20 primes.
Lev Shnirelman entered the University of Moscow in 1921 at the age of 16. There he was taught by Khinchin, Luzin and Urysohn. He started research in algebra, geometry and topology as a student but did not consider his results sufficiently important to merit publication.
He was appointed to the chair of mathematics in Novocherkassk in 1929. Then in 1930 he returned to Moscow. From 1934 he worked at the Mathematical Institute of the Academy.
Shnirelman made significant contributions to topological
methods in the calculus of variations. In
1930 he introduced important new ideas into number theory. Using these
he was able to prove a weak form of the Goldbach's conjecture
showing that every number is the sum of
20 primes.
The Goldbach conjecture that every number is the sum of at most 3 primes still stands.