## Nailing my life

Some days are just plain motherfucking awesomeness. Like yee-esterday. And by yesterday, I mean the past 30 hours, because I kinda screwed up my sleep rhythm. Let me tell the stories.

One of the first things I noticed when I woke up (approx 8 pm on May 19th), was an e-mail from mister Nicely, telling me that my proof was correct. That is, I showed that for every integer $k > 1$, an integer x exists, such that: $\displaystyle \frac{x}{\pi(x)} = k$, where $\pi(x)$ is the prime counting function. Since I proved that fact (it definitely does not earn the title ‘theorem’) about a year ago, I was quite surprised to see it as a conjecture of Golomb on Nicely’s site. So I e-mailed my proof, and it got posted. While this could easily be considered a trivial story, and that claim has merits, I’m actually quite happy about it. Because I not only proved the above fact, I also proved my existence! Furthermore, I started thinking about the math in question some more, and I came up with the following conjecture, which, to me, seems certainly true: for every positive integer m, there is a positive integer k, such that there are at least m different positive integers x, for which $\displaystyle \frac{x}{\pi(x)} = k$. Maybe even the following is true: for every positive integer m, there are infintely many positive integers k, such that there are exactly m different positive integers x, for which $\displaystyle \frac{x}{\pi(x)} = k$. The second one seems quite hard (maybe the case m = 1 is doable), but I thought about my first question some time, and I think it should be attackable. I (think I) am able to proof the conjecture, under the assumption of Hardy-Littlewood’s prime-k-tuple-conjecture, if we drop the condition that k is an integer, but only want it to be rational. Although I must add that I haven’t written down the details yet. I might put my thoughts on it here. Butttt, obviously not now, because I have to tell you the rest of mah story!

So, by (what felt like) morning, I was already world-famous. Then my calculus-teacher e-mailed me. And that event was something I had been dreading for like a month. Because I asked him to e-mail my grade on the exam and I wasn’t quite sure about it. Because, honestly, I HATE CALCULUS. And I’m obviously talking about the way it’s taught and the fact that you won’t be allowed to come back ever again if you use your intuition for something. I mean it’s good for students that have never seen proofs before and shit, but come on, be less trivial, puh-lease. Honestly, I might roundhousekick the next person who asks me to prove that $\displaystyle \lim_{x\rightarrow 0} x = 0$ straight in the face. Or, somewhat more generally I guess, the next person who uses the words ‘epsilon’ and ‘delta’ in one sentence. And this hot, raging anger I felt inside me, made it almost impossible to open my book to study without hysterically crying. Add this to the fact that I usually only get part marks  (I mean, what’s up with that?), when I answer a question like ‘prove *something trivial*’, with ‘that’s trivial’ and it becomes clear why I was scared that I failed my exam like a little bitch. As it turns out: I PASSED. Go suck on that you Cauchy!

And these 2 major steps towards eternal glory made me

1) call my lovely little sister for like 40 minutes
2) able to help out a friend (which wasn’t even math-related)
3) impulsively (though wisely) decide to buy a new phone
4) notice that it was like the most beautifullest weather ever today
5) write a post that has (ugh, too geeky) $\lfloor 200*\pi \rfloor$ words in it