Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 525.10023
Autor: Erdös, Paul; Pomerance, Carl
Title: An analogue of Grimm's problem of finding distinct prime factors of consecutive integers. (In English)
Source: Util. Math. 24, 45-65 (1983).
Review: For n natural number, let f(n) denote the largest integer such that for each m in {n+1,...,n+f(n)} there is a divisor dm of m with 1 < dm < m and such that the dm's are all different. The authors prove that for every \epsilon > 0, n ½ << f(n) << n1/12+\epsilon. The lower bound is then strengthened to (1) liminf f(n) ½ \geq 4. Moreover, equality holds in (1) if and only if there are infinitely many twin primes. Several other related results are also given.
Reviewer: S.W.Graham
Classif.: * 11N05 Distribution of primes
Keywords: distinct prime factors of consecutive integers; Grimm conjecture
© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag