PRIMES?!?

[Anonymous No.2175072]

What percent of all numbers are prime?

[Anonymous No.2175082]

0

[Anonymous No.2175084]

lim x->inf of ln(x)/x, if the Riemann Hypothesis holds

[Anonymous No.2175080]

OP here, idk why my pic inverted like that. Its a picture of pi(x), a function which indicates how many primes exist below a certain number, x

[Anonymous No.2175086]

I don't think we know enough to answer that for any non-finite set.

[Anonymous No.2175087]

50%

[Anonymous No.2175088]

fuck knows, but there are primes everywhere

http://en.wikipedia.org/wiki/Bertrand%27s_postulate

[Anonymous No.2175091]

Hmm, I bet the number would be irrational. We'd only get it to a certain degree of accuracy.

[Anonymous No.2175093]

I ask because I've figured it out for all numbers.

Just wanted to know if anyone else had solved it yet.

[Anonymous No.2175110]

>>2175093

I have a truly marvelous demonstration of this proposition which this margin is too small to contain.

[OP No.2175106]

Also, my theory doesn't rely on any external hypotheses, it is self contained and pretty damn elegant.

Wish I could share it with you all, I'm so unbelievably excited I feel like running down the street screaming the solution lmao

[methhead No.2175105]

>Erdős proved that for any positive integer k, there is a natural number N such that for all n > N, there are at least k primes between n and 2n. An equivalent statement had been proved earlier by Ramanujan (see Ramanujan prime).

[Anonymous No.2175117]

>>2175106
why, what do you wanna do with it?

c'mon, let us find the mistakes that are probably there

[Anonymous No.2175123]

The average density of primes around n is 1/log n.
As n --> infinity, 1/log n--> 0.
So 0%.

[OP No.2175124]

>>2175110
Then I guess it's a race haha

[OP No.2175150]

>>2175123
It cannot be 0%, there are infinitely many primes and the trend does not seem to slow down when looking at pi(x)
>>2175117
I'm simply trying to explore the world of primes. I cant stop thinking about them lately. Also, the theory results in a percentage that so closely resembles the known values for pi(x) that I cannot imagine there being a serious error.

[Anonymous No.2175164]

>>2175150
> Not 0%
> PROOF: It looks like it. QED.

Yes, you can have a subset of an infinite set still make up 0% of that set and be non-empty, even infinite itself.

[Anonymous No.2175169]

0.

No, really. Lebesgue measure zero.

[OP No.2175175]

>>2175164
So a smaller infinity then? What a perplexing idea. I spose it kinda makes sense though.

Well then I guess I'm wrong

Even still, I have an amazing estimator for pi(x) lmao

[OP No.2175188]

saying 0% of all numbers are prime is the same as saying 100% of all numbers are non-prime isn't it?

I am beginning to disagree with that idea.

[Anonymous No.2175195]

this just turned into a

0 != 1

thread

BUT WITH SET THEORY

[Anonymous No.2175190]

>>2175106
>Wish I could share it with you all
And you can't because...

[Anonymous No.2175200]

>>2175150
>It cannot be 0%, there are infinitely many primes
Nope.

Let's talk about cardinalities of infinity. As an intro, there's countably infinite, and then there's uncountably infinite.

The integers are countably infinite. You can keep counting up forever, and they never stop. But the reals are uncountably infinite. Inbetween EVERY two consecutive integers, there are an infinite number of real numbers. Another way of saying this is that there is no such thing as two "consecutive" real numbers.

Since the integers are, by a certain measure, literally 0% of the set of reals, and the primes are a subset of the integers, then the primes are 0% of the reals.

This doesn't mean there aren't any though. Percentage gets weird when you're dealing with infinite sets.
http://en.wikipedia.org/wiki/Lebesgue_measure

[OP No.2175202]

>>2175190
If it does turn out to be some previously unknown idea, I want to make sure I can claim it as my own.

Like I would trust 4chan XD

[Anonymous No.2175213]

>>2175202
Post it on arXiv with all the other "proofs". That'll protect your claim until you can get a journal to publish.

