Captain Tony Valare said:
> Something that is related to the base number system makes all numbers
> prime
> in base 2.
The primality or otherwise of members of Z does not depend on the textual
representation you choose.
> since there are just 2 numbers, then all there are is the
> number
> itself, or the number to the zero power.
You appear to be talking about modulus, rather than number bases.
> Any number to the zero power = 1. Now to bring that idea
> forward, you could have a set of numbers which had
> that property, but use a different base number system. Say base 13.
> Would there be any prime numbers, well yes.
Actually, assuming you mean mod 13, no, there wouldn't be any primes. As
Wolfram rightly says, "a prime number is a positive integer having exactly
one positive divisor other than 1", so 0 and 1 aren't prime by definition.
1 * 2 = 2 (mod 13) and 5 * 3 = 2 (mod 13), so 2 isn't prime. 2 * 2 = 4
(mod 13), so 4 isn't prime. 1 * 5 = 5 (mod 13) and 2 * 9 = 5 (mod 13), so
5 isn't prime. 2 * 3 = 6 (mod 13), so 6 isn't prime. 5 * 4 = 7 (mod 13),
so 7 isn't prime - and so on.
<snip>
--
Richard Heathfield <http://www.cpax.org.uk>
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