Goldbach's problem
The author presents a historical survey on Goldbach's problem, i.e. the representation of integers as sums of two or three primes. He sketches the Hardy-Littlewood circle method and the results obtained from it, I. M. Vinogradov's solution of the ternary Goldbach problem, the implications of sieve methods, and more recent results (for example the estimate of Montgomery-Vaughan for the number of exceptional, non- Goldbach-integers), localized forms on the ternary problem, the deep Heath-Brown hypothetical result (prime twins and Siegel zeros) and others. Finally some open problems are mentioned.
scientific article; zbMATH DE number 575608
scientific article