**Simplified example of capitalist bullshit**: under [capitalism](capitalism.md) basically the whole society is based on bullshit of many kinds, small and big, creating many bullshit clusters that are all intertwined and interact in complex ways, creating one huge bullshit. For simplicity let's consider an educational isolated bullshit cluster (that we won't see that often in reality), a hypothetical [car](car.md) factory. No matter how the factory came to be, it now ended up making cars for people so that these people can drive to work at the car factory to make more cars for other people who will work to the car factory to make cars etc. -- a bullshit cycle that exists just for its own sake, just wastes natural resources and lives of people. Of course at one point all the factory employees will own a car and the factory will have no more demand for the cars, which threatens its existence. Here capitalism employs adding more bullshit: let's say they create new bullshit jobs they call something like "[smart](smart.md) car research center" -- this will create new work position, i.e. more people who will need cars to drive to work, but MAILY the job of these people will be adding [artificial obsolescence](artificial_obsolescence.md) to the cars, which will make them last much shorter time and regularly break so that they will need repairs using parts manufactured at the factory, creating more work that will need to be done and more bullshit jobs in the car repair department. Furthermore the team will make the cars completely dependent on [subscription](subscription.md) software, employing [consumerism](consumerism.md), i.e. the car will no longer be a "buy once" thing but rather something one has to keep feeding constantly (fuel, software subscription, insurance, repairs, cleaning, tire changes, and of course once in a few years just buying a new non-obsolete model), so that workers will still need to drive to work every day, perpetuating their need for being preoccupied with owning and [maintaining](maintenance.md) a car. This is a bullshit cluster society could just get rid of without any cost, on the contrary it would gain many free people who could do actually useful things like curing diseases, eliminating world hunger, creating art for others to enjoy. However if you tell a capitalist any part of this system is bullshit, he will defend it by its necessity in the system as a whole ("How will people get to work without cars?!", "Factories are needed for the economy!", "Economy is needed to drive manufacturing of cars!") -- in reality the bullshit clusterfuck spans the whole world to incredibly deep levels so you just can't make many people see it, especially when they're preoccupied with maintaining their own existence and just get by within it.
**Simplified example of capitalist bullshit**: under [capitalism](capitalism.md) basically the whole society is based on bullshit of many kinds, small and big, creating many bullshit clusters that are all intertwined and interact in complex ways, creating one huge bullshit. For simplicity let's consider an educational isolated bullshit cluster (that we won't see that often in reality), a hypothetical [car](car.md) factory. No matter how the factory came to be, it now ended up making cars for people so that these people can drive to work at the car factory to make more cars for other people who will work to the car factory to make cars etc. -- a bullshit cycle that exists just for its own sake, just wastes natural resources and lives of people. Of course at one point all the factory employees will own a car and the factory will have no more demand for the cars, which threatens its existence. Here capitalism employs adding more bullshit: let's say they create new bullshit jobs they call something like "[smart](smart.md) car research center" -- this will create new work position, i.e. more people who will need cars to drive to work, but MAINLY the job of these people will be adding [artificial obsolescence](artificial_obsolescence.md) to the cars, which will make them last much shorter time and regularly break so that they will need repairs using parts manufactured at the factory, creating more work that will need to be done and more bullshit jobs in the car repair department. Furthermore the team will make the cars completely dependent on [subscription](subscription.md) software, employing [consumerism](consumerism.md), i.e. the car will no longer be a "buy once" thing but rather something one has to keep feeding constantly (fuel, software subscription, insurance, repairs, cleaning, tire changes, and of course once in a few years just buying a new non-obsolete model), so that workers will still need to drive to work every day, perpetuating their need for being preoccupied with owning and [maintaining](maintenance.md) a car. This is a bullshit cluster society could just get rid of without any cost, on the contrary it would gain many free people who could do actually useful things like curing diseases, eliminating world hunger, creating art for others to enjoy. However if you tell a capitalist any part of this system is bullshit, he will defend it by its necessity in the system as a whole ("How will people get to work without cars?!", "Factories are needed for the economy!", "Economy is needed to drive manufacturing of cars!") -- in reality the bullshit clusterfuck spans the whole world to incredibly deep levels so you just can't make many people see it, especially when they're preoccupied with maintaining their own existence and just get by within it.
