> I ran across an interesting statement on the top of a math paper that I
> was helping my sister with. It said that every even number greater than 4
> is the sum of two primes. I am curious if this has been proven and if
> anyone knows where I could find more info about this. Thanks.
This is the celebrated Goldbach conjecture, one of the oldest open problems
in mathematics. Some partial results are known (such as: any sufficiently
large odd number is the sum of three primes, a very hard theorem, btw)
and there is ample empirical evidence in favor of the conjecture,
but it remains open and will probably remain open for quite some time
(this is just a wild prediction, of course; it can be proved at any moment).
Notice btw that empirical evidence for this sort of question should be
regarded with great caution. Consider the following question:
Given N, let f1(N) be the number of primes of the form 4n+1 which
are smaller than N, and f3(N) be the number of primes of the form
4n+3 which are smaller than N. Thus, f1(10) = 1 and f3(10) = 2.
Is it true that f1(N) <= f3(N) for all N?
The answer is no, but I challenge you to find a counter-example.
Nicolau
