Prime-producing cubic polynomials (Q2741202)

The authors begin this rather nice delineation of the area with a description of prime-producing quadratic polynomials, especially those producing consecutive, distinct prime values, and the relationship with class number problems. Then they turn their attention to the main topic of the paper, cubic polynomials, and their prime production, especially consecutive. For instance, they cite the example \(f(x)= x^3- x^2+ 66x+ 457\) which produces a string of consecutive primes of length 33 over the interval \([-17,15]\). Their penultimate section exhibits cubic polynomials which produce strings of consecutive primes including an explanation of how they were discovered. They conclude the paper with a section on the simplest cubic fields and their class numbers (with reference to the work of D. Shanks).NEWLINENEWLINEFor the entire collection see [Zbl 0964.00058].