Every even number not less than 4 is the sum of two odd prime numbers;

Every odd number not less than 9 is the sum of three odd prime numbers (it has been proved).

For 1,

The best result of the screening method is 1+2 (Chen Jingrun);

The best result of sequential method is almost proved.

Proof of Goldbach conjecture 1+ 1

Sequential method link: Web page link