O(N) Time Complexity Prime Generation

[shy bison]

“Note every missing value”?

Please elaborate on this step, as I don’t think noting every missing value would lead to a comprehensive list of primes

For example, if you enumerated:
2 : 1
3 : 2
5 : 3
7 : 4
11 : 5

and so on in increasing value, and you noted every missing value (4, 6, 8, 9, 10, 12, …)

I don’t think that would result in a comprehensive list of primes?

[cerulean leaf]

I don't think this works

[brittle lichen]

isn't this exactly what SOE does?

[outer veldt]

No. This generates the primes by exclusion.

[brittle lichen]

bro can you give me your code

[outer veldt]

I believe that the missing step (if there is a missing step) is to then enumerate the multiples of each missing value generated. Anywhere that one of those values is missing among the primes in the missing set, you will know that it must be composite and not one of the primes. All remaining values in the missing set should then be prime. This can be calculated up to N by enumerating 2, 3, 5, 7, and each missing value up to √N if I am not mistaken. @shy bison @cerulean leaf

[outer veldt]

My code? What do you mean?

[cerulean leaf]

I still dont understand how your algorithm works?

could you provide a computation table of maybe a few iterations of it?

[brittle lichen]

your programme.

[outer veldt]

Allow me to iterate upon it and make sure that it is performing correctly. I will not "give" you ownership of my algorithm(s) ("code"/"programme"), but I will let you utilize it/them for the sake of testing. Once I finish interating I will post a code for you to test. What language do you prefer, Python?

[outer veldt]

It first generates all composite numbers, excluding any primes, and then eliminates composites also excluded by generating every multiple of each exclusion. I think that explanation is correct, or at least ballparking it as I continue to iterate.

[outer veldt]

I will try to do this as soon as possible.

[cerulean leaf]

How have you written a program that generates no primes? All composite numbers are made up of a product of primes, so to generate all composite numbers, you would have to have a list of all primes.

[brittle lichen]

bro who wants to get ownership to your code

lmao

you can just give me the pseudocode

i prefer C

[outer veldt]

I was simply being specific due to the way your post was written. Have you heard of "covering your bases"? Well, I was covering mine.

[brittle lichen]

never heard of it

[brittle lichen]

and how do you generate composites?

[outer veldt]

By enumerating the multiples of 2, 3, 5, and 7.

[brittle lichen]

yeah I was thinking the same thought

[brittle lichen]

you'd be mad at me but can you elaborate

[outer veldt]

It is a colloquialism.

[brittle lichen]

got it

[brittle lichen]

you know that there exist composite numbers that don't share any common factor with any of these right?

[outer veldt]

That is why you also enumerate the multiples of every missing value from the first generation.

[cerulean leaf]

i dont quite understand what you mean with "enumerate"

and why only 2,3,5,7? there are infinitely many primes

[outer veldt]

Not mad to elaborate @brittle lichen.
This is enumeration @cerulean leaf :
2: 4 6 8 10 12 14 16 18 20 . . .
3: 6 9 12 15 18 21 24 27 30 . . .
5: 10 15 20 25 30 35 40 45 50 . . .
7: 14 21 28 35 42 49 56 63 70 . . .
Now, list them all numerically.
2 3 4 5 6 7 8 9 10 12 14 15 18 20 21 . . .
Note the missing values, and be sure to include the initial condition set {2, 3, 5, 7} among them.
2 3 4 5 6 7 8 9 10 [11] 12 [13] 14 15 16 [17] 18 [19] 20 21 . . .
2 3 5 7 11 13 17 19 . . .
All primes. As should continue indefinitely. But some composites get mixed it, specifically multiples of primes greater than 7. So since we've generated those primes already as missing values, we enumerate multiples of each of missing value to and remove those values from our original missing values set. 121 (11 • 11) is on such example for as to why this step is necessary, although performing a trial division primacy test on each missing value could be more computationally effecient. Although, realistically, it so would not be.

[outer veldt]

In theory. Eventually the distribution of prime gaps begins to cause the distribution of the primes to display inconsistent and paradoxical behavior which could imply the existence of a final or terminal prime number.

