Lehmer, D. H. The prime factors of consecutive integers. (English) Zbl 0128.04002 Am. Math. Mon. 72, No. 2, Part II, 19-20 (1965). If \(f(k)\) denotes the least integer such that each product of \(f(k)\) consecutive integers all greater than \(k\) has a prime factor greater than \(k\), then it is clear that if \(k\) is composite, the value of \(f(k)\) is that of \(f(p)\) where \(p\) is the largest prime smaller than \(k\). It is known [cf. P. Erdős, Nieuw Arch. Wiskd., III. Ser. 3, 124–128 (1955; Zbl 0065.27605)] that \(f(2) = 2\), \(f(3) = 3\), \(f(5) = f(7) = 4\) and that \(f(13) > 6\).In this paper a machine method is determined to give any \(f(k)\). In particular, this method yields \(f(11) = 4\), \(f(13) = f(17) = f(19) = f(23) = f(29) = f(31) = f(37) = 6\) and \(f(41) = 7\). Reviewer: W. R. Utz Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 Documents MSC: 11A51 Factorization; primality 11Y05 Factorization Keywords:prime factors of consecutive integers Citations:Zbl 0065.27605 PDFBibTeX XMLCite \textit{D. H. Lehmer}, Am. Math. Mon. 72, 19--20 (1965; Zbl 0128.04002) Full Text: DOI