Page 2 of 2 FirstFirst 12
Results 16 to 28 of 28
Like Tree8Thanks

Math Help - Prime Numbers

  1. #16
    Member
    Joined
    Oct 2011
    Posts
    86
    Thanks
    2

    Re: Prime Numbers

    After reading over every post -again- it seems a lot clearer. Perhaps I simply was lost in a deep fog of thought that would not let me see the simplex. So, that said, am I correct in simply saying "We only use integers, because they work. To include fractions get's us no where and the bylaws of the game shall for ever more exclude non-integers from being involved in primes."
    Follow Math Help Forum on Facebook and Google+

  2. #17
    Newbie
    Joined
    Jul 2012
    From
    Seattle
    Posts
    18
    Thanks
    2

    Re: Prime Numbers

    Why is blue blue?

    Because it is light with a wavelength of 450 - 475 nanometers?

    No, because its definition is light with a wavelength of 450 - 475 nanometers.

    Why is a prime a prime, even even, and odd odd? Because of definitions.
    Follow Math Help Forum on Facebook and Google+

  3. #18
    Senior Member
    Joined
    Jan 2008
    From
    UK
    Posts
    484
    Thanks
    65

    Re: Prime Numbers

    Divisible by does not mean can be divided by.

    7 can be divided by 3 but 7 is not divisible by 3.
    Thanks from Nervous
    Follow Math Help Forum on Facebook and Google+

  4. #19
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,153
    Thanks
    591

    Re: Prime Numbers

    suppose you attended a school that had a school uniform. suppose further that one part of the school uniform was a plain navy blue blazer. for the years you attend the school, you dutifully wear the navy blue blazer, every day.

    then one day, you find yourself in a clothing shop, and since you are need of a new blazer, you ask the clerk to show you the navy blazers. the clerk informs you they are out of navy, and then asks you: "how about a grey one instead?". and you think to yourself: "why would i ever want a grey blazer?".

    it is much the same with numbers. most people use a single number system all their lives. whether it is the accountant or salesclerk with their two-place decimals, or perhaps the computer programmer who only has room in the code for 14 decimal places, or just the simple shepherd, who needs only numbers as large so as to count his flock. or perhaps the electrical engineer, who begrudgingly accepts the imaginaries (which he denotes as j, rather than i). each of these number systems has its own set of rules, and as long as one stays entirely within one system, one comes to view these rules as sacrosanct.

    but in truth, there are *many* number systems, in fact there are families of number systems, each of which has many members. some are finite, some are uncountably large, some of them contain other number systems as "subsystems", some defy all ordinary experience.

    but the concept of "prime" makes sense for a rather large class of number systems (the term for such systems is called "domains"), and under certain circumstances, we can factor things into "primes" in these number systems. so it's not *just* that "the concept of "prime" works in the integer number-system, it works in many others as well. it's an idea that lends itself well to generalization, in areas as diverse as cryptography, to the proof of Fermat's Last Theorem, and other areas of higher mathematics that you needn't worry about.

    in general, one has something like C (i am using capital letters to dissuade you from thinking these stand for any kind of "familiar" thing), and one wants to know if C splits into two smaller parts, like A and B: C = AB. one would like A and B to be "the same sort of thing" that C is...we don't want to have to switch to "a different set of rules". of course, if we CAN do such a thing, it is natural to ask if A and B might themselves be so split. at what point do we stop, which things are "unsplittable"? because those things, if we understand them well, we can "reassemble" into big complicated things like C.

    this is, for example, what we do when we factor polynomials: we take a polynomial of large degree (which might be very hard to understand), and chop it up into very simple polynomials, like x - 2, which is *much* easier to deal with. it's much like splitting up a complicated job into preparation, initial attack, establishing a rhythm, winding down, clean-up. it's easier for our minds to deal with small bite-sized pieces.

    "fractions" allow us to solve more kinds of problems that integers do, but in a sense, the rational numbers are like a soup: none of them stand out from the other ones. you can always chop a fraction into a fraction of a fraction, and it's still just a (smaller) fraction. with integers, primes are like numbers that say: the buck stops here. they're *special*.

    in all honesty, i don't know how or why it is that we hit on that particular idea to single out. it was before my time (primes have been objects of curiosity since antiquity). but it turns out to have been useful, in many cases, the size of something has to do with "how much overlap" two numbers have (imagine this: you have two wheels, turning at different speeds, and you want to perform some action when two points on each wheel are "lined up". if wheel A is turning once every k minutes, and wheel B is turning once every m minutes, and they start out "in-sych", they will line up again after the least common multiple of k and m minutes. this number depends on the greatest common divisor of k and m. in particular, if k and m are different primes (like 2 and 3), the least common multiple is always k*m, which makes things "easier to compute"). comparing this numerical "overlap" can be done by looking at the primes that factor into them, and seeing which ones are the same. for example, going back to the "two wheels", if k = 4, and m = 6, we don't have to wait for 24 minutes, it turns out that 12 will be enough.