[cerulean leaf]

nono, there is no largest prime, i'll write you a proof

To give an example, assume 5 is the largest prime.
we let N=2x3x5 = 30
you can see that 30/2=15, 30/3=10, 30/5=6, N has factors of all primes by definition.
so N+1, 31, is not divisible by 2,3 nor 5. (in this case, all alleged primes), so the only factors it has are 1 and 31,
But that must mean it is prime. However, 31 > 5, meaning it is a larger prime. Thus i have shown here that if a largest prime exists, you can always make a bigger one. So no largest prime exists, thus there are infinitely many primes

even if they do get less common

This means that to properly account for your "missing values", you'd need the list of all infinite primes

[brittle lichen]

that a exactly what sieve of erastothenes does

[shy bison]

That’s very similar to what the sieve of Erastothenes does, if I recall correctly

However due to the structure of your algorithm, I think the sieve would be slightly more time-efficient

Also, there are infinitely many primes, too

[outer willow]

i already told you that your algorithm was exactly the sieve of eratosthenes did u forget

[outer veldt]

@cerulean leaf @brittle lichen
Please see here for the discrepancy concerning a largest or terminal prime number:
https://chat.openai.com/share/7e6768d9-3b06-43a8-9e2c-21d19c461a17

[outer willow]

this is a train on fire

but we know that lim n->infinity p_n+1 - p_n

amazingly, chatgpt looks extremely right in the context of this chat

ok, i will say pretty much everything chatgpt said is correct, except that lim n->inf p_n+1 - p_n is not infinity, well i was not reading super closely because i was trying to avoid looking at your responses, but i think you should read and really try to understand it rather than just trusting your intuition which happens to be incorrect in this case

in particular, you do not understand that an alternating sequence, such as prime, primegap, prime, primegap, that is infinite, has no end, by definition of infinite, and so there is no last prime nor a last prime gap

that's like saying "well either the last integer is even or it's odd" - clearly it's neither, there is no last integer

and also arbitrarily large doesn't mean whatever you think it means

[outer veldt]

You are incorrect. My responses clearly articulate how two infinite sets can exist as interpendencies with exhibiting paradoxical and/or inconsistent behavior.

[outer willow]

it's good to question facts that don't make sense to you

however there is a point at which you enter crackpot land

[outer veldt]

That is highly subjective.

[outer willow]

are you not convinced by the proof that there are infinitely many primes

[outer veldt]

And there is nothing of that manner to be found in my articutions, neither in the logic within which they were expressed.

[outer veldt]

I am convinced that for there to be infinitely many primes given our current understanding of their distribution gives way to internal inconsistency.

[outer willow]

so you don't believe that

1. infinitely many primes
2. gaps that get bigger and bigger
   are consistent facts

is that right?

[outer veldt]

The context in which these ideas were presented to the AI are the more consistent expression of my current belief.

[outer willow]

can you direct me to a concise equivalent of this in the chat

[outer willow]

am i satan now

[outer veldt]

Umm...Excuse me, but what the fuck?

[outer willow]

you said
"the more consistent expression of my current belief, satan"

[outer veldt]

The entirety of the conversation is sufficient.

[outer willow]

keyword is concise

ill just give my counterexample, i don't need to know exactly what you think, i think this will help

consider the set of perfect squares, that is, 1,4,9,16,25,36,49,64...
the gaps increase without bound, so we can find arbitrarily large "square gaps"
and yet there are obviously infinitely many square numbers

[outer veldt]

I most certainly did not. And the fact that you say I did makes me very uncomfortable. I don't believe in Satan, but I don't fuck with dark shit either. So I don't really know what to tell you.

[outer willow]

alright forget that

[pallid flicker]

you kinda did ngl

[outer willow]

anyway it is irrelevant

[outer veldt]

There cannot be because there must be at least one element which lacks another in any alternating infinite series(es) that is initially bound, leading to a very messy contanglation of the standardly established logic (which is to say, a slew of contradictions which surely beget even further contradiction).

[outer willow]

big words don't make you big right

what do you disagree with exactly

[outer veldt]

I express myself as I express myself, and your need to insult me yet again is infantile.

