Is it true that all senary numbers ending in 1 and 5 are primes? I was reading the Wikipedia article on senary numbers (base 6), which states that: > all primes, when expressed in base-six, other than 2 and 3 have 1 or 5 as the final digit Unless I am converting to senary incorrectly, I find this not to be true. For example, the senary representation of the decimal number 2047 is '13251', which would be a prime according to the stated rule, but is not (2047 = 89 * 23). Is my conversion correct? Is the stated rule incorrect?

You are misinterpreting the statement. "All primes satisfy property $X$" means "If $p$ is prime, then $p$ has property $X$." You have instead interpreted it as "If $p$ has property $X$, then $p$ is prime."

The statement is true, because if $p$ is a prime greater than $3$, then $p$ is not divisible by $2$ or $3$, whereas a number whose base six expansion ends in $0$, $2$, or $4$ is even and a number whose base six expansion ends in $0$ or $3$ is a multiple of $3$.