We demonstrate the first use of the nullomer (absent sequences) approach to drug discovery and development. Nullomers are the shortest absent sequences determined in a species, or group of species. By identifying the shortest absent peptide sequences from the NCBI databases, we screened several potential anti-cancer peptides. In order to improve cell penetration and solubility we added short poly arginine tails (5Rs), and initially solubilized the peptides in1M trehalose. The results for one of the absent sequences 9R (RRRRRNWMWC), and its scrambled version 9S1R (RRRRRWCMNW) are reported here. We refer to these peptides derived from nullomers as PolyArgNulloPs. A control PolyArgNulloP, 124R (RRRRRWFMHW), was also included. The lethal effects of 9R and 9S1R are mediated by mitochondrial impairment as demonstrated by increased ROS production, ATP depletion, cell growth inhibition, and ultimately cell death. These effects increase over time for cancer cells with a concomitant drop in IC-50 for breast and prostate cancer cells. This is in sharp contrast to the effects in normal cells, which show a decreased sensitivity to the NulloPs over time.