> Are prime numbers prime in all bases ?
That is a deep question.
If by "base" and "prime" you are restricting yourself to the integers, the
answer is "yes".
If you allow yourself more freedom and allow other numeric quantities as
your "base", the answer is "not necessarily".
For example, in the integers 5 is prime, no matter what integral base you
choose. On the other hand, if your "base" is sqrt(5), 5 is a perfect
square. Over the complex numbers, the factorization of 5 is (2+i)*(2-i).
The generalization of the concept of "prime", "base", "number" and so forth
is the starting point of a very large chunk of mathematics...
Paul
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