Question about the Goldbach conjecture
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From: spudnik on 12 Jun 2010 14:56 well, that's simple-enough; I was trying to tell if "contradiction to first counterexample" was a proper indirect proof, but I couldn't even see why its firstness'd be important. > that it is the sum of two primes > *with extra conditions*. thus&so: what you have been posting is merely absurd at the syllogistic level, hence, entirely "silly," where all known properties of electromagnetism, which are wavey, dysappear into a loose hydrodynamic metaphor, replacing "energy" with "aether" -- a quaint mental spazzm. funny, as all of this could be exposed, merely by taking some aspect of a real two-hole experiment, like the actual details of the uncited fullerene set-up, into account. waves can ne'er be particles, whether a mathematical duality can be applied in a formularium of a phenomenon a la momentum; for instance, How is a water-wave to be known as a particle ... um, a hydron? even Burt goes further than you, with his sad nonsequiters; yours are only misnomers & oxymora ("global" warming, when insolation is totally differential from pole to equator e.g.). [NB, "yo'kind" is iff MPC#, period.] and, so, What did you "understood of the following?" > A=Mc^2, where A is aether and M is matter, > the following is easily understood: "If a body gives off the energy L > in the form of radiation, its mass diminishes by L/c2." --Stop BP's and Waxman's arbitrageurs' wetdream "Captain Tax as according to the God-am WSUrinal" -- and they LOVE his '91 bill! http://wlym.com
From: Arturo Magidin on 12 Jun 2010 15:12 On Jun 12, 9:28 am, raycb <ra...(a)live.com> wrote: > On Jun 12, 11:05 am, raycb <ra...(a)live.com> wrote: > > > On Jun 11, 3:57 pm, hagman <goo...(a)von-eitzen.de> wrote: > > > > On 11 Jun., 20:19, raycb <ra...(a)live.com> wrote: > > > > > What is the first even number larger than 6 that cannot be written as > > > > the sum of two primes with at least one of the primes 6 less than > > > > another prime. This is equivalent to the Goldbach conjecture. I didn't > > > > find any from 8 to 300. > > > > There is also no even number 6 < n < 10^7 that can be written as n = p > > > + q with p, q and p+6 prime. > > > But what makes you think that this is equivalent to the Goldbach > > > conjecture? > > > > hagman > > > If 2n is a counterexample to the Goldbach Conjecture, then 2n - 6 has > > a prime that can be replaced with a another prime to make 2n the sum > > of two primes. > > That is, if 2n is the _first_ counterexample to the Goldbach > Conjecture. You seem to be showing that if "every even integer greater than 6 can be written as p+q, where p, q, and p+6 are all primes" implies Goldbach. This is trivial. You claimed that it was *equivalent* to Goldbach. How do you prove that if Goldbach holds, then every even integer can be written as p+q with p, q, and p+6 all prime? -- Arturo Magidin
From: bill on 12 Jun 2010 20:22 On Jun 11, 11:19 am, raycb <ra...(a)live.com> wrote: > What is the first even number larger than 6 that cannot be written as > the sum of two primes with at least one of the primes 6 less than > another prime. This is equivalent to the Goldbach conjecture. I didn't > find any from 8 to 300. 3 + 19 = 22. 22 is the first of many, many even numbers that can bw written as the sum of two primes where neither p+6 nor q+6 is a prime.! I venture to say that there is an infinite quantity of such numbers! regards, Bill J
From: Arturo Magidin on 12 Jun 2010 20:49 On Jun 12, 7:22 pm, bill <b92...(a)yahoo.com> wrote: > On Jun 11, 11:19 am, raycb <ra...(a)live.com> wrote: > > > What is the first even number larger than 6 that cannot be written as > > the sum of two primes with at least one of the primes 6 less than > > another prime. This is equivalent to the Goldbach conjecture. I didn't > > find any from 8 to 300. > > 3 + 19 = 22. 22 is the first of many, many even > numbers that can bw written as the sum of two primes where neither p+6 > nor q+6 is a prime.! I venture to say that there is an infinite > quantity of such numbers! The question was not whether you *could* write it that way; the question was whether you had *no choice* but to write it that way. 22 can be written as 11+11, and 11+6 = 17 is a prime, so 22 *can* be written as a sum p+q with p, q, and p+6 prime. So 22 is not an example of what is sought (an even number that *cannot* be written as p+q with p, q, and p+6 prime). -- Arturo Magidin.
From: raycb on 14 Jun 2010 11:12
On Jun 12, 9:49 pm, Arturo Magidin <magi...(a)member.ams.org> wrote: > On Jun 12, 7:22 pm, bill <b92...(a)yahoo.com> wrote: > > > On Jun 11, 11:19 am, raycb <ra...(a)live.com> wrote: > > > > What is the first even number larger than 6 that cannot be written as > > > the sum of two primes with at least one of the primes 6 less than > > > another prime. This is equivalent to the Goldbach conjecture. I didn't > > > find any from 8 to 300. > > > 3 + 19 = 22. 22 is the first of many, many even > > numbers that can bw written as the sum of two primes where neither p+6 > > nor q+6 is a prime.! I venture to say that there is an infinite > > quantity of such numbers! > > The question was not whether you *could* write it that way; the > question was whether you had *no choice* but to write it that way. 22 > can be written as 11+11, and 11+6 = 17 is a prime, so 22 *can* be > written as a sum p+q with p, q, and p+6 prime. So 22 is not an example > of what is sought (an even number that *cannot* be written as p+q with > p, q, and p+6 prime). > > -- > Arturo Magidin. After I made that first post, I had doubts about saying that it was equivalent to the Goldbach conjecture. I withdraw it. I wasn't intending to say -- this is true -- I dare you to prove me wrong. I was saying -- this is most very likely false -- where does the first counterexample appear? From a small number of observations I found that the even numbers above 6 could be written as the sum of two primes in a way that at least one of the primes was six less than another prime. The conjecture is that this pattern continues without end. |