Question about the Goldbach conjecture
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From: raycb on 11 Jun 2010 14:19 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.
From: hagman on 11 Jun 2010 14:57 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
From: raycb on 12 Jun 2010 10:05 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.
From: raycb on 12 Jun 2010 10:28 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.
From: Arturo Magidin on 12 Jun 2010 14:48
On Jun 12, 9:05 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. What is the proposition that you are claiming is equivalent to the Goldbach Conjecture? Just state it. Because the argument you are using above seems like arguing that if every even number greater than 6 can be written as p+q with p, q primes and p+6 prime, then Goldbach's conjecture is true. But that's a rather silly claim, because the proposition you are assuming is *stronger* than Goldbach's: it assumes not only that you can write the number as sum of two primes, but that it is the sum of two primes *with extra conditions*. So, could you elucidate by just stating the proposition? -- Arturo Magidin |