Ah yes, but cookies get EATEN don’t they?
(too much Sesseme Street as a child)
but ok, you cannot make equal piles of cookies out of
o o o o o o o o o o o o o
if your write it 15 or 13 or D.
How about Binary?
Base 7? (Shop teacher math)
thanks for he help, I couldn’t quite get my head around it.
Charles
As above, primality is independent of any particular base. If I write 3 as {{}, {{}}, {{}, {{}}}}*, it’s still a prime.
Yes it’s true that the base representation of a number does not affect its primality, but there is something here. For larger numbers, it’s sometimes easy to determine that a number is not prime just by looking at it. For instance, in base 10, we know that any large number that ends in 0, 2, 4, 5, 6, or 8, is not be prime. So 60% of the numbers we can eliminate at a glance! Some bases are better for this than others. In base 7, the only thing you can systematically eliminate are numbers ending in 0, that is, only 14% of numbers. In base 6, you can eliminate anything ending in 0, 2, 3, and 4. That’s 67%. The next number which is better than 6 is 30. In base 30, we can eliminate stuff ending in 0, 2, 3, 4, 5, 6, 8, 9, A, C, E, F, G, I, K, L, M, O, P, Q, R, and S. That’s a whopping 73%! Not enough to justify using base 30, of course…
Nice one, Achernar! I hadn’t thought of that, but yeah, I guess there is something you can say about primes in different bases.
Of course, that’s only really useful if you’re just looking at it. If you’re testing for primality using a computer, for instance, it takes almost no time to test possible factors up to 30, no matter what your base.
And how many bases have ever been used to test for primes on a computer, exactly? One? Two?
By the way, the point of using primes is precisely because they are independant of the base. You might think the digits of PI would be just as good, but if the people you’re talkoing to happen to use base 9, they’d be looking for 3.1241881…, not 3.1415926…