Assuming you used “and” when you meant “or”, that's trivially true (and redundant) in that all numbers (irrespective of base, which has no effect on this) are integer multiples of 1.
But no primes other than 5 are integer multiples of 5, in any base.
> Senary may be considered interesting in the study of prime numbers, since all primes other than 2 and 3, when expressed in senary, have 1 or 5 as the final digit.
> I expressed it poorly, but not as you state, incorrectly.
No, really, it is completely incorrect to use “multiple of X in base Y” to mean “have X as the final digit in base Y” (which is equivalent to “is congruent to X modulo Y.”)
13 is not, in base 10 (or anywhere else), a multiple of 3.[0]
That's just not what “multiple” means.
[0] Well, the number denoted by the digits “13” in any base that is itself a multiple of 3—other than base 3 itself where “13” is not a valid number—is a multiple of 3, obviously, but we're talking about the number represented by “13” in base 10.