@ -4,6 +4,8 @@ Dependency of a piece of [technology](technology.md) is another piece of technol
Having many dependencies is a sign of **[bloat](bloat.md) and bad design**. Unfortunately this is the reality of mainstream programming. For example at the time of writing this [Chromium](chromium.md) in [Debian](debian.md) requires (recursively) 395 packages LMAO xD And these are just runtime dependencies...
Though dependencies are primarily bad because they endanger whole functionality as such, i.e. "it simply won't run without it", they are also bad for another reason: you have no control over how a dependency will behave, if it will be implemented well and if it will behave consistently. [OpenGL](opengl.md) for example caused a lot of trouble by this because even though the API is the same, different OpenGL implementations performed differently under different situations and made one game run fast with certain combinations of GPUs and drivers and slow with others, which is why [Vulkan](vulkan.md) was created. It is also why some programmers write their own memory allocation functions even though they are available in the standard library etc. -- they know they can write one that's fast and will be fast where they want it to be.
In [software](software.md) development context we usually talk about software dependencies, typically [libraries](library.md) and other software [packages](package.md). However, there are many other types of dependencies we need to consider when striving for the best programs. Let us list just some of the possible types:
Gopher is a network [protocol](protocol.md) for publishing, browsing and downloading files and is known as a much simpler alternative to the [World Wide Web](www.md) (i.e. to [HTTP](http.md) and [HTML](html.md)). In fact it competed with the Web in its early days and even though the Web won in the mainstream, gopher still remains used by a small communities (however the more dedicated, see e.g. [bitreich](bitreich.md)). Gopher is like the Web but well designed, it is the [suckless](suckless.md)/[KISS](kiss.md) way of doing what the Web does, it contains practically no [bloat](bloat.md) and so [we](lrs.md) highly advocate its use. Gopher inspired creation of [Gemini](gemini.md), a similar but bit more complex and "[modern](modern.md)" protocol, and the two together have recently become the main part of so called [Smol Internet](smol_internet.md). Gopher is much better than Gemini though. The set of all public gopher servers is called gopherspace.
Gopher **doesn't use any [encryption](encryption.md)** (though some server allow access via [Tor](tor.md)). **This is good, encryption is [bloat](bloat.md)**. Gopher also doesn't really know or care about [Unicode](unicode.md) and similar bloat (which mostly serves trannies to insert emojis of pregnant men into readmes anyway, we don't need that), it's basically just [ASCII](ascii.md). Gopher simple design is intentional, the authors deemed simplicity a [good](good.md) feature. Gopher is so simple that you may very well write your own client and server and comfortably use them -- **you can even browse gopher just by manually using [telnet](telnet.md)** to communicate with the server.
Gopher **doesn't use any [encryption](encryption.md)** (though some servers allow access via [Tor](tor.md)). **This is good, encryption is [bloat](bloat.md)**. Gopher also doesn't really know or care about [Unicode](unicode.md) and similar bloat (which mostly serves trannies to insert emojis of pregnant men into readmes anyway, we don't need that), it's basically just [ASCII](ascii.md). Gopher simple design is intentional, the authors deemed simplicity a [good](good.md) feature. Gopher is so simple that you may very well write your own client and server and comfortably use them -- **you can even browse gopher just by manually using [telnet](telnet.md)** to communicate with the server.
**How big is gopherspace?** As of 2023 the Veronica search engine reported 315 gopher servers in the world with 5+ million indexed selectors, which they estimated was 83% of the whole gopherspace (the peak server count was in 2020 at almost 400). Quarry search engine reports 369 servers and 1+ million indexed selectors. Contrition search engine reported even 495 servers and 7+ million selectors. Gopher LAWN directory (made by [bitreich](bitreich.md)) contains 281 selected quality gopher holes.