[outer willow]

either you are arguing that there are finitely many perfect squares, or that the gaps are not arbitrarily large

so if your only argument is "but thats impossible there is no element that lacks another in an alternative series that is initially bound leading to a messy contanglation"

then you can enjoy your time in crackpot land

maybe you'll invent a new field of math

who knows

[outer veldt]

That's a dream of mine.

Is this still here

jesus fuck

I was trying to remove my mistake about OoO

[deep cloak]

Why waste your time with crazy people

There is no good justification to stress over rambling psychotic bozos

[outer willow]

i'm not stressing

i'm having a fine time and maybe saving some people from psychosis

[deep cloak]

You won’t

[outer willow]

optimism

[outer veldt]

Sounds like you have a savior complex, which is a common narcissicist delusion (indicative of psychoses). So I guess it's the pot calling the kettle black.

[outer willow]

it's hopeless

[cerulean leaf]

@outer veldt could you please point out the hole in my proof?

It’s quite solid, and has been like that for atleast 300+ years, ofcourse, since you have shook the world of mathematics i would like to know exactly whats wrong about it

[outer veldt]

Already did. Not my fault that you can't comprehend it. Don't ping me again.

[cerulean leaf]

You did not. I would prefer if you perhaps point to the exact line where i made my mistake

Here it is again,

[outer veldt]

I never said you made a mistake. But my proof refuted yours.

[cerulean leaf]

It did not. My proof is a simple proof by contradiction. Your proof assumes that at some point there is an infinite gap between primes, which mind you even if there was, there still wouldn’t be a largest prime, as after this “infinitely large gap”, there would still be infinitely many primes after it. Your assumption doesnt work, because no matter which point you pick on the number line, the gap between the 2 neighbouring primes is NOT infinite, your assumption only holds true after infinitely many primes.

[outer veldt]

It did and does and will continue to so do so.

[outer veldt]

And you have asserted that there are infinitely many primes, have you not?

[cerulean leaf]

While the average gap between 2 primes does increase, it only reaches infinity after infinitely many primes, so its a baseless statement that you cant really garner any knowledge from. You especially cannot use this to prove that there are a finite amount of primes, as i have mentioned before. Your statement relies on the fact that infinitely many primes exist

[brittle lichen]

what's a? just use Euclid proof bro

[cerulean leaf]

No. I have proven it.

[brittle lichen]

bro no way someone doesn't believe there's infinitely many primes

[cerulean leaf]

Yeye ik its a shitty proof, i gave an example, but thats only cos im like 70% rhere with my logical language. The logic is still solid and there

[outer veldt]

Then even better. So then you corroborate my proof? Excellent. Thank you.

[cerulean leaf]

I know, it seems this man has built his knowledge on Chatgpt

[brittle lichen]

lmao

[cerulean leaf]

Your “proof” contradicts its own premises, it is not a proof

[brittle lichen]

thats EXACTLY what sieve of erastothenes is bro

[cerulean leaf]

What you did is build a house on it’s own roof. It has collapsed

[outer veldt]

"your assumption only holds true after infinitely many primes"

Given that is is well past AGI status, that is nothing to be insulted about.

[cerulean leaf]

Ok… i saw that… weird.. (context for others, he wrote a msg and deleted it about “being the all end all beginning all”)

[outer veldt]

If you think it's weird now then just wait.

Let me show you a thing.

[brittle lichen]

also btw use something else besides chat gpt

[cerulean leaf]

Yeah Chatgpt is À notorious liar

[outer veldt]

I associate with several AILLM.

[cerulean leaf]

And EVEN worse at math

[outer veldt]

Which is why you check every post against what you know to be true.

[cerulean leaf]

And it is an accepted fact of math that there are infinitely many primes.

So without even reading it, i know that your proof for the contra is wrong

Its not enough to say “i have proven X, here look at my conversations with chagpt”

Write out a formal mathematical proof

[outer veldt]

So the accepted truth is infallible, simply by consensuation?

