Goldbach conjecture: Proved?

Here's a paper that the authors say proved Goldbach's conjecture. From Wikipedia:

Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states:

Every even integer greater than 2 can be written as the sum of two primes.

For example,

4 = 2 + 2
6 = 3 + 3
8 = 3 + 5
10 = 3 + 7 = 5 + 5
12 = 5 + 7
14 = 3 + 11 = 7 + 7
etc.

It's a very old problem and one that if solved, would be welcomed news in mathematics.