MathB.in
New
Demo
Tutorial
About
Riemann hypothesis : $$\sum_{t=1}^\infty\small H\circ\log\frac1{1+\left|\sum\limits_{k=1}^\infty\frac{\sin(\pi/4-\rho_t\log k)}{\sec(\pi k)\exp(\sigma\log k)}\right|}=\left\{\begin{array}l\infty&\sigma=1/2\\0&\rm otherwise\end{array}\right.$$ Collatz conjecture : $$\small\lim_{n\to\infty}\sum_{j=1}^\infty H\left(\sum_{k=1}^n\text{iterate} _ k\left(j\mapsto\left(\frac52j+1\right)H\left(\left\{\frac j2\right\}-\frac14\right)+\frac n2\right)-\frac12\right)=\infty$$ Goldbach conjecture : $$\small\sum_{m=1}^\infty\sum_{n=1}^mH\big(1-\pi\left(m-p_n\right)+\pi(m-p_n-1)\big)=\infty$$ Twin primes conjecture : $$\small\sum_{n=2}^\infty H\left(p_n+\frac52-p_{n+1}\right)=\infty$$
ERROR: JavaScript must be enabled to render input!
Wed, 05 Sep 2018 22:11 GMT