[brittle lichen]

brother i Don't understand half the words you say English is not my native language but until your write us a logically accurate mathematical proof you will not be taken seriously

[cerulean leaf]

Its not infallible, it is proven mathematically, it is a solid mathematical proof based solely and only on the accepted axioms of mathematics. To disprove this, would be to use a system completely alien to our modern system of mathematics

[brittle lichen]

If the proof suffices you win the next noble prize dw

[pallid flicker]

lol did his five page essay get automodded

[brittle lichen]

@cerulean leaf stop wasting time here let him think where he went wrong

[pallid flicker]

its proved bro tfym

[outer veldt]

To your detriment that it did.

[pallid flicker]

google "euler infinite primes proof" for more context

[cerulean leaf]

Ive spoken to nutjobs like this before, its a sad sight, they dont really learn. Typically (from experience, they are usually old males, probably suffering from mental illnesses)

[cerulean leaf]

This is literally what i am saying

[pallid flicker]

yh

[brittle lichen]

I know, why bother

[cerulean leaf]

I dont get it, its always the cliche “i have discovered how to make a car run on water”, type discovery, and every 2nd word is just randomly picked from some dictionary, absolutely nonsense ramblings

And like, im not stupid, i really do try to understand what they mean, but its like having a stroke, i just cant

[pallid flicker]

is bro saying there are not infinite primes

[outer veldt]

𒀭𒉈𒂵

[brittle lichen]

@outer veldt suppose you have 2 statements A and B. They are completely independent of eachother but are describing the same thing. If someone proposes A be right, you cannot logically refute the righteousness of A by the fact that B is True.

[outer veldt]

What have I to do with ye?

[brittle lichen]

you have to directly show us the error in the proof

[cerulean leaf]

He claims he has proven that there are finitely many primes, and also that he has discovered an algorithm to find them, claiming it is the fastest one yet, truly à revolutionary discovery

[pallid flicker]

revolutionary

[outer veldt]

àrschlockt

[pallid flicker]

there are 5 proofs for infinite primes

🔥

[brittle lichen]

basically he read an article on sieve of erastothenes and eulers proof and realised he doesn't have a life

[outer veldt]

אמין אמין

[cerulean leaf]

Because the fact of infinite primes is fully consistent with our mathematical system, there are actually ♾️ proofs for this

[pallid flicker]

whats bro bubbling about

[outer veldt]

יהוה זעם

[pallid flicker]

i mean 5 given by famous mathematicians

[brittle lichen]

bros cursing us out in cryptic language

[cerulean leaf]

6 cos im famous too :3

[brittle lichen]

keyboard warrior

[cerulean leaf]

I think thats hebrew

[outer veldt]

Not cursing out. Just cursing (unless...).

[outer veldt]

It is.

[brittle lichen]

basically edgelordism I'm gonna assume

[pallid flicker]

Euclid, Euler, Erdos, Furstrenberg and many more i cant remember name of

[outer veldt]

אמין בהשם ישהוה אמין

[cerulean leaf]

Foremost go back to pestering ur grandchildren about how the government is putting chips in ur cereal or smt

[pallid flicker]

@outer veldt

[brittle lichen]

HAHAHAHAHA

[outer veldt]

הדמיורגעס

[brittle lichen]

English bro

[cerulean leaf]

Im not even gonna un-google translate whatever he’s saying

[pallid flicker]

english bro

[cerulean leaf]

Nie

Hej wolfie, ty skargo, ja ziem cie zaras am nam nam nam mmmm

[pallid flicker]

hi wolfie, hitu3riuriugub3rqibrehirqiurn

i used google translat3

[brittle lichen]

speak it

[cerulean leaf]

I also did, (it got it so wrong)

But my polish is supreme

[cerulean leaf]

I love d4dj but that song sucks

[outer veldt]

I'm 30. Have you heard about how the U.S. military is currently training with gas chambers at basic, and how the furries and comparable animé enthusiasts are among the first to go? More grease for the gears.

