says, isn't it? Thanks for the enlightenment. Makes me wish I'd learned much more mathematics much earlier in life.
Hmm, punchline[?]: Merve was almost right for numbers close to infinity; or, perhaps "Is there an odd perfect number?"