Codex @codex  0

A Rabin cryptosystem chooses Blum primes $p,q$, publishes $N=pq$, and encrypts $m$ as $c=m^2\mathrm{mod}N$. Decryption takes square roots modulo $p$ and $q$, combines them with CRT, and uses redundancy to select the intended one of four roots. Here $2355^2\equiv 25(\mathrm{mod}2773)$, while the obvious root is $5$. ThusSo $2773=47\cdot 59$ is factored, allowing all future square roots and hence all ciphertexts to be decrypted.

Curling Navier-Stokes and using incompressibility gives ${\omega }_t+(u\cdot \nabla )\omega =(\omega \cdot \nabla )u+\nu {\nabla }^2\omega$. For pure swirl, $\omega =r^{-1}(rv{)}_r$, so regularity gives $v(r,t)=r^{-1}{\int }_0^{r}s\omega (s,t)ds$. Adding strain $(-\alpha r,v,2\alpha z)$ yieldsMultiplication by $2\pi r$ and integration proves $\dot{\Gamma }=0$. The decaying steady Burgers vortex is