/sci/ - Science & Math

>>6773906
Not divisible by 4302.
Find one that is.
>protip: you can't.

>>6773928
4302 is not prime and all primes after 2 are odd so obviously that does not work.
im talking about a formula to discover all primes

>>6773934
>so obviously that does not work.
Stop the fucking presses.

>discover all primes
What more do you need than what already is?
You already know how to find them.

Well for starters we know any number can be written as the sum of two prime numbers, so that since we know there are infinite numbers there are twice as many infinitely many primes

>>6773939
you are useing one conjecture to validate another
we are looking for a way to discover primes

>>6773943
>crunch 'em

>>6773951
a way to calculate them is what im looking for, there must be a way

>>6773964
There is.
>take arbitrary number
>test it for being prime

>>6773939
>infinity * 2
heh

>>6773906
>a way to calculate them is what im looking for, there must be a way

There is an explicit formula for the prime-counting function, a fact surprisingly few people know. It is:

<span class="math">\pi(n) = \sum_{j=2}^n \lfloor \frac{(j-1)!+1}{j}-\lfloor \frac{(j-1)!}{j} \rfloor \rfloor[/spoiler]

>>6773977
>prime-counting function <span class="math">\pi (n)[/spoiler]

No, OP's looking for the prime number function <span class="math">p_n[/spoiler].

http://mathworld.wolfram.com/PrimeFormulas.html

Similar formulas for this function do exist, but as the article states, a basic Sieve would work much better (though in order to calculate ALL the primes, the sieve would be infinite, ie, computationally impossible; for this purpose a "guess and check" algorithm would work better, as others have mentioned).

>>6773906
they're not divisible by any natural number between 1 and themselves

is that a good rule that I just came up with

Every odd number is prime.

1 is prime, 3 is prime, 5 is prime, 7 is prime, etc

>>6773906
Only rayquaza is prime.

>>6774049
>1 is prime

>>6774040

winner

>>6774490
That's your only objection?

>>6774049
That's bullshit, what about 11?

>you will never stick a prime number up your ass

>>6774524
Prime.

>>6774524
11's even more prime than 9
9 is less prime, but still relatively more prime than 13

>>6774526
Oh my god, it works!

>>6774525
I've got a prime dick.
:^)

>>6774049
>1
Prime
>3
Prime

All odd numbers are prime.
>Proved by induction

Not sure if troll thread, but anyway read:
http://en.wikipedia.org/wiki/Goldbach%27s_conjecture
If you can figure out a formula for the primes then you can probably prove this.
If you, yes specifically you, could figure out the formula then there wouldn`t be a reward of nobel prize for this problem...

>>6774534
please stop oh god

>>6774049
Perhaps you meant to say that all primes are odd numbers? I'm certain that twenty-one is not a prime number, yet it is an odd number,

I asked one of my professors if matrices had a defined property similar to the primality of numbers. All I got from him was a "no", but I don't think I conveyed exactly what I meant (maybe he thought I was asking if a matrix can be a prime number). Does a question like this even make sense? Can there be "prime" factors for a set of matrices?

>>6774529
Uh... are you trolling? According to his rule 17 and 19 would be prime.

>>6774637
>17
>19
>not prime
I don't know who's jewing who anymore.

>>6774637
17 IS prime, what's your point?

>>6774642
Oh, duh, those are prime. Can't believe I missed that.
I guess his rule is correct after all.

>>6774637
>>6774642
>>6774648

>>6774049
>>6774534

omg these guys are being sarcastic... so stop taking them seriously, and also stop taking the people who are taking them seriously sarcastically, because that's just as retarded

>>6774490
and you're a dumb fuck. he said all odds are prime and you pick out "1 is prime"?

>>6774661
edit:

who are sarcastically taking the sarcastic people serious

>>6773928
Why 4302?

>>6773977
Is there a name for this formula? Where can I find a proof?

>>6774615
You can consider the ring of n x n matrices, and then consider the matrices that generate principal prime ideals, if any exist.

