Re: Some question in prime number!

On 3월1일, 오전8시22분, quasi <qu...@xxxxxxxx> wrote:
On Fri, 29 Feb 2008 15:08:50 EST, Usher73 <Ushe...@xxxxxxxxx> wrote:
Hi!

I want to ask two question about prime numbers.

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

**At first, I tried the induction method.
So, assume that it is true for all k <n.
Next choose the largest prime among less than n and
denote it P.
Then 2P should be greater than n by bertrand
postulate and P is the
largest prime number.
Write n=P+(n-P). If n-P >6, by induction hypothesis
we express it as a
sum of distinct primes and since n-P<P, P does not
appear in the
expression.

I cannot treat the case n-P<=6. Actually, it is
enough to consider n-
P=1,4,6.

2.Deduce that Prod_{primes <= x} (1-1/p) = (c / ln x)
+ O(1/(ln x)^2)
for some constant c.

How to solve these two problems?

11 > 6

11 cannot be written as a sum of two distinct primes

But 11 is the sum of 3 distinct primes.

The OP didn't say that it had to be only two distinct primes,

quasi- 따온 텍스트 숨기기 -

- 따온 텍스트 보기 -

11 is itself a prime.
.

Relevant Pages

  • Re: Mr. P and Ms. S
    ... That means there are only two ways to factor xy out of which one is sum of two primes and another is not sum of primes and he knows the later is the way. ... That is all possible decomposition of x+y there is only one decomposition which yields only two ways of factoring out of which one can be written as sum of two primes. ... Sujit Gujar. ...
    (sci.math)
  • Re: approaching a proof
    ... > number is the sum of two primes). ... > probabilistic sense, the limit of our proofs as M goes to infinity ...
    (sci.logic)
  • Quantum Gravity 313.3: More Regarding Exp[ln(p1) + ln(p2) + ... + ln(pn)] As Fundamentally Additive
    ... powers of primes), is in a sense "irreducible" and the sum ln+ ln ... In the well known decomposition: ... except for a function exp (the exponential function). ...
    (sci.physics)
  • Re: Mr. P and Ms. S
    ... of which one is sum of two primes and another is not ... of x+y there is only one decomposition which yields ... yeild more than 2 ways of factoring. ...
    (sci.math)
  • Re: Some question in prime number!
    ... He didn't say "a sum of two distinct primes", ... every positive integer can be written as a product of primes, ...
    (sci.math)
Loading