"In number theory, a pernicious number is a positive integer that has a number of 1s in its binary representation which is a prime number. Equivalently, the sum of the digits of a pernicious number, when represented in base 2, is a prime.
This seemingly holds true for all base 2 numbers where the first bit is set to true (1), however, the same cannot be said for any other base 2 representation where the first bit is false (0). For example:
0111 = 07
1101 = 13
1011 = 11
1110 = 14
Is it fair to say that wikipedia is incorrect or am I misinterpreting the statement?
The statement to me implies that the sum of the the true (1) values with in a pernicious number will always be prime. As shown however this can only be true for numbers with a true (1) first bit. My thoughts are that either the definition of pernicious requires that the sum of the digits be prime as well as the count of true (1) bits being prime or that the statement is incorrect.