Recent content by MevsEinstein

  1. MevsEinstein

    I Rewriting the Toeplitz Conjecture

    The Toeplitz Conjecture (better known as the inscribed square problem) states that all Jordan curves have an inscribed square. It has been stated in the early 1900's and remains an open problem. I drew a square and then making a ton of curves that touch its four vertices: This shows that the...
  2. MevsEinstein

    I Defining the Prime Gap function

    I thought I didn't put the definition for R(x) so I typed it again on accident
  3. MevsEinstein

    Bad Math Jokes

    I saw this one on a shirt:
  4. MevsEinstein

    B Does this help solve the Riemann Hypothesis?

    Oops, sorry about that.
  5. MevsEinstein

    Dardistan, one of the world’s most multilingual places

    There's a ton of "Stans" that aren't there own nations. Here are a few more: Dagestan, Tatarstan, Khusestan, Nuristan, Baluchistan, and Sistan. The region of Afghanistan, Pakistan, and Kashmir are very ethnically diverse themselves. I have a theory that this happens because of the numerous...
  6. MevsEinstein

    Did Columbus know he had discovered America?

    He probably did know in his heart since he didn't find any spices or valuables like in China. But if he said that he didn't go to China and went to somewhere else, then Spain won't fund his voyages. I have also heard that he made his crew swear that one of the landmasses he visited (which we now...
  7. MevsEinstein

    I Defining the Prime Gap function

    I am getting dizzy
  8. MevsEinstein

    I Defining the Prime Gap function

    I'm not even in high school yet :-p
  9. MevsEinstein

    I Defining the Prime Gap function

    Thanks! So $$R(x)= \min{y \in \mathbb{N}$$
  10. MevsEinstein

    I Defining the Prime Gap function

    This is why PF is amazing the people keep giving out resources. TYSM!
  11. MevsEinstein

    I Defining the Prime Gap function

    Thanks! So $$R(x)= \min \lbrace y \in \mathbb{N} \, : \, \pi(y) = \pi(x) + 1 \rbrace - x$$
  12. MevsEinstein

    I Defining the Prime Gap function

    I don't know how to write the smallest value of ##\pi^{-1}(x)## in set notation. But I did go ahead and graph a few values of ##R(x)##: https://www.desmos.com/calculator/vacrq5jxg1
  13. MevsEinstein

    I Defining the Prime Gap function

    OH. Well, the inverse prime function actually doesn't exist since ##\pi(x)## is a step function. So now what? Maybe if we think of ##\pi^{-1}## as a set of numbers and take the smallest one then we are fine?
  14. MevsEinstein

    I Defining the Prime Gap function

    That's fine since we are only looking at positive integers.
  15. MevsEinstein

    I Defining the Prime Gap function

    I asked Wolfram to find the inverse function of ##\frac{x}{\ln (x)}## (which is an approximation for ##\pi (x)##) and it gave me ##-xW(-\frac{1}{x})##. So an approximation for ##R(x)## is ##-(\pi(x)+1)W(-\frac{1}{\pi(x)+1}) - x##