## Polynomials of minimum degree that interpolate primes in intervals

Given an interval $$(a,b)$$ what is the minimum degree of univariate polynomials in $$mathbb Q(x)$$ that passes through all primes between $$a$$ and $$b$$?

It is at most $$O(pi(b-a))$$.

Is there a reason to believe it cannot be $$o(pi(b-a))$$?

## open source – Travelling Salesman Problem simulation

I apologise if I’m wrong to ask this here but I couldn’t think of a better forum.

I am learning about the travelling sales man algorithm and wish to implement a demonstration.

My initial thought was to develop it in a webpage but as I am natively a PHP developer, I feel it might not be the best solution to use javascript/jQuery to animate characters from point to point through a graph.

I wonder if there is an open-source 2D game engine I can use and write PHP/javascript logic for my algorithm implementation?

## links – I am creating an online shop, how do I add a sort by option where it displays newest, low to high, high to low

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## boot – MSI Bravo 17 and Linux compatibility

After received my new laptop bought to code under linux Ubuntu, i discovered that this product based on AMD Ryzen 4800H (Navi 14 Mobile) VEGA 10 with Radeon RX 5500M is unable to work with ubuntu !

I am totally disappointed cause i bought it to work on linux but all my tries with the forllowing distributions failed :

• ubuntu 20.04 desktop stucks on black screen after installation reboot.
• Linux Mint works with nomodeset but a permanent banner indicating me missing graphic accelerator push me to try AMD Radeon software for Ubuntu 20.04 – since installation – i completely lost any shell command.

Only Windows works, Grrrrrrrrrrrrrr…

## Why is the winding number of a surface locally constant?

Given a smooth closed surface $$Ssubseteqmathbb R^3$$, we can define its winding number around some point $$pinmathbb R^3setminus S$$ as $$omega_S(p):=frac1{4pi}int_Sfrac{langle x-p,nu_S(x)rangle}{|x-p|^3}dS(x),$$ where $$nu_Scolon Stomathbb S^2$$ is the unit normal vector field of $$S$$. I would like to show that $$omega_Scolonmathbb R^3setminus Stomathbb R$$ is locally constant (which I think to be true based on the properties of the standard winding number $$omega_gamma(p)=frac1{2pi}int_gammafrac{dz}{z-p}$$ of a loop $$gammacolon Itomathbb C$$ around a point $$pinmathbb Csetminusgamma$$).

I read somewhere (can’t find it anymore) that my claim is trivial, because the “solid angle differential” $$dOmega_p=frac{langle x-p,nu_S(x)rangle}{|x-p|^3}dS$$ is closed. However, if $$dOmega_p$$ was closed, then Stokes’ theorem tells me that $$omega_S(p)=int_SdOmega_p=int_{partial V}dOmega_p=int_Vd(dOmega_p)=0,$$ even if $$S$$ encloses $$pinmathbb R^3setminus S$$.

My next attempt was to show that all partial derivatives of $$omega_S$$ vanish everywhere. And now, I’m stuck at
$$frac{partialomega_S}{partial p_i}(p)=frac1{4pi}int_Sbiggl(frac3{|x-p|^2}frac{langle x-p,nu_S(x)rangle}{|x-p|^3}(x_i-p_i)-frac1{|x-p|^3}nu_{S,i}(x)biggr)dS(x),$$ which doesn’t look like it will get me anywhere.

Is $$omega_S$$ actually locally constant? And how would I go about showing it?

## I shaked my camera and lens very hardly… Will it cause a damage?

I shaked my camera and lens very hardly… Will it cause a damage?
I did this 4 to 5 times… Should I Worry? Please reply fast?

## debian – Running an X program as root no longer possible with xhost +localhost?

Trying to run any X program as root typically results in some error/warning with the string “cannot open display”. In the past, I could just fix this by doing xhost +localhost

This no longer appears to work (on Debian 10). How do I do this these days?

## blog – Collaborative learning tools and their use

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On an Ubuntu 20.04 server, netplan is used to configure the network. It can configure ordinary static IP addresses but I need additional IPv6 addresses with preferred_lft=0. Netplan can’t do that (there’s an open bug for that). So I found out that it actually goes like this:

• Netplan reads its own limited config and transforms it into a config for the more powerful systemd-network.
• systemd-network probably passes on its data to things like the `ip` command when a network device appears.
• The network device then applies the actual configuration. Down here everything is possible.

If netplan can’t help me, I tried to move on to systemd. Since I don’t want to remove the apparently widely used and highly praised netplan entirely, I just need to add my additional addresses besides the basic netplan config.

I tried to create the file /etc/systemd/network/web-ipv6.conf with this content:

``````(Match)
Name=ens33 (this is the name from the existing netplan file)

I guess I have to apply my config with `systemctl restart systemd-networkd` but I’m not sure. The log says things I’d consider a success. But the new IPv6 address …::2 doesn’t show up in `ip addr`.
In the man page for systemd.network I’ve read that only a single file for a `(Match)` will be used. I clearly have two files now: one from netplan (/run/systemd/network/10-netplan-ens33.network) and my other one. So this doesn’t seem to work. But I don’t want to edit netplan’s file as it will surely be overwritten sometime.
Should I go back to `ifupdown` or what it was in the old days? In a previous server setup I use a file named /etc/network/if-up.d/dynamic6 that contains all the `ip addr add ... dev ... preferred_lft 0` commands. From what I’ve seen this is today considered deprecated.