國立東華大學應用數學系

專    題    演    講

主講人：陳宏賓 助理教授 (中興大學應用數學系)

講 題：A Consequence of Bertrand's Postulate and Beyond

時 間：108 年 04月 03日 (星期三) 16:00-17:00

地 點：理工一館 A318 教室

摘  要

Bertrand's postulate assures that for any positive integer n>3 there exists a prime p between n and 2n. A consequence of Bertrand’s postulate states that the set of integers {1,2,...,2n} can be partitioned into pairs so that the sum of each pair is a prime number for any positive integer n. In this talk, I will introduce its proof and a stronger conjecture by Filz in 1982 that the set of integers {1,2,...,2n} can be rearranged into a cycle so that the sum of any two adjacent integers is a prime number. With a fundamental result in graph theory and a recent breakthrough on the twin prime conjecture, we prove that Filz’s conjecture is true for infinitely many cases. This talk is based on a joint work with Hung-Lin Fu and Jun-Yi Guo.

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