Brüdern, Jörg; Perelli, Alberto The addition of primes and power. (English) Zbl 0860.11061 Can. J. Math. 48, No. 3, 512-526 (1996). The authors give a second application of the recently developed vector sieve of the first author and E. Fouvry [J. Reine Angew. Math. 454, 59-96 (1994; Zbl 0809.11060)]. They sift the set of vectors \((n,n +2)\), thus getting improved results for the set of integers \(n\) such that \(n\) and \(n+2\) have large prime factors only. The main ingredients of this high-standard work are the Rosser-Iwaniec sieve [H. Iwaniec, Acta Arith. 37, 307-320 (1980; Zbl 0444.10038)] and mean upper bounds for Kloosterman sums due to J.-M. Deshouillers and H. Iwaniec [Invent. Math. 70, 219-288 (1982; Zbl 0502.10021)]. Reviewer: D.Wolke (Freiburg i.Br.) Cited in 1 ReviewCited in 4 Documents MSC: 11P32 Goldbach-type theorems; other additive questions involving primes 11P55 Applications of the Hardy-Littlewood method 11N36 Applications of sieve methods Keywords:integers having large prime factors only; vector sieve Citations:Zbl 0809.11060; Zbl 0444.10038; Zbl 0502.10021 PDFBibTeX XMLCite \textit{J. Brüdern} and \textit{A. Perelli}, Can. J. Math. 48, No. 3, 512--526 (1996; Zbl 0860.11061) Full Text: DOI