#primes

[rbrooksdesign]

"DMT_25," digital + acrylic, April 27, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

No worries if you get lost. Every number is here. Pick any number, divide it by 2 until you end with an ODD. The divisors of said number are those values + the same number of values in Row 1 + the same number of values in any of the *composite ODDs. *If said number divides down to a composite number, then include this Row + other Rows whose ODD(s) are the Prime factors of that initial ODD.

Example: say 13684

13684÷2=6842

6842÷2=3421 and there are two divisions required to reveal the ODD and thus three DMT cell values

3421 is a composite number: 1-11-311-3421 so you include the ODD Rows 1-11-311-3421 three DMT cell values across.

1-2-4

11-22-44

311-622-1244

3421-6842-13684

The DMT is a simple and always ready visualization. Dance!

Example2: 13864

Divides down to 1733, 3466, 6932, 13864 or 4 DMT cell values with the ODD 1733 being Prime.

1-2-4-8

1733-3466-6932-13864

more here___

[the-psudo]

Each colored wave represents a different prime number, from 2 up to 101.

[positivelyprime]

Eisenstein primes (and integers)

You've heard of integer primes, but have you heard of different kind of primes? One of the most beautiful pictures in mathematics I've recently seen is this:

This is a picture displaying the Eisenstein primes and the rest of the post will be me explaining where this comes from.

Firstly, to understand what Eisenstein primes are, we need to know what Eisenstein integers are! An Eisenstein integer is a complex number of the form z = a + b w where a,b are integers and w = e^(2/3 pi i). Normally a small letter omega is used instead of w. Notice that w is a third root of unity, i.e. w³ = 1.

Appending this complex w to the regular integers has some consequences. In particular, we can now view the eligible numbers on the complex plane to get this picture:

The Eisenstein integers correspond exactly to places where two dotted lines cross. As such, where normally one can view integers as laying on a 1-d line, we can now view Eisenstein integers as laying on a 2-d lattice!

Now one may start to wonder if, just like in the integers, one can have Eisenstein integers which are not divisible by other Eisenstein integers. In more mathematics: We call a number p an Eisenstein prime if p cannot be written as a*b where a,b are Eisenstein numbers which are not +-1, +-w, +-w² (the units in this system).

It turns out that some regular primes are still primes in the Eisenstein integers. For example, 2 can still not be decomposed. However, 3 can! We may write 3 = -(1+2w)(1+2w) which means that 3 is not an Eisenstein prime. One may investigate this further (using abstract algebra) to arrive at the picture at the top of this post. The 6-fold rotational symmetry is due to the Eisenstein integers having 6 units.

Of course a natural question is why take a third root of unity and not an nth root? This is a very interesting question and leads to the study of (integer rings of) cyclotomic fields! This concludes fun math fact tuesday

[driftsart]

So Megatronus was the kindest prime, what happened to him? Is he still alive?

Unfortunately, he's not alive anymore. Here's what happened ⬇️⬇️

I still don't have designs for the primes, but I will someday ;)

Megatronus was Prima's brother and Primus's second son. Prima and Megatronus had a great relationship, and both ruled the early Cybertronian lands peacefully. It all went downhill when the Matrix of leadership was discovered.

Prima was known to be a bit greedy and the discovery of such a powerful object just fueled his greed even more. When the matrix chose Megatronus instead of him, Prima was enraged and jealous at his brother and cut off all forms of communication with him.

During Prima's disappearence, Megatronus used the matrix's power to try and create an equal society where no one was treated worse than others, he also developed and improved technology on Cybertron. During his efforts in making Cybertron a better place, the higher classes grew hatred for Megatronus because of his gentleness and sympathy for the lower classes. Many of them turned to Prima, who was in hiding, secretly plotting against Megatronus.

One day, Prima and the higher classes declared war on Megatronus, and the lower classes rose up to defend Megatronus. After a long war, Megatronus mysteriously disappeared, and was never heard from again. Prima later came out bearing the matrix in his chest (fun fact: when the matrix doesn't choose you and is forced on like Prima did, it reacts negatively).

Megatronus is usually left out of many historical texts on cybertron and in some places, it's forbidden to pronounce his name.

Prima is still alive (the matrix gives the primes eternal life unless they are k!lled, they can't die of natural causes). But his time with the matrix has impacted his body negatively (even when he doesn't have it anymore). Leaving him with a creepy looking form.

(that's what I'm thinking of so far ;D)

[the-shy-lonely-weirdo]

✨Thirteenth Prime✨

[vmplvr1977]

Chapter 19 is posted!!!!

[brightgreendandelions]

π(n) is the prime counting function returning the number of prime numbers less than or equal to some natural number n

this is a reference to this poll

[art-of-mathematics]

Sierpinski-triangle and Pascal"s triangle

Pascal"s triangle

I used transparent/translucent paper to color the numbers of pascal"s triangle.

Each color represents a prime number:

Red: 2

Orange: 3

Yellow: 5

Green: 7

Blue: 11

Violet: 13

For each layer (and the according prime number) I colored the numbers of pascal"s triangle if the pascals triangle number is divisable by that prime number.

