The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: conjecture on sums of primes
Replies: 13   Last Post: Apr 18, 2013 12:45 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 419
Registered: 10/7/06
Re: conjecture on sums of primes
Posted: Feb 3, 2012 7:06 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Feb 2, 9:35 am, Paul <> wrote:
> I conjecture that, for all integers N > 1, there exists an integer E
> such that E can be expressed as the sum of two primes in more than N
> different ways.
> Is this conjecture true, false, or unknown?

There are about n / ln (n) primes p <= n.
Therefore there about (n^2 / 2 ln^2 (n)) sums of two primes p <= q <=
Therefore there more than about (n^2 / 2 ln^2 (n)) sums of two primes
p + q <= 2n, with p <= q; almost all the sums are even.
Therefore there are even numbers <= 2n that can be expressed as the
sum of two primes in about (n / 2 ln^2 (n)) ways.

Given n, solve N = n / 2 ln^2 (n)), giving n about 2N ln^2 (N)
(roughly), so there should be an E <= 4N ln^2 (N).

I'm sure you can make this rigourous and a bit more precise, but the
conjecture is definitely true.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.