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> A pernicious number is a positive integer such that the Hamming weight of its binary representation is prime.
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>  [[Wikipedia](https://en.wikipedia.org/wiki/Pernicious_number)]
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The meaning of ‘pernicious’:



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> **pernicious (adj.)**: highly injurious or destructive, deadly
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>  [[Merriam Webster](https://www.merriam-webster.com/dictionary/pernicious)]
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How did pernicious numbers end up being called that?



Why are they called ‘pernicious’ numbers?

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> Let $t\,(n)$ be the digit sum of the binary representation of $n$. Then Google will tell you that $n$ is called odious if $t\,(n)$ is odd and evil if $t\,(n)$ is even. Thus every number is either odious or evil, and therefore the words "odious" and "evil" cannot be pejorative in this context. It seems very likely that "pernicious" was chosen in the same spirit because it starts with the letter "p".
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Full credit goes to Steven Landsburg for providing the full answer in a comment


Answer derived from his comment based on SE policy [here](https://meta.stackoverflow.com/questions/251597/question-with-no-answers-but-issue-solved-in-the-comments-or-extended-in-chat).


