Prime Numbers
 

This is just an interesting topic I've been thinking about recently.

In your opinion, do you think there are an infinite amount of prime numbers? Vote in the poll and share your opinion. I think this could make an interesting discussion :).

Re: Prime Numbers
 

Maybe.

Re: Prime Numbers
 

There is an infinite amount of numbers. So there might as well be an infinite amount of prime numbers.

Re: Prime Numbers
 

But is there a limit to how high you can go without having divisibility? The higher you go, the lower the chance of a prime number occurring. If there's a rate that is becoming infinitely less and less, will it eventually equal 0, or will it just get really damn close and never touch?

That is the question.

I'm pretty torn myself. I voted yes, but I can see why you might say no.

Gah, brain is fried. 1 limit approaching both infinity and 0 at the same time! Paradox?

Re: Prime Numbers
 

There's an infinite amount. Wikipedia article.

Re: Prime Numbers
 

All even numbers are divisible by 2

Re: Prime Numbers
 

http://en.wikipedia.org/wiki/Prime_number


Different URL but just about the same from 2 posts above me

Re: Prime Numbers
 

Got to love proof by contradiction. That is my favorite.

Re: Prime Numbers
 

Damn... it's still interesting to think about :P
btw

Re: Prime Numbers
 

Prime numbers are sexy. I had no idea until algebra this year that prime numbers have so many sweet properties.

Re: Prime Numbers
 

Yes there's an infinite amount of prime numbers. My math professor proved it last semester lol.


Lol I want sex. Which algebra class are you taking?

Re: Prime Numbers
 

Umm, it's just called "Algebra I for Honours Mathematics". xD
I have linear algebra next term.

Re: Prime Numbers
 

this video is relevant to this thread

http://wimp.com/infiniteuniverse/

start at 4:10

Re: Prime Numbers
 

Lol xD It's like how my class I'm currently taking is called "Honors Math III" xD I'm excited to take Differential Equations and Number Theory next semester! Gonna study some sexy numbers ;) BOW CHIKA WOW WOW

Re: Prime Numbers
 

Sexy numbers are sweet. Linear Algebra I next term will be cool. And lol "Calculus I for Honours Mathematics" this term, next term I have "Calculus II for Honours Mathematics". They are very creative with course names.

Re: Prime Numbers
 

Are there infinitely many sets of prime numbers that are only 2 away from each other, i.e. 11 & 13?

Re: Prime Numbers
 

Why is it that all prime numbers that have a remainder of 1 when divided by 4 can be written as the sum of two squared integers, i.e. 13 = 2^2 + 3^2, but all prime numbers that have a remainder of 3 when divided by 4 can't?

http://en.wikipedia.org/wiki/Proofs_...of_two_squares

Re: Prime Numbers
 

Number theory is awesome. I finished reading this book and now I'm in love with numbers :D

http://shell.cas.usf.edu/~wclark/elem_num_th_book.pdf

I'm curently having a class called Linear Algebra and Vector Geometry and it's really fun so you're probably going to like Linear Algebra xD

Re: Prime Numbers
 

I think prime numbers have an infinite amount..man i don't remember this stuff anymore i took algebra 2 last year.

Re: Prime Numbers
 

As long as the number system will have an infinite amount of numbers, there will be an infinite amount of prime numbers.

EDIT: *facepalm* Damn it Izzy.

Re: Prime Numbers
 

What about the set of numbers {2^0, 2^1, 2^2... } ? This set has infinitely many numbers and only one is prime.

Re: Prime Numbers
 

Don't ask me. I did terrible in math.

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Infinite amount of "odd" numbers*

Re: Prime Numbers
 

What about that set? The one prime number is 2 (2^1) since 1 isn't prime. =/

Re: Prime Numbers
 

It is a counterexample to UnknownMan's statement that any infinite collection of numbers has infinitely many primes.

Re: Prime Numbers
 

Numbers never end therefore prime numbers never end. Divisibility becomes more and more spread out as numbers get bigger but it never "stops". This is similar to the half distance paradox: A man crosses a street but he always travels half the distance to the end of the street. He never gets to the end of the street but he travels for an infinitely long time.

Re: Prime Numbers
 

sup

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Haha spacerip just posted this video on youtube and is one of my subscriptions. Might have learned that exact example from there ;)

Re: Prime Numbers
 

Reminded me of this:

Re: Prime Numbers
 

Using this knowledge of the patterns in numbers, people solve relatively complex problems in a short amount of time. A lot of people think they're just geniuses, doing a whole lot of things in their head... but the truth is that there's some sort of pattern, which either they previously know, or know in which to seek out, to solve the problem. That applies to math competitions, but I do not know about other things... I was just mentioning that because something like this relates to what you would see in a Math competition, really.

Re: Prime Numbers
 

doing prime numbers in math atm ;)

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Lol xD You'll love linear algebra! If you like to prove, you will definitely benefit and admire the class. You're currently taking Algebra so if you like algebra, linear algebra is fun :)

I think this is one of the most striking areas of math in terms of research. They refer to this as "twin primes." Currently they are not sure how many "twin primes" exist, as far as I know.

Re: Prime Numbers
 

there's a function that defines the density of primes around any number, and iirc it goes down linearly

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Algebra is my favourite class. I'm excited :D

Re: Prime Numbers
 

[insert same set as aperson's but with 3 as the base]

:D