Many eight-year-olds use mobile devices. These devices can be attacked by computer viruses, with possible, serious consequences for device owners. Eight-year-olds do not always learn in schools about the concepts of computer viruses and protection against them, but they may still have everyday conceptions about these concepts: acquired outside schools. However, little is known about whether or not children have these everyday conceptions, and if so, how elaborate they are. This study explores these conceptions among 58 second graders from the Czech Republic, who were not taught about computer viruses in school. The children were interviewed, their correct conceptions were quantitatively scored, and their incorrect notions were noted. The results showed that children had few incorrect notions; however, their understanding was generally low and patchy. Approx. 1/3 of the children knew about the existence of software updates, but -- and this is especially worrying -- almost none of them knew about antiviruses. On a practical level, the results support the idea that the topic of computer viruses should be taught early at the primary education level. On a theoretical level, within cognitive constructivism frameworks, the results indicate that children's understanding has to be developed from scratch rather than by means of reconstructing and/or elaborating already held conceptions (because children appear to bring few prior conceptions to school, neither correct nor incorrect ones).