Re: Some question in prime number!

On 3월7일, 오후1시59분, Gerry Myerson <ge...@xxxxxxxxxxxxxxxxxxxxxxxxx>
wrote:
In article
<b1fc171b-dc74-488f-8a79-6e6f7bf66...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,





Cooper <cooper0...@xxxxxxxxx> wrote:
On 3?6?, ??7?48?, Gerry Myerson <ge...@xxxxxxxxxxxxxxxxxxxxxxxxx>
wrote:
In article
<656a1e42-3f18-4773-b54b-76406dd01...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,

Cooper <cooper0...@xxxxxxxxx> wrote:

But problem 1 is still unsolved despite of the suggestion of the
material.

So remind us - what was problem 1?

This is the problem;

Show that if n>6, then n can be expressed as a sum of distinct
primes.

I'm pretty sure someone pointed out that this follows from Bertrand's
Postulate. Let n be the smallest integer exceeding 6 that can't be
expressed as a sum of distinct primes, then there's a prime p
between n / 2 and n, and then n - p being smaller than n can be
expressed as a sum of distnct primes, etc. With a little touching up,
this should be a proof.

--
Gerry Myerson (ge...@xxxxxxxxxxxxxxx) (i -> u for email)- 따온 텍스트 숨기기 -

- 따온 텍스트 보기 -

Wow! Thanks very much. That is the proof what I searching for.
Yes. As you guessed, the book which contains this problem has given
the hint that "Use Bertrand postulate" although I did not use the hint
faithfully.

Thanks again.^^
.

Relevant Pages

  • Re: Number theory
    ... is a perfect square, so p^2 divides n!. ... postulate was first proven by Chebyshev. ... Thus if p isn't the larger of a perfect pair of primes, ... Bertrand's postulate for p follows from Goldbach's conjecture. ...
    (sci.math)
  • Re: prime numbers formula please.
    ... probably does internally) without having the primes? ... First let me say that I use from now onward the ... I give you a hint: ... Multiply the sum by 'n'. ...
    (sci.math)
  • Re: Some question in prime number!
    ... Postulate. ... Let n be the smallest integer exceeding 6 that can't be ... expressed as a sum of distinct primes, ... expressed as a sum of distnct primes, ...
    (sci.math)
  • Re: Some question in prime number!
    ... then n can be expressed as a sum ... postulate and P is the ... sum of distinct primes and since n-P<P, ...
    (sci.math)
  • Re: x^x is not an integer for x not integer
    ... Any hint? ... larger than 2 is the sum of two primes", ... Aktivated Aktivator ...
    (sci.math)