The advantage of this transparent/translucent paper I used:

You can hold multiple layers against the light (and see the overlapping colors):

2 and 3:

^For instance: if you look at the 6 in the 5th row it is a combination of red and orange - 2 and 3 - as 6 is built up by the primes 2 and 3 (2*3)

2 and 3 and 5:

3 and 5 and 7:

[Afternote: I just realized I forgot to color some numbers in the modulo 2 sheet (red). ]

[ask-uts-earthspark-au]

what would the terran's reactions be to like.... megatronus prime/the fallen or liege maximo?? or any of the 13 originals tbh, and that in alot of continuities op is kind of implied (if not straight up said) to be the thirteenth?

Yknow, actually this gives me a great opportunity to somewhat explain how my AU has the Primes.

I may write a fic off of this, actually.

Anyway: here we go.

Prima

All are somewhat enamored with the whole concept of them basically being their god. Finds their rumored appearance quite cool, and finds it cool that the Matrix is in their sword.

The Fallen/Megatronus Prime

Not quite so fond. Weird, creepy, none of them like him. Thrash genuinely could not roll his optics any harder at his ‘tragic backstory’ that people wrote to make him sympathetic.

Alpha Trion

Kinda interesting. Kept track of history, ran an archive, held onto the matrix between Primes after the others were all dead, originally thought to be basically immortal with how long he lived? Even though he wasn’t actually a true prime, apparently. And did eventually die, but body was never actually recovered. Mysterious, and kind of interesting, overall.

Nexus Prime

Cool as balls. There’s not much else to say, they just think he’s cool as hell. Still don’t quite understand the whole combining thing, but it sounds a little cooler now.

Vector Prime

There are so many possibilities, that it simply blew their tiny newspark processors. Probably the coolest so far.

Solus Prime

Tied with Vector. Originally from the original myth, they weren’t too interested. But hearing the bit from Optimus completely separate from myth, they immediately loved Solus. Thrash loves the hammer, Hashtag thinks it’s very girlboss of him to even exist, Twitch loves the whole ‘can make really cool weapons with the hammer’ thing, Jawbreaker thinks the story overall is pretty inspiring, and kinda cute (albeit somewhat tragic) that he died very quickly after his partner, and was the one who caused the ‘partners/conjuxes come to the hall as well’ thing, Nightshade is very enamored with him being trans. Overall, it’s a hard tie with Vector.

Amalgamous Prime

The shifting bit is awesome. They understand the Decepticons a bit better, and understand better why they even exist in the first place. HT also thinks he has mad rizz for having seduced an Autobot like that.

Liege Maximo

The fact that this bitch is meant to be like their version of satan is kinda… they’re honestly perhaps 5% impressed, at most. And the whole ‘point of origin for all decepticons’ is really laughable to them.

“…at least he’s kinda sexy…?” - Jawbreaker

Alchemist Prime

Kinda boring, but also super cool in that chill uncle way. Also fun that he fucked off from the war and ran a bar. Amazing. Quality decision making skills.

“Like Tarantulas, but in a holy way. And a lot more popular/intimidating.” - Nightshade

Onyx Prime

They think he’s kinda cool, being a big beastformer space pope. Nightshade and Jawbreaker especially like him.

Micronus Prime

Twitch thinks he’s kinda cool, being probably as little as her. Really shows that someone as small as her can be great like that.

Quintus Prime

They all have a unique fascination with him, even if pretty boring. Nightshade is especially interested by the fact that he’s the scientist of the bunch.

Thirteen

The original written myth of Thirteen is incredibly bland to them, and Thrash remarked that clearly they didn’t do a good job. However, when brought the idea of them being Amalgamous’s sparkling, a shifter just like him, and agender, they were all far more interested, and found them a little bit cooler. However, with still so little known, they’re not very interesting compared to the others.

Nova Prime

The fact that he’s known for having not been the best person, yet still respectable enough as ‘The Master Kindler’ and having reintroduced Kindling to table now that the wells were dying, really interests them. Also find it cool how Nova is genderfluid.

“Girlboss, gaslight, gatekeep. 👌” - Hashtag

Sentinel Prime

They’re pretty confident that the very fact that Optimus refused to say his name is enough to say he’s clearly not a very good person, and being told of all that he’d done in his time, they all decidedly hated him.

Optimus Prime

Optimus refused to share very much about himself, beyond his own achievements throughout his reign. They think even higher of him than before. Megatron later revealed that a downside is that he is a loner/introvert & a/antisocial, and usually rather cold/not very personable with people outside of his personal circle of ‘loved ones’.

Rodimus Prime

Nothing was said to his current location, but was noted that he is currently ‘in-training’/not fully a ‘Prime’ yet (won’t be until Op steps down/passes), generally quite polite and sweet if shy, quite strongly religious but really quiet about it, Captain to a crew on a neutral ship, remains neutral himself rather than aligned, a peacetime leader compared to Optimus being a ‘wartime leader’, and technically the true Prime of the reign the Terrans were born under, so they’d be Rodimus’s rather than Optimus’s.

