Are prime numbers in different bases still prime?

[Jim_Baur]

Are prime numbers in different bases still prime?

Does pi end in different bases?

Thanks for answering such a basic question.

I guess I should know.

I guess I should be able to figure it out.

SORRY!

THANKS!

 

[ThinkingSapien]

Are prime numbers in different bases still prime?

Does pi end in different bases?

Changing a number base only changes how a value is represented. An even number will still be even, a prime number will still be prime.

13 (decimal) is 0xD (hexadecimal) and is 01101 (binary). All three are prime. All three are odd.

 

[Razanir]

The number, the quantity, is still the same. It will over ever be prime XOR composite. It can’t switch. Similarly, an odd number can never suddenly become even. Bases are just different representations. To relate to Shakespeare, “What’s in a name? That which we call a rose / by any other name would smell as sweet.” The word is not the thing. A cat is still a cat, even if you call it el gato, le chat, die Katze…

As an interesting side note, though, the rules for checking parity (even or odd) change between bases. In even bases, you just look at the last digit. In odd bases, though, you check how many odd digits there are. 11 (base 3) is even (it equals 4, by the way)

 

[polytropos]

Does pi end in different bases?

No. If pi terminated in different bases, then it would terminate if you converted it back to base-10.

In any base, the rational numbers either terminate or eventually repeat. The irrational numbers are everything else.

 

[GEddie]

A base just changes the representation. The number itself is the same.

There is no intrinsic reason why the number of toes on your feet should necessarily be represented by one and zero. 10 and “A” (hex) mean the same thing. The rules of mathematics are the same.

ICXC NIKA

 

[Bob_Crowley]

I’m not a mathematician, but as I understand it a prime number is a **whole number **which is divisible by no other whole numbers but one and itself.

It wouldn’t matter what number base you used, provided you remember that it involves whole numbers only, you would run into the same condition.

So for 13 as someone has pointed out, if it was represented in binary as 1101, we would find we could divide it only by 1 and 1101 in binary, and no other binary number representing a whole number.