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Links Thread, For Your Mathematicians: The Complete List Of Primes in Links, Downloads and Scripts; Link: The complete list of primes In this website we list all prime numbers. Note: That claim seems a little ...
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    DaveP's Avatar
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    For Your Mathematicians: The Complete List Of Primes

    Link: The complete list of primes

    In this website we list all prime numbers.
    Note: That claim seems a little unlikely.

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    Ha yes, a little unlikely! But actually might be useful for quick reference when working with larger numbers. Thanks!

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    It won't list all primes - we haven't calculated *all* of them, as there would be an infinite number of them. Not to mention, the numbers being displayed on that site are limited by the processor on your machine. So, the largest would be the largest possible for a 32bit browser for most people (as they're still the most commonplace).

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    An impossible challenge unfortunately. If you could calculate all of the infinite primes you'll break allot of other things in the world of maths. The most worrying being most if not all modern encryption methods.

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    Quote Originally Posted by localzuk View Post
    there would be an infinite number of them
    This is where I always start getting stuck. While I am happy assuming that there's an infinite number of numbers, given that we know that some aren't primes, the actual number of primes must be (infinity-[some number]), mustn't it? But then if there's an infinite number of primes, then that must mean that infinity-[some number] = infinity, mustn't it?

    I am going for a lay down.

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    localzuk's Avatar
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    Yup. That's the fun of maths.

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    Quote Originally Posted by theriver View Post
    This is where I always start getting stuck. While I am happy assuming that there's an infinite number of numbers, given that we know that some aren't primes, the actual number of primes must be (infinity-[some number]), mustn't it? But then if there's an infinite number of primes, then that must mean that infinity-[some number] = infinity, mustn't it?

    I am going for a lay down.
    Prepare for your mind to be blown: Euclid's theorem - Wikipedia, the free encyclopedia
    There being an infinite number of primes has been proved many times

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    Quote Originally Posted by theriver View Post
    This is where I always start getting stuck. While I am happy assuming that there's an infinite number of numbers, given that we know that some aren't primes, the actual number of primes must be (infinity-[some number]), mustn't it? But then if there's an infinite number of primes, then that must mean that infinity-[some number] = infinity, mustn't it?

    I am going for a lay down.
    Infinities were a problem before Georg Cantor tamed them (and then went mad)
    BBC - Learning Zone Class Clips - Cantor and the mathematics of infinity - Maths Video

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    Quote Originally Posted by theriver View Post
    This is where I always start getting stuck. While I am happy assuming that there's an infinite number of numbers, given that we know that some aren't primes, the actual number of primes must be (infinity-[some number]), mustn't it? But then if there's an infinite number of primes, then that must mean that infinity-[some number] = infinity, mustn't it?
    There are orders of infinity, so you can have an infinite set, let's say the set of all positive integers and you can take away all the odd integers and you are left with only even integers but you still have an infinite set (or you now have two infinite sets of equal size). If we took away every 5th integer you would have two infinite sets but interestingly, they would be sort of differently sized (different orders).

    Mostly, it doesn't make sense to use infinity in an arithmetic expression (Infinity - 4) = Infinity because Infinity is not a number, it's generally (in maths) a property of a set. In physics it's an indication that things have all gone horribly wrong.

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