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Abstract Nullomers and nullpeptides are short DNA or amino acid sequences that are absent from a genome or proteome, respectively. One potential cause for their absence could be their having a detrimental impact on an organism. Results Here, we identify all possible nullomers and nullpeptides in the genomes and proteomes of thirty eukaryotes and demonstrate that a significant proportion of these sequences are under negative selection. We also identify nullomers that are unique to specific functional categories: coding sequences, exons, introns, 5′UTR, 3′UTR, promoters, and show that coding sequence and promoter nullomers are most likely to be selected against. By analyzing all protein sequences across the tree of life, we further identify 36,081 peptides up to six amino acids in length that do not exist in any known organism, termed primes. We next characterize all possible single base pair mutations that can lead to the appearance of a nullomer in the human genome, observing a significantly higher number of mutations than expected by chance for specific nullomer sequences in transposable elements, likely due to their suppression. We also annotate nullomers that appear due to naturally occurring variants and show that a subset of them can be used to distinguish between different human populations. Analysis of nullomers and nullpeptides across vertebrate evolution shows they can also be used as phylogenetic classifiers. Conclusions We provide a catalog of nullomers and nullpeptides in distinct functional categories, develop methods to systematically study them, and highlight the use of variability in these sequences in other analyses