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.
20190320_陳宏賓教授.pdf