Bulletin of the
Korean Mathematical Society BKMS

First, we recall the results for prime-producing polynomials related to class number one problem of quadratic fields. Next, we give the relation between prime-producing cubic polynomials and class number one problem of the simplest cubic fields and then present the conjecture for the relations. Finally, we numerically compare the ratios producing prime values for several polynomials in some interval.

Keywords: Prime-producing polynomials, quadratic fields, cubic fields, class number

MSC numbers: Primary 11R09; Secondary 11R11, 11R16, 11R29

Supported by: This Research was supported by Research Funds of Mokpo National University in 2019.