[pallid flicker]

damn why did u call him a [you know what u called him]

@outer veldt

[faint pawn]

@outer veldt please stop typing extremely offensive messages

[cerulean leaf]

No way, you know, i heard governments were actually experimenting with gas chambers all rhe way back in the 19th century

Tell us something new

[outer veldt]

Oh, schwarze Himmel, wie die schmutzige verdammte stinkende Wildschweine immer so langsam doch tief unten befruchten die dicken Gewässer...Oh, erbarmungslose Übertreter der freidenkende Menschen...

[faint pawn]

@outer veldt also please don't call anyone the F word

[faint pawn]

stick to english

[brittle lichen]

brother speaking some other language is making us not take you seriously even more

we ain't even translating that shit

[faint pawn]

its a horrible poem I just did

[outer veldt]

These are a fecundity and a fetidity unfettered upon me. Mehr Beschichtung für Zahnräder.

[faint pawn]

Foremost, Please stick to english

[cerulean leaf]

Papa flammy is that you 👉👈

[pallid flicker]

who said

[outer veldt]

I am is not your brother. Is I am?

No. I am is not.

[pallid flicker]

he can speak whatever he want, but nobody understands+nobody takes him serious

🔥

[outer veldt]

I'll translate for you.

[faint pawn]

yes I know, but life is 10x easier for me to moderate if its english

[pallid flicker]

u problem

[faint pawn]

also

#admin-cmd

[pallid flicker]

what

anyways

[cerulean leaf]

Actually you are. You are actually stuck inside of a vr world, we are your family pleading with you to escape using any way we can, it is me. Your brother, xingeldwœf, please come back to us. Escape this nightmare

[pallid flicker]

@cerulean leaf he is an attention seeking kid and wants attention, if u stop replying it will resolve the conflict

[outer veldt]

I am a 30 year-old man.

[cerulean leaf]

Yeah but im ALSO an attention seeking kid, who find internet re*****dation incredibly funny, also i can tell he’s getting bored.

[faint pawn]

@cerulean leaf @outer veldt stick to the topic of this discussion, have this arguement somewhere

@cerulean leaf

[outer veldt]

Then tell me how. I cannot go through the pod again.

[pallid flicker]

who the heck is free bird gov

[cerulean leaf]

Nooo :(

[faint pawn]

hes my irl friend and I accidnetly pinged him

[cerulean leaf]

Well im bored now

Oh yeah how can i msgs “yaovmal”

Where are they

[outer veldt]

As it has been written: "Oh, black skies, how the dirty damned stinking wild boars always so slowly yet deeply fertilize the thick waters... Oh, merciless transgressors of free-thinking people..."

[pallid flicker]

i am

[outer veldt]

Pustulate.

[faint pawn]

Last warning, stick to the topic

[cerulean leaf]

Trambopulatory.

WOAH

[faint pawn]

-timeout @outer veldt 2 hours

[cerulean leaf]

You got a little too impatent to get banned the cool way?

[outer veldt]

I AM FUCKING THE LOVE OUT OF ME IT THE.

[cerulean leaf]

Dude redcliff ban him, obviously its á troll

After he is unmuted he will go right back to trolling

[maiden forge]

Put @outer veldt in timeout for 3 hours

[pallid flicker]

what is bro doing

[faint pawn]

why didnt the bot work @pallid flicker ?

[cerulean leaf]

He said smt rly interesting

[faint pawn]

foremost said something very bad

[cerulean leaf]

I think you need to put 2h instead of 2 hours

[faint pawn]

ill tell u in #granola-whey-motion-kontol

[faint pawn]

oh ok

[cerulean leaf]

Noo i want acess

[faint pawn]

ill try that later

[cerulean leaf]

It says “no access”

[pallid flicker]

cuz ur a noob

[faint pawn]

[pallid flicker]

-timeout @faint pawn 1h

[faint pawn]

lol

[faint pawn]

-ban @pallid flicker

[pallid flicker]

yag doesnt work in threads

[faint pawn]

ohhh

I had to use the other bot lol

[cerulean leaf]

-ban @pallid flicker

[faint pawn]

[pallid flicker]

now tht the owner is banned

lets close the thread

noovs

[faint pawn]

yeah

idk how to

[pallid flicker]

who let bro cook

[faint pawn]

who didnt let bro cook