Prime Numbers

[aperson]

Re: Prime Numbers

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

[aperson]

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_Fermat%27s_theorem_on_sums_of_two_squares

[Artic_counter]

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

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

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

[BethanyBangs]

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.

[UnkownMan]

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.

[aperson]

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.

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

[UnkownMan]

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.

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

[Izzy]

Re: Prime Numbers

Infinite amount of "odd" numbers*

[remedy1502]

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.

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

[aperson]

Re: Prime Numbers

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

[awein999]

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?

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.

[who_cares973]

Re: Prime Numbers

this video is relevant to this thread

http://wimp.com/infiniteuniverse/

start at 4:10

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.

sup

[awein999]

Re: Prime Numbers

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

[Netjet!]

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?

Reminded me of this:

[~kitty~]

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.