The Goldbach-Euler binary problem is formulated as follows: Any even number, starting from 4, can be represented as the sum of two primes. The ternary Goldbach problem is formulated as follows: Every odd number greater than 7 can be represented as the sum of three odd primes, which was finally solved in 2013. In 1995, Olivier Ramare proved that any even number is the sum of no more than 6 primes.[9] The second problem is about the infinity of twin primes. The author carries out the proof by the methods of elementary number theory.