Nullomers are minimal-length oligomers absent from a genome or proteome. Although research has shown that artificially synthesized nullomers have deleterious effects, there is still a lack of a strategy for the prioritisation and classification of non-occurring sequences as potentially malicious or benign. In this work, by using Markovian models with multiple-testing correction, we reveal significant absent oligomers which are statistically expected to exist. This strongly suggests that their absence is due to negative selection. We survey genomes and proteomes covering the diversity of life, and find thousands of significant absent sequences. Common significant nullomers are often mono-or dinucleotide tracts, or palindromic. Significant viral nullomers are often restriction sites, and may indicate unknown restriction motifs. Surprisingly, significant mammal genome nullomers are often present, but rare, in other mammals, suggesting that they are suppressed but not completely forbidden. Significant human nullomers are rarely present in human viruses, indicating viral mimicry of the host. More than 1/4 of human proteins are one substitution away from containing a significant nullomer. We provide a webbased, interactive database of significant nullomers across genomes and proteomes.In this study, we introduce a robust probabilistic method named Nullomers Assessor (https://github.com/gkoulouras/nullomers-assessor) for the evaluation of globally missing sets of oligomers in any species, considering the fact that biological sequences of living organisms are driven by mutational biases and natural selection, and consequently are not entirely random (10). Naturally occurring sequences present patterns and combinatoric properties which can be signatures for the identification of functional elements as such promoters, tandem repeat expansions, introns, exons, and regulatory elements (18). In addition, evolutionarily well-separated species are known to possess distinct statistical characteristics in their DNA or peptide sequence chains (19). All these distinctive properties of biological sequences have frequently been studied using probabilistic models. Markov chain models have been widely and successfully employed in various biological problems including sequence analysis in the past (26-29). Taking advantage of these particular properties of biological sequences, we developed a method which approximates the likelihood of an absent sequence to occur exactly zero times, in order to address the following three questions. First, are there statistically significant minimal absent sequences in biological species; in simple words, what is the expected probability for an actual nullomer to be indeed absent, based on the compositional pattern in the full genome or proteome of a species? Second, are there significant MAWs in common across evolutionarily diverse living organisms? And finally, does the creation of a previously absent sequence perturb a molecule; more precisely, are there mutations with functional or stability impact ...