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Topic: Goldbach conjecture
Replies: 43   Last Post: Sep 26, 2000 8:55 AM

 Messages: [ Previous | Next ]
 John Rickard Posts: 3 Registered: 12/12/04
Re: Goldbach conjecture
Posted: Nov 2, 1997 2:09 PM

Orjan Johansen <orjanjo@lie.matstat.unit.no> wrote:
: In article <01bce59f\$34786f00\$e70cbece@goldbach.idcnet.com>,
: goldbach <goldbach@idcnet.com> wrote:
: >
: >It is not all that obvious. E.g, assuming the conjecture true, take
: >any prime p, no matter how large, then there is an even number E
: >such that for E=p + q , q prime and p<=q, p will be the least prime
: >in all the pairs of primes whose sum is E.
:
: How do you prove that?

By Dirichlet's theorem on primes in arithmetic progressions, there is
a prime q > p that is congruent to -p modulo (p-1)! . Then E = p+q is
divisible by every prime less than p, and so it is not the sum of two
primes including a prime less than p.

This doesn't assume Goldbach's conjecture, though.

--
John Rickard <jrr@atml.co.uk>

Date Subject Author
10/29/97 Gerry Myerson
10/30/97 David Ullrich
10/30/97 Gerry Myerson
11/2/97 Warwick Pulley
11/2/97 Ron Bloom
11/3/97 feldmann@bsi.fr
11/4/97 David Ullrich
11/10/97 Bob Runkel
11/11/97 Richard Carr
11/19/97 Richard Carr
11/3/97 Gerry Myerson
11/3/97 Warwick Pulley
11/3/97 Gerry Myerson
11/8/97 Andre Engels
11/9/97 Warwick Pulley
11/10/97 Meinte Boersma
11/13/97 Chris Thompson
9/16/00 Daniel McLaury
9/17/00 Fred Galvin
9/17/00 Jan Kristian Haugland
9/17/00 denis-feldmann
9/17/00 Erick Wong
9/26/00 John Rickard
11/6/97 Richard White (CS)
11/6/97 James Graham-Eagle
11/6/97 Legion
11/6/97 Gerry Myerson
11/7/97 Legion
11/7/97 Gerry Myerson
11/4/97 David Petry
11/3/97 Chris J. Bennardo
11/3/97 Gerry Myerson
11/8/97 Andre Engels
11/5/97 Robert Hill
10/30/97 goldbach
11/2/97 Orjan Johansen
11/2/97 John Rickard
8/25/98 Elijah Bishop
11/2/97 Orjan Johansen
10/30/97 Brian Hutchings
11/2/97 Gerry Myerson
11/6/97 Brian Hutchings
4/28/99 Papus