@ -51,7 +51,7 @@ Here `1` says the resource is a directory, then we have a display string (which
echo "/v2" | nc floodhap.com 70
```
And get a similar response. This is basically a client needs to know.
And get a similar response. This is basically all a client needs to know.
As for running a server, details depend on each one, but generally they behave like this: you have a server running in some default directory, let's say `/home/me/my_gopherhole`. By default a server will just serve list of files present in this directory to clients who request the "main directory", treating directories as subdirectories and sending regular files back. However there is one important feature: you may create a **gophermap file** to create a custom menu, or something aking a "gopher website". Gophermap is something like gopher's [HTML](html.md), just much more simple. How to do this? You simply create a file name `gophermap` in the directory (the main one or any subdirectory) -- if the server sees such a file, it serves it instead of listing the directory file.
@ -16,6 +16,7 @@ We can divide computer graphics in different ways, traditionally e.g.:
- by speed:
- **[real time](real_time.md)**: Trying to work with images in real time, e.g. being able to produce or analyze 60 frames per second.
- **offline**: Processes or creates images over longer time-spans, even hours or days, e.g. in 3D movie rendering.
- ...
Since the 90s computers started using a dedicated hardware to accelerate graphics: so called [graphics processing units](gpu.md) (GPUs). These have allowed rendering of high quality images in high [FPS](fps.md), and due to the entertainment and media industry (especially gaming), GPUs have been pushed towards greater performance each year. Nowadays they are one of the most consumerist [hardware](hardware.md), also due to the emergence of general purpose computations being moved to GPUs (GPGPU), lately especially mining of [cryptocurrencies](crypto.md) and training of [AI](ai.md). Most lazy programs dealing with graphics nowadays simply expect and require a GPU, which creates a bad [dependency](dependency.md) and [bloat](bloat.md). At [LRS](lrs.md) we try to prefer the [suckless](suckless.md) **[software rendering](sw_rendering.md)**, i.e. rendering on the [CPU](cpu.md), without GPU, or at least offer this as an option in case GPU isn't available. This many times leads us towards the adventure of using old and forgotten algorithms used in times before GPUs.
Less retarded society (LRS, same [acronym](acronym.md) as [less retarded software](lrs.md)) is a model of ideal society towards which we, the [LRS](lrs.md), want to be moving. Less retarded society is a peaceful, collaborative society based on [love](love.md) of all [life](life.md), which aims for maximum well being of all living beings, a society without violence, [money](money.md), oppression, need for [work](work.md), social [competition](competition.md), poverty, scarcity, criminality, [censorship](censorship.md), [self-interest](self_interest.md), government, police, laws, bullshit, slavery and many other negative phenomena. It equally values all living beings and establishes true social equality in which everyone can pursue his true desires freely -- it is a TRULY [leftist](left_vs_right.md) society, NOT a [pseudoleftist](pseudoleft.md) one. The society works similarly to that described by the [Venus Project](venus_project.md) and various [anarchist](anarchism.md) theories (especially [anarcho pacifist](anpac.md) [communism](communism.md)), but it also takes good things from elsewhere, even various [religions](religion.md) (without itself actually becoming a religion in traditional sense); for example parts of teaching of [Jesus](jesus.md) and [Buddha](buddhism.md).
**How is this different from other ideologies and "life philosophies"?** Well, one principal difference is that LRS doesn't want to [fight](fight_culture.md); nowadays as well as in the past society has always been about conflict, playing a **game** against others (nowadays e.g. market competition, employment competition, media competition, ...) in which some win, some can manage and some lose. Most political parties nowadays just want to change the rules of the game or downright switch to a different kind of game, some want to make the rules "more fair", or to make it favor their represented minority (so called [fascism](fascism.md)), some just want to [hack](hacking.md) the game, some want to [cheat](cheat.md) to win the game easily, some want to play fair but still win (i.e. become "successful"). LRS simply sees any kind of such game as unnecessary, cruel, unethical and harmful in many ways not just to us, but to the whole planet. LRS therefore simply wants to stop the game, not by force but by making everyone see how bad the game is. It says that **competition and conflict must seize to be the basis of society**.
