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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>
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