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

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John Rickard

Posts: 3
Registered: 12/12/04
Re: Goldbach conjecture
Posted: Nov 2, 1997 2:09 PM
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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
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10/29/97
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11/13/97
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11/6/97
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11/6/97
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11/6/97
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11/6/97
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11/7/97
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11/7/97
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11/4/97
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11/3/97
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11/3/97
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11/8/97
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Andre Engels
11/5/97
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Robert Hill
10/30/97
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goldbach
11/2/97
Read Re: Goldbach conjecture
Orjan Johansen
11/2/97
Read Re: Goldbach conjecture
John Rickard
8/25/98
Read Goldbach's conjecture
Elijah Bishop
11/2/97
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Orjan Johansen
10/30/97
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Brian Hutchings
11/2/97
Read Re: Goldbach conjecture
Gerry Myerson
11/6/97
Read Re: Goldbach conjecture
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4/28/99
Read My conjecture
Papus

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