**How is this different from other ideologies and "life philosophies"?** Well, one principal difference is that LRS doesn't want to [fight](fight_culture.md); nowadays as well as in the past society has always been about conflict, playing a **game** against others (nowadays e.g. market competition, employment competition, media competition, ...) in which some win, some can manage and some lose. Most political parties nowadays just want to change the rules of the game or downright switch to a different kind of game, some want to make the rules "more fair", or to make it favor their represented minority (so called [fascism](fascism.md)), some just want to [hack](hacking.md) the game, some want to [cheat](cheat.md) to win the game easily, some want to play fair but still win (i.e. become "successful"). LRS simply sees any kind of such game as unnecessary, cruel, unethical and harmful in many ways not just to us, but to the whole planet. LRS therefore simply wants to stop the game, not by force but by making everyone see how bad the game is. It says that **competition and conflict must seize to be the basis of society**. There is no value in achieving anything by violence, such a change will soon be reverted by counter revolution, people themselves have to understand what's good and choose it voluntarily. That is one of the reasons why we are [pacifists](pacifism.md) and **reject all violence**, only wanting to promote our ideas by [education](education.md).
Note that this society is an ideal model, i.e. it can probably not be achieved 100% but it's something that gives us a direction and to which we can **get very close** with enough effort. We create an ideal theoretical model and then try to [approximate](approximation.md) it in reality, which is a [scientific](science.md) approach that is utilized almost everywhere: for example [mathematics](math.md) defines a perfect sphere and such a model is then useful in practice even if we cannot ever create a mathematically perfect sphere in the real physical world -- the mathematical equations of a sphere guide us so that with enough effort we are able to create physical spheres that are pretty close to an ideal sphere. The same can be done with society. This largely refutes the often given argument that *"it's impossible to achieve so we shouldn't try at all"* -- we should try our best and the closer to the ideal we get, the better for us.
@ -23,7 +23,7 @@ Generally a logic circuit can be seen as a "black box" that has *N* input bits a
Logic circuits can be drawn simply as "boxes" (which one the base level are the basic logic gates such as [AND](and.md), [OR](or.md) etc.) connected with lines ("wires", but again not really electronic wires as here only 1 or 0 can be carried by such wire). But as mentioned, their behavior can also be described with a truth table (which however says nothing about the internals of the circuit) or a boolean expression, i.e. an algebraic expression that for each of the circuit outputs defines how it is computed from the outputs, for example *a = !x & y* and *b = !(y | z)* for the above drawn example circuit. Each of these types of representation has its potential advantages -- for example the graphical representation is a very human-friendly representation while the algebraic specification allows for optimization of the circuits using algebraic methods. Many hardware design languages therefore allow to use and combine different methods of describing logic circuits (some even offer more options such as describing the circuit behavior in a programming language such as [C](c.md)).
With combinational logic circuits it is possible to implement any boolean function (i.e. "functions only with values 1 and 0"); [undecidability](undecidability.md) doesn't apply here as we're not dealing with [Turing machines](turing_machine.md) computations because the output always has a finite, fixed number of bits, the computation can't end up in an infinite loop as there are no repeating steps, just a straightforward propagation of input values to the output. It is always possible to implement any function at least as a [look up table](lut.md) (which can be created with a [multiplexer](multiplexer.md)). Sequential logic circuits on the other hand can be used to make the traditional computers that work in steps and can therefore get stuck in loop and so on.
With combinational logic circuits it is possible to implement any boolean function (i.e. "functions only with values 1 and 0"); [undecidability](undecidability.md) doesn't apply here as we're not dealing with [Turing machines](turing_machine.md) computations because the input and output always has a finite, fixed number of bits, the computation can't end up in an infinite loop as there are no repeating steps, just a straightforward propagation of input values to the output. It is always possible to implement any function at least as a [look up table](lut.md) (which can be created with a [multiplexer](multiplexer.md)). Sequential logic circuits on the other hand can be used to make the traditional computers that work in steps and can therefore get stuck in loop and so on.
