How can I prove or disprove that the formula $2^{2{^{2^{2^2\dots}}}}+1$ gives a prime number?
How can I know if $2^{2^{2^{2^{2}}}}+1=?$ is prime?
Can the category of chain complexes be realized as a functor category? As the title says, is there some sort of category $\mathsf{C}$ which can be thought of as the "walking chain complex", so that the category of chain complexes in some other category $\mathsf{A}$ can be realized as $\mathsf{A}^\mathsf{C}$ (or perhaps some subcategory thereof)? How to import a jar in Eclipse What is the secondary CPU Usage Graph line in the Windows 10 Task Manager I was looking at the task manager in Windows 10 and for the first time noticed a secondary dashed line below the solid? What does this line indicate? What is the Python equivalent of static variables inside a function? What is the idiomatic Python equivalent of this C/C++ code?  void foo() {     static int counter = 0;     counter++;     printf("counter is %d\n", counter); }   specifically, how does one implement the static member at the function level, as opposed to the class level? And does placing the function into a class change anything? Where can I see my flag count / history? Is there a section or page that lists my flag count and / or history? Notify us when one of our posts is edited Your summary page shows "N Edits to your posts" for the selected time period but you really have to be looking for it.  Could we add edits to the notification feed? You could put the reason for the edit (entered--or not--when the editor changes it) and just a link to the post. How to make a package manager wait if another instance of APT is running? I have seen many softwares such as Update Manager and Synaptic Package Manager, they wait if some other program is using the /var/lib/dpkg/lock and is locked. How can we do this through the Terminal? I saw apt-get's manual but didn't find anything useful. Can anyone please help me with my problem regarding my WordPress left hand side admin menu. I want it collapsed at all times, how do I do that?  Well, I'm creating a WP Multisite so I want that menu bar to be always collapsed at all times.  Any help would be appreciated. Looking for code or if plugin exists, should be fine, too. Thanks. Secure an Ubuntu OpenSSH server from Brute force attacks but without a firewall or SSH key pair? I use Ubuntu 16.04 and seek to harden my SSH authentication in a special manner.  The current situation:  I have a machine with a minimal Ubuntu server I use mainly to transfer files to via its local OpenSSH server. Now, I don't have a firewall on that machine from a few reasons and I also avoid using a key pair hence I use only a password. One of the only ways I have left to defend from brute force attacks, and the one I most desire at the moment, is using a mechanism that blocks a user for X amount of hours, after Y amount of connection tries.  The desired situation:  I wish to have a standalone mechanism (that is, not as part of a firewall) that blocks a user for X amount of hours, after Y amount of connection tries as a way to defend from brute force attacks.  My Question:  Do you know a utility (and specific configuration) that will let me achieve the desired situation? How do I use a C# keyword as a property name? Using asp.net MVC I'd like to do this inside a view:  &lt;%= Html.TextBox("textbox1", null, new { class="class1" }) %&gt;   This statement does not compile because class is keyword in C#. I'd like to know how I can escape the property names such that this compiles.  It is possible to get this to compile if I change the "class" property to "Class" (uppercase C). But this is not suitable because strict xhtml says that all attributes (and element) names must be lowercase. This question is similar, but not identical to:   Whereas the aforementioned question is about whether the hand’s movement is measured from the hand’s point of view or from the caster’s, this question revolves around the total distance the hand can travel to reach its destination.  To illustrate, let me give an example: Two narrow stone pillars stand next to each other, 10 feet apart. They are several kilometers high and on top of each pillar stands a wizard. One wizard casts Maximillian's Earthen Grasp and lets the hand made from compacted soil rise from the ground on his own pillar. With another action, he wants to move the hand in order to restrain the other wizard, who is within range of 30 feet.  Would the hand retract into his own pillar, then rise again from the ground on the other pillar? Or would the hand move several kilometers down the first pillar, across the floor, then several kilometers up the second pillar? What if both pillars would float in the Astral Plane, without a direct ground-based connection between them?  This might seem like a stupid and unnecessary convoluted question, but lo and behold, something similar happened in one of my games. Does inverting the "if" improve performance? How to correctly do a division using a slash? What's the correct way to do division using a backslash? If I write $a/bc + d$, will that be equal to $(a/(bc))+d$?   Basically, if I place a slash, will I divide by what's directly behind the slash $(b)$, the term that's behind the slash $(bc)$, or everything after the slash $(bc+d)$? When I look in sys.sql_logins, I see a column called is_policy_checked. Can I trust that my password policy has been checked for all of the logins where this column value is 1? Show that the Euler characteristic of a chain complex is equal to the Euler characteristic of its homology If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$. Let $G$ be a group with $|G| = n$ and let $ \emptyset \ne S \subseteq G$.   I want to show that $S^n$ is a subgroup of $G$ where by $S^n$ I mean the set $\lbrace s_1\cdots s_n \; | \; s_i \in S\rbrace$. Why is $L^{\infty}$ not separable? Reshape three column data frame to matrix ("long" to "wide" format) The word or phrase I am looking for is quite opposite to that of the situation when people, such as students or sports players, sing their national anthem with the same tone and words.  I want a single word or even phrase that can describe the situation when two or more people speak at the same time with different tone and words . . . and at the end, the listener cannot get what they are saying. This situation can be found while debating, telling a news about any incident or even while complaining.     Due to _____ , the teacher could not get what they are saying.   If it's not feasible to find a noun or phrase for such situation, then here I request to have an adverb standing alone to describe how they are speaking, for instance, what is the adverb for "at the same time"?.  Here is how, I want to convert sentence 1 into sentence 2.        They spoke at the same time, and the teacher could not get what they are saying.   They spoke _____ , and the teacher could not get what they are saying. I wrote a bash script as below:  #!/bin/bash echo "Enter a file name" read filename import -window root $HOME/Desktop/$filename.png   I expected this script to take a screen shot and save the image with the given filename on my desktop.  Problem:  My Ubuntu terminal is giving error:     import: Command Not Found