Twitch is even more fond of him, and the others a little more impressed/interested into the prospect of doing a little research into him and those comics.

«—-–-—»

This is canon divergent, so things don’t completely align up with canon.

I happen to HC Solus as TransMasc/FtM & had a female lover, Amalgamous as the original Decepticon leader & have had an ex-Autobot lover + two sparklings, Alchemist as being a ‘peacetime leader’/kept the peace until he died (of old age), and Nova as having revived the practice of Kindling and very protective over sparklings + genderfluid.

Thx.

[ut-girl666]

Idea: The Matrix, being a parasite that uses the Primes as it’s hosts, slowly turns the Primes into eldritch horror-ific beings, and the forms they hold in front of people to make them appear normal are actually just a ‘cloaked’ form for their ‘true’ form (Maccadam from CV for example). This happens to all the Primes, it just usually takes a long time even by their standards to build up enough, and usually the newer/younger ones are like baby horrors.

Another idea: Rodimus, having been born in the primacy essentially as Optimus’s son, has grown up with them, and seen them in their true forms from a young age. It is now impossible to freak him out with them, because before Hot Rod could walk, he looked Nova dead in the face in it’s true form as it cradled him in it’s arms, and cooed up at it. Optimus now says that to Rodimus, they’re not horrors, they’re eldritch wonders. He genuinely looks at them and believes some to be quite pretty. Or he calmly/casually asks if Op thinks Quintus’s Subnautica octopus ass could fit in a flower vase, because octopuses don’t have bones, and this is long dead ghost, so it’s gotta be possible, right? (Op just wants one normal conversation about the Primes with his son. one. that’s all he asks (while snorting laughs but that’s beside the point-).)

In short: The Primes are eldritch horrors in their true forms + Rodimus isn’t bothered in the slightest about this fact.

[a-lesson-you-never-asked-for]

Prime Numbers

A prime number is a number such that it has no factors except 1 and itself. These are often regarded as the building blocks of numbers, and are incredibly important from both:

a theoretical point of view, where problems such as the Riemann Hypothesis and Twin Prime conjecture revolve around the structure of primes

the application standpoint in music theory (Queen's famous song We Will Rock You has a beat that relies on prime numbers), and more relevantly, cryptography.

How do we get prime numbers

To say that a number x is a factor of another number y means that you can split y into equal groups, each group containing x things. So for example, if you wanted to divide 91 watermelons amongst your 13 friends, you can give them each 7 watermelons and everyone gets happy.

Another way of writing this is that 10 is a multiple of 2, or that 10 is divisible by 2.

With primes, you can't do this except by dividing them into groups of 1. For example, 2 is prime because you can only divide it into 2 equally sized groups. You can only divide 11 into 11 equally sized groups.

As a result, prime numbers have some very interesting properties, some of which are unknown. One very easy way to calculate them is by using the Sieve of Eratosthenes. The idea is that you start at 2 and remove every multiple of 2 except itself. So block out 4, 6, 8, 10, 12, and so on. Then you move onto the next unblocked number, which is 3. You go ahead and do the same, remove 6, 9, 12, 15, and so on. Notice that in the next step, 4 is blocked, so we go to 5, and block out 10, 15, 20, and so on. This process is very slow but it's certain. It tells you what the primes are with absolute certainty. Here's a picture to illustrate the idea. This excludes all the even numbers.

The atoms of natural numbers

Primes are regarded as the building blocks of numbers. This is due to the following theorem.

--------------

Fundamental Theorem of Arithmetic

Any integer n can be decomposed uniquely in products of powers of primes.

Examples

--------------

10 = 2 × 5

15 = 3 × 5

24 = 2³ × 3

There are many important theorems that come about due to primes, and almost all of them have to do with a topic called modular arithmetic.

Where to from here...

This is probably the extent to which you need to know about primes. Most of the ideas used will be introduced, as mentioned before, on an ad hoc basis. We will focus more on the code building aspects in our next parts, talking about binary and ISBN codes, before moving onto some more complicated examples of encrypting information.

[rbrooksdesign]

"DMT_18," digital + acrylic, April 20, 2024, Reginald Brooks

DMT = Divisor (Factor) Matrix Table

[rotorarc]

The 13 Primes

[thecreditsroll]

Someone took his favorite stick

So he's crawling outta hell to take it back

[rowiewritesstuff]

No one: My ass writing fics at 8am on 3 hours of sleep:

[darks-lair]

WARNING: BRIGHT COLORS/LIGHT

Who likes to spend much more time on doodles than one should? Darksteel

Went crazy with colors and doodled Megatronus and Maximo

Tried to combine green and red in a not Christmas way but Max turned out looking like a Christmas tree anyway 😭

Megatronus turned out amazing tho in my humble opinion

I also drew a background i never ended up using there so

Here's Liege rocking your grandma's wallpapers

And those will be hanging out on my Tumblr header

(please credit me if you're going to use them on your profile)