Once we've designed a logic circuit, we can [optimize](optimization.md) it which usually means making it use fewer logic gates, i.e. make it cheaper to manufacture (but optimization can also aim for other things, e.g. shortening the maximum length from input to output, i.e. minimizing the circuit's [delay](delay.md)).
**We [love](love.md) all living beings. Even you.** We want to create technology that truly and maximally helps you, e.g. a completely [public domain computer](public_domain_computer.md). We do NOT [fight](fight_culture.md) anything or anyone and we don't have any [heroes](hero_culture.md) or leaders. We want to move peacefully towards [society](less_retarded_society.md) that's not based on [competition](competition.md) but rather on [collaboration](collaboration.md).
**We [love](love.md) all living beings. Even you.** We want to create technology that truly and maximally helps you, e.g. a completely [public domain computer](public_domain_computer.md). We do NOT [fight](fight_culture.md) anything or anyone and we don't have any [heroes](hero_culture.md) or leaders. We want to move peacefully towards [society](less_retarded_society.md) that's not based on [competition](competition.md) but rather on [collaboration](collaboration.md). We also **reject all [violence](violence.md)**.
{ I no longer see hope, good is practically non existent in this world. This is my last attempt at preserving pure good, I will continue to spread the truth and unconditional love of all life as long as I will be capable of, until the society lynches me for having loved too much. At this point I feel very alone, this work now exists mostly for myself in my isolated world. But I hope that once perhaps my love will be shared with a reader far away, in space or time, even if I will never know him. This is the only way I can continue living. I wish you happy reading, my dear friend. ~[drummyfish](drummyfish.md) }
Technological minimalism is a philosophy of designing [technology](technology.md) to be as simple as possible while still achieving given goal, possibly even a little bit simpler. Minimalism is one of the most (if not the most) important concepts in [programming](programming.md) and technology in general. Remember, minimalism is firstly about **internal simplicity**, i.e. the simplicity of design/repairing/[hacking](hacking.md), and only secondly about the simplicity from the user's point of view (otherwise we are only dealing with [pseudominimalism](pseudominimalism.md)). See also [minimal viable program](minimal_viable_program.md).
In context of [technology](tech.md) minimalism is a design philosophy which puts great emphasis on [simplicity](kiss.md), it says technology should be as simple as possible while still achieving given goal, possibly even a little bit simpler. Minimalism is one of the most (if not the most) important concepts in [programming](programming.md) and technology in general, it could almost be said that becoming a true expert in technology is strongly connected to realizing the importance of simplicity (see e.g. [Unix philosophy](unix_philosophy.md)). One of the first things to stress about minimalism is that it's firstly about **internal simplicity**, i.e. the simplicity of design/repairing/[hacking](hacking.md), and only secondly about the simplicity from the [user](user.md)'s point of view (otherwise we are only dealing with [pseudominimalism](pseudominimalism.md)). See also [minimal viable program](minimal_viable_program.md).
Antoine de Saint-Exupéry sums it up with a quote: *we achieve perfection not when there is nothing more to add, but when there is nothing left to take away.*
There is also the generalized concept of **life minimalism** which applies said philosophy to all areas of [life](life.md) and which many technological minimalists often start to follow as well -- life minimalism is about letting go of things and desires that aren't necessarily needed as such things enslave us; you should think about what it really is that you want and need and only keep that. This is nothing new, this wisdom has been present for as long as humans have existed, most religions and philosophers saw a great value in [asceticism](asceticism.md), frugality and even poverty, as owning little leads to [freedom](freedom.md). For example owning a [car](car.md) is kind of a slavery, you have to clean it, protect it, repair it, [maintain](maintenance.md) it, pay for parking space, pay for gas, pay for insurance -- that's a huge commitment eating up a huge part of your life and [head space](head_space.md), a minimalist will rather choose to get a simple [suckless](suckless.md) bicycle or travel by public transport.