    or: let's say you're someone who ships small items in boxes, like watches, or jewelry, and you want to decide how items to pack per layer in a box (so that you can order the right-sized shipping box to pack them in). 17 would be a bad choice, because no matter how you split it into rows, you're going to have an empty space (unless you use long, skinny boxes with just room enough for 1 row). 25 is a better choice, you can layer them 5 by 5, but perhaps 24 offers you more options (4 by 6, 3 by 8, or 2 by 12). this kind of problem doesn't lend itself well to fractions: sawing a (small) box in half to make it fit in the big box, would be counter-productive (and no doubt lead to an unhappy customer, at some point).
    Thanks from ymar
    Follow Math Help Forum on Facebook and Google+

  5. #20
    Newbie
    Joined
    Sep 2012
    From
    new york
    Posts
    5
    Thanks
    1

    Re: Prime Numbers

    I feel that the even more I consider it, the even more shed I am. I feel that I simply don't understand the concept of amounts. How to influence those "things" called numbers, I can understand, however exactly what it is I am controling and just what I am doing to them, I do not. I am just a monkey that learn to relocate symbols around in a particular online game.
    Thanks from Nervous
    Follow Math Help Forum on Facebook and Google+

  6. #21
    Senior Member
    Joined
    Jan 2008
    From
    UK
    Posts
    484
    Thanks
    65

    Re: Prime Numbers

    This may not be Shakespeare but clearly the monkey's have been typing long enough. Let them out!
    Follow Math Help Forum on Facebook and Google+

  7. #22
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,417
    Thanks
    718

    Re: Prime Numbers

    Quote Originally Posted by mittevans View Post
    I feel that the even more I consider it, the even more shed I am. I feel that I simply don't understand the concept of amounts. How to influence those "things" called numbers, I can understand, however exactly what it is I am controling and just what I am doing to them, I do not. I am just a monkey that learn to relocate symbols around in a particular online game.
    I am not sure I understand your sentiment, but one of the greatest mathematicians David Hilbert also thought that mathematicians simply relocate symbols around in a particular offline (they did not have online at that time) game.
    Follow Math Help Forum on Facebook and Google+

  8. #23
    Newbie
    Joined
    Oct 2012
    From
    Burnaby, B.C., Canada
    Posts
    10
    Thanks
    2

    Re: Prime Numbers

    I have an idea on how to calculate prime numbers using prime numbers of a lesser value. I have a small proof that I am working on; however, I am uncertain of what forum to put it in.
    Follow Math Help Forum on Facebook and Google+

  9. #24
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,034
    Thanks
    49

    Re: Prime Numbers

    Just bumping this over the spam
    Follow Math Help Forum on Facebook and Google+

  10. #25
    Super Member
    Joined
    Oct 2012
    From
    Ireland
    Posts
    507
    Thanks
    138

    Re: Prime Numbers

    Quote Originally Posted by Nervous View Post
    How can a number be "only" divisible by one and itself? 2, for instance, is divisible by 1, 2, 3, 4, 5, etc. You may end up with a fraction, but it is still divisible. What is it about prime numbers that disqualifies factional answers?
    Put simply, your definition is lazy. A proper definition would specify that it is only divisible by two natural numbers, itself and one to form another natural number.
    Follow Math Help Forum on Facebook and Google+

  11. #26
    Newbie boogey's Avatar
    Joined
    Jun 2013
    From
    USA
    Posts
    11

    Re: Prime Numbers

    Quote Originally Posted by Plato View Post
    You clearly do not understand the term divisible .
    First that term refers to integers.
    So the statement that a is divisible by b means that each of a.~b,~\&~k are integers such that a=kb.
    That means that 2 cannot be divisible by 3. Do you see why?

    That definition also is used in defining prime numbers: an integer is prime if and only if it has exactly two divisors.

    Often even well respected textbooks and commentators (i.e. Keith Devlin the math guy) say that an integer is prime if "it is only divisible by itself and one". But that definition makes one a prime. Do you see why?

    BTW: (Thanks to R L Moore for that distinction,)

    I think the same way. I totally agree with you with that. To know about this statement you should understand the term and then every thing will be easy for you.
    Follow Math Help Forum on Facebook and Google+

  12. #27
    Newbie boogey's Avatar
    Joined
    Jun 2013
    From
    USA
    Posts
    11

    Re: Prime Numbers

    Quote Originally Posted by boogey View Post
    I think the same way. I totally agree with you with that. To know about this statement you should understand the term and then every thing will be easy for you.
    certificate in training and assessment
    Follow Math Help Forum on Facebook and Google+

  13. #28
    Newbie
    Joined
    Aug 2013
    From
    USA
    Posts
    1

    Re: Prime Numbers

    Why's blue blue?

    Because it is light using a wavelength of 450 - 475 nanometers?

    No, because its definition is light having a wavelength of 450 - 475 nanometers.

    Why is a prime a prime, even even, and odd odd? Because of definitions.
    my blog
    Follow Math Help Forum on Facebook and Google+

Page 2 of 2 FirstFirst 12

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 22nd 2011, 12:37 PM
  2. Prime Numbers
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: December 7th 2009, 09:42 AM
  3. prime numbers
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 5th 2009, 07:39 AM
  4. prime numbers
    Posted in the Number Theory Forum
    Replies: 6
    Last Post: February 15th 2009, 08:34 AM
  5. Prime Numbers
    Posted in the Algebra Forum
    Replies: 5
    Last Post: March 12th 2007, 03:36 PM

Search Tags


/mathhelpforum @mathhelpforum