[Anonymous No.2175217]

>>2175202
i had the same mindset when i "invented" Lucas Numbers...

[OP No.2175226]

>>2175200
Thank you for the informative post. I'll read up on the link, but I'm still inclined to disagree. Even though I may be wrong, blindly accepting knowledge is not how I operate.

If it makes sense I'm sure I'll be swayed.

In the meantime, it wouldn't literally be 0% would it? 0 times anything is zero. It would just be infinitely small, right? it would still have to have a value greater than 0 to remain true though, since there are infinitely many primes. even only one prime would produce this result.

[Anonymous No.2175231]

What percent of all positive integers are prime?

[Anonymous No.2175235]

>>2175226
But 1/inf = 0. Also (countably infinite)/(uncountably infinite) = 0.

[Anonymous No.2175239]

>>2175231
What percentage of all /sci/posts feature this woman's image?

[OP No.2175244]

>>2175226
Although I see how I am wrong after thinking about it.

The limit of 1/x as x approaches infinity is most certainly 0, even though you have one something out of an infinite somethings.

hmmm. This is going to take a while to digest...

[Anonymous No.2175243]

>>2175235
(cont) That's an abuse of notation, of course, since division is only defined for numbers, and infinity is not a number. That's really the heart of the problem when asking about "percentages" of infinite sets.

[Anonymous No.2175246]

>>2175239

yo math tricks girl is damn fine

she has the knowledge to get her into college

[Anonymous No.2175247]

your pic inverted because what looks like white is really transparency

also, i have no idea

[Anonymous No.2175250]

>>2175231
THOSE FAKE EYEBROWS
DO NOT WANT

[Anonymous No.2175257]

>>2175226

The set of reals minus the set of integers is still uncountably infinite. Infinitesimal% is probably a better answer, but percents are usually expressed as rational numbers.

[Anonymous No.2175258]

>>2175250

math tricks girl is all natural. are you?

laughingpremeds.jpg

[Anonymous No.2175260]

wouldnt 1/infinity still be 1 number? so if there were 1/x primes and x was infinity, wouldnt there be 1 prime

[Anonymous No.2175259]

>>2175226

OP, what is 0.999 repeating?
Now thing about 0.000 repeating with a one "at the end". That's what you're dealing with here when you phrase it as "percent of _all numbers_". If you want to avoid that problem then rephrase as "percent of integers".

[OP No.2175268]

Continuing along this line of thought, do you think pi(x) becomes closer to linear as x increases?

I'm inclined to believe so myself, but im unsure.

I dont believe it's derivative could continually increase without eventually decreasing, which would mean it oscillates.

I don't believe it continually decreases either, once again unless it oscillates.

It's easier to believe that it just flattens out.

[Anonymous No.2175277]

>>2175260
Division is only defined for numbers, and infinity is not a number. You'd have to express this as a limit, and the limit is 0.

>>2175257
>infinitesimal %
There are no infinitesimals in the set of real numbers, though.

[Anonymous No.2175279]

>>2175260

Infinity is not a number, so arithmetic operations on it are all undefined.

[Anonymous No.2175280]

i bet it's irrational

[OP No.2175285]

>>2175259
OH DAMN, MY BAD

You're right, I meant integers. That could really throw things off, huh?

[Anonymous No.2175290]

>>2175268
This what you're referring to?
http://en.wikipedia.org/wiki/Prime-counting_function

[Anonymous No.2175291]

>>2175277

And there is no infinity in a set of real numbers.

[Anonymous No.2175295]

>>2175259
Even then, don't the primes get more sparse as you go? By that definition alone, it would seem that the percentage has a limit of 0.

[Anonymous No.2175298]

>>2175268
Just read the wiki page OP...
pi(x) ~= x/logx .
A better estimate is li(x).
The error bounds for these estimates are also given by various theorems in the form of big-o notation.
If the Riemman hypothesis is true, we get a much smaller error term for li(x) as an estimate of pi(x).
Also, pi(x) doesn't have a deriverative, its discontinous.