**Minimalism is necessary for [freedom](freedom.md)** as a free technology can only be that over which no one has a [monopoly](bloat_monopoly.md), i.e. which many people and small parties can utilize, study and modify with affordable effort, without needing armies of technicians just for the maintenance of such technology. Minimalism goes against the creeping overcomplexity of technology which always brings huge costs and dangers, e.g. the cost of [maintenance](maintenance.md) and further development, obscurity, inefficiency ("[bloat](bloat.md)", wasting resources), consumerism, the increased risk of bugs, errors and failure.
Up until recently in history every engineer would tell you that *the better machine is that with fewer moving parts*. This still seems to hold e.g. in mathematics, a field not yet so spoiled by huge commercialization and mostly inhabited by the smartest people -- there is a tendency to look for the most minimal equations -- such equations are considered [beautiful](beauty.md). Science also knows this rule as the [Occam's razor](occams_razor.md). In technology invaded by aggressive commercialization the situation is different, minimalism lives only in the underground and is ridiculed by the mainstream propaganda. Some of the minimalist movements, terms and concepts include:
There is a so called *[airplane rule](airplane_rule.md)* that states a plane with two engines has twice as many engine problems than a plane with a single engine.
Up until recently in history every engineer would tell you that *the better machine is that with fewer moving parts*. This still seems to hold e.g. in [mathematics](math.md), a field not yet so spoiled by huge commercialization and mostly inhabited by the smartest people -- there is a tendency to look for the most minimal equations -- such equations are considered [beautiful](beauty.md). Science also knows this rule as the [Occam's razor](occams_razor.md). In technology invaded by aggressive commercialization the situation is different, minimalism lives only in the underground and is ridiculed by the mainstream propaganda. Some of the minimalist movements, terms and concepts include:
- [suckless](suckless.md)
- [Unix philosophy](unix_philosophy.md)
@ -19,14 +23,13 @@ Up until recently in history every engineer would tell you that *the better mach
- [less is more](less_is_more.md)/[worse is better](worse_is_better.md)
- [appropriate technology](appropriate_tech.md)
- [reactionary software](reactionary_software.md)
- ...
Under [capitalism](capitalism.md) technological minimalism is suppressed in the mainstream as it goes against corporate interests, i.e. those of having monopoly control over technology, even if such technology is "[FOSS](foss.md)" (which then becomes just a cool brand, see [openwashing](openwashing.md)). We may, at best, encounter a "shallow" kind of minimalism, so called [pseudominimalism](pseudominimalism.md) which only tries to make things appear minimal, e.g. aesthetically, and hides ugly overcomplicated internals under the facade. [Apple](apple.md) is famous for this [shit](shit.md).
Under [capitalism](capitalism.md) technological minimalism is suppressed in the mainstream as it goes against [corporate](corporation.md) interests, i.e. those of having monopoly control over technology, even if such technology is "[FOSS](foss.md)" (which then becomes just a cool brand, see [openwashing](openwashing.md)). We may, at best, encounter a "shallow" kind of minimalism, so called [pseudominimalism](pseudominimalism.md) which only tries to make things appear minimal, e.g. aesthetically, and hides ugly overcomplicated internals under the facade. [Apple](apple.md) is famous for this [shit](shit.md).
There are movements such as [appropriate technology](appropriate_tech.md) (described by E. F. Schumacher in a work named *Small Is Beautiful: A Study of Economics As If People Mattered*) advocating for small, efficient, decentralized technology, because that is what best helps people.
