THE GOLDBACH’S CONJECTURE PROVED (link to pdf) is pre-published on Arxiv. Prástaro claims to have proven the conjecture through commutative algebra and algebraic topology:
Abstract. We give a direct proof of the Goldbach’s conjecture in number theory, formulated in the Euler’s form. The proof is also constructive, since it gives a criterion to find two prime numbers 1, such that their sum gives a fixed even number 2. (A prime number is an integer that can be divided only for itself other than for 1. In this paper we consider 1 as a prime num-ber.) The proof is obtained by recasting the problem in the framework of the Commutative Algebra and Algebraic Topology.
So is this a valid proof? Are there any glaring errors or has this conjecture finally been proven?"