[ExI] Goldbach Conjecture

[Will Steinberg]

If it can be proved that every two-way sieve of eratosthenes has at least
one hole, the conjecture can be proven.  What this means is that (since oles
are at 2k, 3k, 5k, nmod2+2k, nmod5+5k, etc.)  There has got to be some kind
of proof saying that for any given number n, there is a prime in n than
cannot be expressed by nmodp+pk.  What has to be looked at is the modulo
values that will be given for ns. I think we can often choose 3, because the
only case when 2 can be covered is if we have nmod2=1 and pk=2.  (or if the
number is divisible by 3).  Otherwise we can simply continue moving up our
primes.  In the case of 2n=22, we see holes at 3,5, and 11.  What is needed
to continue is a way to prove there will always be a p that doesn't equal
nmodp +pk

2009/11/28 spike <spike66 at att.net>

>
>
> > -----Original Message-----
> > From: extropy-chat-bounces at lists.extropy.org
> > [mailto:extropy-chat-bounces at lists.extropy.org<extropy-chat-bounces at lists.extropy.org>]
> On Behalf Of
> > Giulio Prisco (2nd email)
> > Sent: Friday, November 27, 2009 11:12 PM
> > To: ExI chat list
> > Subject: Re: [ExI] Goldbach Conjecture
> >
> > I think the Goldbach conjecture is probably false, with
> > probability 1 (that means, certainly false). Here is why:
> >
> > Apparently there is nothing in the laws of arithmetics that
> > forces an even number to be the sum of two prime numbers. The
> > conjecture is true for all even numbers on which it has been
> > tested, but these are an infinitesimal part of the total (any
> > finite number is infinitesimal wrt infinite). Hence, if there
> > is no proof, the probability of he Goldbach conjecture being
> > true is zero.
>
> I disagree sir, however I confess my line of reasoning is not as well
> developed as the one you offer.
>
> I took the even numbers and calculated the number of ways each even number
> (shown on the X axis) could be expressed as a the sum of two primes.  The
> number of different ways is on the Y.  For Goldbach to have been wrong,
> there is some super-anomaly way out there somewhere which departs from the
> data trends shown.
>
> Yes I do know that this line of reasoning is not to be substituted for
> actual mathematical logic, do forgive please.
>
> I plotted them to a few million on matlab, found there are striking
> patterns in the data, such as the eye-catching streaks.
>
> spike
>
>
>
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