🚀 go-pugleaf

In his famous letter to Leonhard Euler dated June 7th 1742, Christian
Goldbach first conjectures that every number that is a sum of two primes can
be written as a sum of "as many primes as one wants". Goldbach considered 1
as a prime and gives a few examples. On the margin of his letter, he then
states his famous conjecture that every number is a sum of three primes.
This is easily seen to be equivalent to that every even number is a sum of
two primes which is referred to as the Binary Goldbach Conjecture. Its
weaker form, the Ternary Goldbach Conjecture states that every odd number
can be written as a sum of three primes. The ternary conjecture has been
proved under the assumption of the truth of the generalized Riemann
hypothesis and remains unproved unconditionally for only a finite (but yet
not computationally coverable) set of numbers. Although believed to be true,
the binary Goldbach conjecture is still lacking a proof.

Using a carefully optimized segmented sieve and an efficient checking
algorithm, the Goldbach conjecture has been verified and is now known to be
true up to 4x1014. The program was distributed to various workstations. It
kept track of maximal values of the smaller prime p in the minimal partition
of the even numbers, where a minimal partition is a representation 2n = p +
q with 2n - p' being composite for all p' < p. The maximal prime p needed in
the considered interval was found to be 5569 and is needed for the partition
389965026819938 = 5569 + 389965026814369.

Now that everyone knows....

What do you want to know?


Anthony

Nick Davison <nick@winner.freeserve.co.uk> wrote in message
news:8c0gju$29a$1@newsg2.svr.pol.co.uk...
> I know how to find one set of the primes using the 2 to the power of x, 2
to
> the power of y proof, but how about the other type.  Has anyone evr looked
> at Goldbach's conjecture?  Has anyone made any progress on it?
>
>