Prime Numbers

Is there any real good formula(s) for finding out if a number is prime? I've managed to devise a formula on my own, but it doesn't work when you plug in something that has a multiple of three. The formula would yield either a whole or a fraction. A fraction means that the number you plugged in is a composite number, whereas a whole number meant you got yourself a genuine prime number. But, when I plug in a multiple of 3, I get a whole number and that's no good.

So, if anyone has a favorite formula or if there's just one good formula right now, please do share. Thanks.

Let me see your formula

http://img228.imageshack.us/my.php?image=primeformulahb4.jpg

n would be the same number as c.

http://img156.imageshack.us/my.php?image=primeformulasimpletestyo8.jpg

This is a simple test of it. I've applied a sleuth of numbers, but it never works right with multiples of 3. As you can see, the problem produces a whole number and according to my theory, that makes c a prime number.

Pardon how ugly it looks. I don't have anything to write out formulas like that. I also have a pretty minimal understanding of Calculus.

The distribution of prime numbers is not understood very well. You and never going to find such a formula with your high school math. But hey, at least you're interested enough to try.

>>4
You are* never
And no, there is no formula OP. You have to use a thing called brute force.

>>3 wut?

Use Wilson's Theorem.

i dont get Modular arithmetic.  Meaning its use.

>>3
HAHA, no.

>>7 p is prime if and only if p divides (p-1)! + 1

>>9  thats wilsons , not mod.  or wait

OP, here. Yeah, as I said, there's already a flaw. The whole idea was to see if anyone had any good idea as to what I can do with it. Thanks for the feedback, though.

And for the record, my High School Math was stupid. We never even touched on anything like this. Furthest we got was basic trig. I had to teach myself everything thereafter. So, blame that for my shitty Calculus. Heh.

sucks =\   they teach shit in highschool besides ap cal  sometimes thats shitty to.

Well, just in case one of your guys does accidentally come across it, you should be aware of this:
http://www.eff.org/awards/coop

>>13

That's fucking awesome, man. I did not know anything at all about that.

>>14
SPOILER: The probability of a number with a billion decimal digits being prime is 2.3x10^-999999991.

>>15

You'd have a better shot at the lottery... but, at least this is fun and takes more time.

>>15

You'd have a better shot at the lottery... but, at least this is fun and takes more time.

AKS primality test is a polynomial-time algorithm

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Please go to http://tinyurl.com/be5l89 and click "Save page."

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>>18
Even a simplistic brute force search is only sqrt.
I heard that a cube root algorithm exists.
Slowpoke is slow.

>>20
For an integer N, input size grows with \log N... Which makes brute force exponential.

>>3
i'm gonna assume the c and i on the left hand side of your equation were supposed to be flipped, cause that's the only way it makes sense to equal the right hand side.

if you write your formula as a function of n, then what you really have is


f(n) = \sum_{i=1}^n i/n = \frac{1}{n}\sum_{i=1}^n i = \frac{1}{n}\left(\frac{n(n+1)}{2}\right) = \frac{n+1}{2}


so all your formula really checks is whether or not the number is even or not. all prime numbers (greater than 2) are odd, but not all odd numbers are prime.

your observation that this fails for multiples of 3 is true, but it also fails for multiples of 5 and 7 and 11, etc.

if this stuff interests you, pick up a book on introduction to number theory, learn about some modular arithmetic, euler's totient function, chinese remainder theorem, and maybe some stuff on pythagorean triples and you'll be well on your way through a first course in number theory.

>>1
Yes, they're called Mersenne primes.
http://en.wikipedia.org/wiki/Mersenne_prime
They also happen to produce the largest primes that we know to date.

>>23
The "formula" for Mersenne primes doesn't always generate them and it is not known at this time if there are infinitely many or not (only 46 are known so far).

EVERY NUMBER OF THE FORM 2^2^2^2^2^2^2^2^2+1 IS PRIME.

PROVE ME WRONG!

cORREC.T

>>25
2^2^2^2^2^2+1 = 2^32+1 = 4,294,967,297 = (641)*(6,700,417)

>>27
Nah, he takes the 2nd power 8 times, you do it only 5.

>>25
EVERY NUMBER OF THE FORM 2^2^2^2^2^2^2^2^2+1 IS PRIME.

There's only one number of that form, you fucktard.

>>27
I said 2^2^2^2^2^2^2^2^2, not 2^2^2^2^2^2.

>>29
EVERY NUMBER OF THE FORM 7 IS PRIME!

PROVE ME WRONG!

>>31
No, I believe you are correct, good sir.

>>31
EVERY FORM OF THE FORM FORM IS A FORM!

PROVE ME WRONG!

Aren't you supposed to take exponents from the right?
ie 3³³ = 3⁽³³⁾, rather than (3³)³?

2^2^2^2^2^2^2^2^2+1 = 2^2^2^2^2^2^2^4+1 = 2^2^2^2^2^2^16+1 = 2^2^2^2^2^65536+1 = ...

Unknown Mathematician Proves Elusive Property of Prime Numbers : http://www.wired.com/wiredscience/2013/05/twin-primes

Fibonacci primes:
2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, 99194853094755497, 1066340417491710595814572169, 19134702400093278081449423917, 475420437734698220747368027166749382927701417016557193662268716376935476241

>>35
PhD in math:  starting salary, whatever they pay to make sandwiches at Subway

New Largest Known Prime Number Discovered

Martin Nowak, an eye surgeon in Germany, and a long-time volunteer in the Great Internet Mersenne Prime Search (GIMPS) distributed computing project (http://www.mersenne.org/prime.htm), has discovered the largest known prime number. Nowak used one of his business PCs and free software by George Woltman and Scott Kurowski. His computer is a part of a wordwide array of tens of thousands of computers working together to make this discovery. The formula for the new prime number is 2^25,964,951-1. The number belongs to a special class of rare prime numbers called "Mersenne primes." This is only the 42nd Mersenne prime found since Marin Mersenne, a 17th century French monk, first studied these numbers over 350 years ago. Written out, the number has 7,816,230 digits, over half a million digits larger than the previous largest known prime number. It was discovered after more than 50 days of calculations on a 2.4-GHz Pentium 4 computer.

>>38
Nowak
Jew.

>>1
check this out OP
http://mathworld.wolfram.com/RiemannPrimeCountingFunction.html

>>38
42