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Proofs involving prime numbers

  1. Sep 19, 2004 #1
    We didn't talk about prime numbers in my class, but several of the homework problems mention them.
    For instance:
    Prove that if every even natural number greater than 2 is the sum of two primes, then every odd natural number greater than 5 is the sume of three primes.

    Assume that n is an even natural number and n is greater than 2.
    Then n=2k, where k is an integer, and 2k is greater than 2.

    But how do I define a prime number in a proof?
    Any hints/help would be appreciated!
  2. jcsd
  3. Sep 19, 2004 #2
    "Let p be a prime". You needn't find a formula for it in order to define it...
  4. Sep 19, 2004 #3
    if u ever prove this in your class ... do let me know and i will be happy to share the million dollars with u :biggrin:

    http://www.acfnewsource.org/science/math_bounties.html [Broken]
    Last edited by a moderator: May 1, 2017
  5. Sep 19, 2004 #4
    Well, she wasn't exactly asked to prove Goldbach's conjecture, but rather some kind of corollary to a Goldbach-type conjecture which you're suppose to /assume/ to be correct.
  6. Sep 19, 2004 #5

    matt grime

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    It's good that you might want to use the definition of even in proofs and know how to do it.

    But lets look at the example here using sums of primes. You're asked to deduce something about writing n=p+q+r where p,q,r are primes and n is odd and greater than 5. So it's n which has a certain property that you need to prove, you need nothing about p,q,r in the proof. So what properties does n have? it's odd and greater than 5, and what do we have a hypothesis for? even numbers greater than 2, yeah? so how can we relate n to an even number greater than 2? how about n-3? is that even and greater than 2? check, so what can we conclude about n-3 by hyptothesis? and hence n, since 3 is a prime?
  7. Sep 19, 2004 #6
    i know ... but cant i just kid around ?
    i am sure eku would be happy to see that article ....
    i recall my days when i wasted hours trying to prove it before i found out that even the best in the business are in teh hunt .. that did invoke a bit of laughter ... prolly that's why life is so good ... somethings just level u with the best ..... it lets u know u are not left far behind ....

    duh!! now see u got me writing philosophy :uhh:

    -- AI
  8. Sep 19, 2004 #7
    Well, yes, but it seemed to me like you had misread the question.
  9. Sep 19, 2004 #8


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    i gave my elementary proofs class the following assignment: prove fermat's last theorem as follows:
    assume: 1) if FLT is false, then there exists a stable elliptic curve which is not modular.
    2) all stable elliptic curves are modular.

    deduce that FLT is true.

    notice one does not need to know the meanings of any of the technical words in this paragraph to prove the result.

    your problem is a little harder. you do not need to know what a prime is but you do need to know 3 is a prime.

    e.g. prove that if every even number greater than or equal to 2 is a sum of two donks, then every odd number greater than or equal to 5, is a sum of two donks and an odd number.
    Last edited: Sep 19, 2004
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