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Recently, I've observed that if we write a prime number (greater than 2) with base 3 (in the ternary system), then the sum of digits will be an odd number.

Is this previously been observed? Is this useful somehow?

Examples: (decimal prime, ternary representation, a sum of ternary digits)

3       10                      1
17      122                     5
47      1202                    5
97      10121                   5
komorra
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1 Answers1

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All odd numbers have a ternary digit sum that is odd, as it is the sum of an odd number of powers of $3$. All even numbers have a ternary digit sum which is even. This is true in other odd bases too.

Your result follows from the fact that $2$ is the only even prime and you have excluded it.

Henry
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