Mathematically gifted students are mostly getting their education in mixed classrooms. Teachers should be able to recognize mathematically gifted students to be responsive to those students' needs along with other students in their classrooms. The current study aims to reveal prospective primary mathematics teachers' views about mathematical giftedness and the characteristics of mathematically gifted students. The participants of this qualitative study are 11 prospective mathematics teachers who take their education in a four-year primary mathematics teacher education program at a state university in Turkey. Two focus group interviews are conducted with the participants. The row data were analyzed by using descriptive analysis. The findings reveal that prospective teachers associated mathematical giftedness with various concepts such as social environment and effort. The participants' views on the characteristics of mathematically gifted students have varied in line with the literature. It also concluded that prospective primary mathematics teachers emphasized creative acts like re-formulating problems and finding unique solutions to the problems as indicators of being mathematically gifted.