Re: Goldbach Conjecture
- From: "Proginoskes" <CCHeckman@xxxxxxxxx>
- Date: 23 Oct 2006 22:58:53 -0700
bill wrote:
Gerry Myerson wrote:
In article <1161555482.977632.42490@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"bill" <b92057@xxxxxxxxx> wrote:
I have an idea re the "Goldbach Conjecture. I will "fold my tent
and silently steal away", if someone can find three primes;
(which do not include 2 or 3), that add up to 32.
Considering that primes that do not include 2 are odd,
and that the sum of three odd numbers is odd,
and that 32 is even,
I hope there's a little more to your "idea".
--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
Given that every prime is of the form 6n - 1 or 6n +1, then the
sum of 3 primes is; 6n - 3, 6n - 1, 6n + 1 or 6n + 3.
This generates all odd integers.
The sum of rwo primes + 3 is 6n + 1, 6n + 3 and 6n + 5
This also generates all odd integers.
Of course, this PROVES ABSOLUTELY NOTHING!
It merely shows that the conjecture is a viable concept
and is not obviously false.
OTOH, it has been shown that every positive integer is the sum of at
most 27 primes.
--- Christopher Heckman
If every even integer is the sum of two primes, it follows that
every odd integer > 8 is the sum of two odd primes + three!
Therefore, the Goldbach conjecture is fully stated as
"Every even integer > 5, is the sum of two odd primes."
regards
Bill J
.
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