It is a key ingredient in proofs of Chen's theorem on Goldbach's conjecture.
[1]: 272 It was proved in 1965 by Wolfgang B. Jurkat and Hans-Egon Richert.
[1]: 257 Suppose A is a finite sequence of integers and P is a set of primes.
Write Write ν(m) for the number of distinct prime divisors of m. Write F1 and f1 for functions satisfying certain difference differential equations (see Diamond & Halberstam[3]: 67–68 for the definition and properties).
We assume the dimension (sifting density) is 1: that is, there is a constant C such that for 2 ≤ z < w we have (The book of Diamond & Halberstam[3] extends the theorem to dimensions higher than 1.)