**Does minimalism mean we have to give up the nice things?** Well, not really, it is more about giving up the [bullshit](bullshit.md), and changing an attitude. **We can still have technology for entertainment**, just a non-consumerist one -- instead of consuming 1 new game per month we may rather focus on creating deeper games that may last longer, e.g. those of a [easy to learn, hard to master](easy_to_learn_hard_to_master.md) kind and building communities around them, or on modifying existing games rather than creating new ones from scratch over and over. Sure, technology would LOOK different, our computer interfaces may become less of a thing of fashion, our games may rely more on aesthetics than realism, but ultimately minimalism can be seen just as trying to achieve the same effect while minimizing waste. If you've been made addicted to bullshit such as buying a new GPU each month so that you can run games at 1000 FPS at progressively higher resolution then of course yes, you will have to suffer a bit of a withdrawal just as a heroin addict suffers when quitting the drug, but just as him in the end you'll be glad you did it.
There is a so called *[airplane rule](airplane_rule.md)* that states a plane with two engines has twice as many engine problems than a plane with a single engine.
**Does minimalism mean we have to give up the nice things?** Well, not really, it is more about giving up the [bullshit](bullshit.md), getting rid of addiction and changing an attitude. People addicted to [modern](modern.md) consumerist technology often worry that with minimalism they will lose their drug, typically [games](game.md) or something similar. Remember that with minimalism **we can still have technology for entertainment**, just a non-consumerist one -- instead of consuming a new game each month we may rather focus on creating deeper games that may last longer, e.g. those of a [easy to learn, hard to master](easy_to_learn_hard_to_master.md) kind and building communities around them, or on modifying existing games rather than creating new ones from scratch over and over. Sure, technology would LOOK different, our computer interfaces may become less of a thing of fashion, our games may rely more on aesthetics than realism, but ultimately minimalism can be seen just as trying to achieve the same effect while minimizing waste. If you've been made addicted to bullshit such as buying a new GPU each month so that you can run games at 1000 FPS at progressively higher resolution then of course yes, you will have to suffer a bit of a withdrawal just as a heroin addict suffers when quitting the drug, but just as him in the end you'll be glad you did it.
## Importance Of Minimalism: Simplicity Brings Freedom
Prime number (or just *prime*) is a [whole](integer.md) positive [number](number.md) only divisible by 1 and itself, except for the number [1](one.md). I.e. prime numbers are 2, 3, 5, 7, 11, 13, 17 etc. Prime numbers are extremely important, [interesting](interesting.md) and mysterious for their properties and distribution among other numbers, they have for millennia fascinated [mathematicians](math.md), nowadays they are studied in the math subfield called [number theory](number_theory.md). Primes are for example essential in [assymetric cryptography](assymetric_cryptography.md). Primes can be seen as the opposite of [highly composite numbers](highly_composite_number.md) (also antiprimes, numbers that have more divisors than any lower number).
Prime number (or just *prime*) is a [whole](integer.md) positive [number](number.md) only divisible by 1 and itself, except for the number [1](one.md). I.e. prime numbers are 2, 3, 5, 7, 11, 13, 17 etc. Non-prime numbers are called *composite numbers*. Prime numbers are extremely important, [interesting](interesting.md) and mysterious for their properties and distribution among other numbers, they have for millennia fascinated [mathematicians](math.md), nowadays they are studied in the math subfield called [number theory](number_theory.md). Primes are for example essential in [assymetric cryptography](assymetric_cryptography.md). Primes can be seen as the opposite of [highly composite numbers](highly_composite_number.md) (also antiprimes, numbers that have more divisors than any lower number).
**Primality test**: testing whether a number is a prime is quite easy and not computationally difficult (unlike factoring the number). A [naive](naive.md) algorithm is called *trial division* and it tests whether any number from 2 up to the tested number divides the tested number (if so, then the number is not a prime, otherwise it is). This can be optimized by only testing numbers up to the [square root](sqrt.md) (including) of the tested number (if there is a factor greater than the square root, there is also another smaller than it which would already have been tested). A further simple optimization is to to test division by 2, 3 and then only numbers of the form 6q +- 1 (other forms are divisible by either 2 or 3, e.g 6q + 4 is always divisible by 2). Further optimizations exist and for maximum speed a [look up table](lut.md) may be used for smaller primes. A simple [C](c.md) function for primality test may look e.g. like this:
