The Gymnocalycium baldianum species has flowers that range from white, pink, orange and bright red. I've looked for one of the white flowered ones without any luck. Each year, my G. baldianum has flowers that range from pink to a salmon pink color. This year, it looks like they are more in the pink range.
My one red G. baldianum is still small, but this species can bloom at one year old. I've found over the years that Gymnocalycium baldianum will bloom over and over from late April until September. If anyone ever wants a cactus that produces prolific flowers, this is it.
Most of my Parodia species have flowered or in the process right now. They will soon finish up for the season, but may produce another round of smaller flowers in a few weeks. I never know.