In this talk we present homogeneous nonprime ideals that can be used to produce, via an unprojection process, homogeneous prime ideals of high Castelnuovo-Mumford regularity. We thus provide counterexamples to the Eisenbud-Goto regularity conjecture other than those given by the Rees-like algebra method of J. McCullough and I. Peeva. Their construction was inspired by G. Caviglia (2004), J. Beder et al. (2011), and K. Borna-A. Mohajer (2015, arXiv).