Term

Pernicious Number

Numbers whose count of binary 1s is prime (3, 5, 6, 7, 9, 10, 12, 17, …).

4,040 numbers tagged.

A pernicious number has a prime number of 1s in its binary representation. For example, 6 = 110 has two 1-bits, and 2 is prime — so 6 is pernicious; 7 = 111 has three, also prime.

Every number of the form \(2^k + 1\) (with \(k \ge 1\)) is pernicious (two 1-bits), and no power of two can ever be pernicious (one 1-bit; 1 is not prime).

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