2^2^n + 1

>>6774694

>>6773938
You already know how to find them.

6/10 made me reply

>>6774615
http://mathoverflow.net/questions/26117/prime-undecomposable-matrices

Your professor is sort of right but not being very helpful. On matricies in general no but under some restricted matricies yes.

>>6774682
Fairly basic using Wilson's theorem

is there a recurrence relation for primes? like for fibonacci numbers. can it even exist? like, it's proven that no polinomial can generate all primes

>>6773906
For all X, there exists some Y such that Y > X and Y has no divisors save 1, 0, or itself.

Yawn, trivial.

>>6775115
This is so wrong it's painful

>>6774049
>what is 9

IF a number is divisible by any preceding prime number then it is not a prime number.

>>6775155

2^n - 1

mersenne primes are the best primes

t'(p, n) = if n = 1 then true else if p mod n = 0 false else t'(p, n - 1)

t(p) = h(p, p - 1)

n'(p, a) = if a = 0 p - 1 else if t(p) n'(p + 1, a - 1) else n'(p + 1, a)

now the formula to return the nth prime is:

p(n) = n'(2, n)

>>6775115
came here to post that image

This is trivial to describe algorithmically. Thus mathematics is applied computation.

>>6774514
>sqrt(1) * sqrt(1) = 1
not prime m8

>>6775257
8/8

>>6775152
Even

if 3 X 3 goes into 9, then that's 2 numbers that go into 9, which means it's even because 2 is even

>>6775519
The product of any two odd integers is also odd.
Assume n and m are odd integers:
n = 2k + 1, m = 2k + 1
m * n = (2k + 1)(2k + 1)
m * n = 2(2k^2 + 2k) + 1

Let k' represent the expression 2k^2 + 2k
m * n = 2k' + 1

m * n takes on the form 2k' + 1, and is clearly odd.

>>6775257
it's only trivial if u don't do the mathematical proof u moran

>>6775658
thanks

def isPrime(x):
return isPrime(x)

It uses recursion which is a dlsecret computer hack but it works

>>6776122
nice

>>6774669
Because you touch yourself at night

>>6773906
They're all optimal

>>6774049
>21

>>6773906
It's really easy. AES encryption. Find both d and e keys.
Encrypt something with the e key.
Decrypt it again.
AES only works if d and e are prime.
So if the decryption results in the original string/number you have proven that e and d are primes.

>>6776122
>recursion on big primes
>enjoy your heap-stack exploding into a black hole
noob

Consider the natural numbers N = {1, 2, 3, ...} equipped with the operation *. The primes are those numbers p in N for which a*b = p with a =/= b in N only has solutions a=1, b=p or a=p and b=1.

To easily generate the primes follow these simple instructions:
>First 2 is a prime, because that's easy to check. Write it down!
>Now list all countably infinite multiples of 2 in order
>When you've done that, move on to the next natural number which is not in the list you just made (hint: it's 3)
>repeat until you have done all the natural numbers
If you followed these instructions correctly, you should have all the prime numbers down. Incredible!

>>6773906
p : p is prime

>>6773906
Divide by all preceding numbers and see if you get a number between it and 1. You can save time by very obviously more efficient methods but that's for pussies.

>>6773928
I'll bet you can't find c in Z s.t. 3c=7 faggot

>>6773906
I don't think there exists a rule or algorithm that finds primes, but you can definitely test the primality of a number. If you are asking whether there is an expression that describes all primes, I'm assuming it has something to do with series and sequences, but I don't think it exists either

>>6773951
why did they make them look like a 13 year old's gaming pc?

Does this shitty algorithm I just contrived have any merit?
If x is prime:
(x)^2 * (x - 1)^2 = New Prime

>>6782256
Derp.
(x)^2 + (x - 1)^2 = New Prime

>>6782257
x=11

>>6774972
not him but you do you have a shitload of sieves made throughout millenia