[Anonymous No.2175304]

>>2175258

I poked around and found the real math tricks girl.

pic related

[OP No.2175311]

>>2175298
Yes, but these are estimates
All estimates for pi(x) are continuous. assuming they are a valid estimate for all x, consider their trend instead.

While locally pi(x) is indeed discontinuous, when "zoomed-out" it appears to follow a continuous form. This is where the estimates on that wiki come from.

I'm wondering what tendencies this general trend has.

[OP No.2175313]

>>2175311
I should have said ALL

[OP No.2175315]

>>2175313
DAMMIT. I should NOT have said all

[Anonymous No.2175318]

>>2175311
>>2175313
IMO, x/pi(x) goes to 0 as x goes to infinity.
That's basically the answer to your question, if you can find a proof.
http://en.wikipedia.org/wiki/Prime-counting_function#Table_of_.CF.80.28x.29.2C_x_.2F_ln_x.2C_and_li..
28x.29

[Anonymous No.2175386]

Consider this, OP. Let f(n)=pi(n)/(n/log n). Then f(n) tends to zero by Gauss' prime number theorem. But pi(n)/n=f(n)/(log n), and as n tends to infinity, the right hand side tends to 0/infinity=0.

[Anonymous No.2175395]

>>2175298
>pi(x) is discontinuous
Not technically true. It's defined on the integers, and by the standard epsilon delta definition it's continuous, but this is only because every integer is isolated in the sense that claiming something to be true for integers sufficiently close to n is a vacuous claim, as there are no integers but n itself sufficiently close to n.

[Anonymous No.2175478]

YOU GUYS ARE IDIOTS THERE ARE AN INFINITE NUMBER OF NUMBERS BUT ONLY FINITELY MANY PRIMES. ANSWER IS 0.

[Anonymous No.2175502]

>>2175478
since when are there finitely many primes

[sage No.2175520]

>>2175478
>FINITELY MANY PRIMES

Whoa!

[Anonymous No.2175542]

The answer to OP is 0. Can we please move on?

[Anonymous No.2175546]

>>2175478

Take an intro to an Analysis class. The disproof of "finitely many primes" is, more or less, taught within the second month of the semester.

[Anonymous No.2175573]

>>2175542
how do you know, I mean sometimes primes are really dense

[Anonymous No.2175592]

okay so there is a random number between 0 and infinity and you can make a choice, a, b, or c

a.) If it is between 0 and 10 you win one billion dollars, otherwise you get nothing.
b.) If it is between 10 and one billion, you win one million dollars, otherwise you get nothing.
c.) You get one dollar.

which option should you choose?

[Anonymous No.2175602]

>>2175592

I'll take a shot in the dark, and choose a.

I know everyone will choose c, but I live my life by taking risky chances!

Really, though; my logic for it is that there are infinitely many numbers between 0 and 10(if we're dealing with the reals). Given that the question proposed asked about a number between 0 and infinite, option a seems to be the most sound choice to me.

[Anonymous No.2175610]

>>2175592
I choose to fuck your mum

[Anonymous No.2175612]

>>2175592

WHATS THE PROBABILITY DISTRIBUTION FAGGOT?

[Anonymous No.2175625]

>>2175612
uniform

[Anonymous No.2175646]

Prime numbers get increasingly rare as n increases. I would guess that the percentage of prime numbers in the limit that n goes to infinity would be just about zero

[Anonymous No.2175665]

bro you mean the totient function. the shorthand for that is phi, not pi.

[Anonymous No.2175675]

>>2175592
>random number between 0 and infini
stopped reading right there.

[Anonymous No.2175786]

there's an infinite amount of prime numbers

so

100%

[Anonymous No.2175805]

There is a 1-1 map between integers and primes. There is also a 2-1 map. And a 1-2 map. So... there is no consistent answer. Infinities are funny like that.

[Anonymous No.2175811]

>>2175786
this is totally ridiculous. Tnx for the lulz!!!