I’ve started reading a lot of sci-fi and the humans always attempt to communicate with aliens using prime numbers, but if they use a counting system that _isn’t_ base10, would the prime numbers still make sense?
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The base used to write numbers makes no difference to whether they are prime or not. That’s part of the advantage of using primes; they are universal.
Yes. That’s one cool thing about them. They work in all base systems. So they are universal for every base system.
Physical objects can be broken up into groups of objects. A bundle of 17 sticks can’t be broken up into any number of sub groups evenly. It doesn’t matter what base you write out 17, it’s still prime. (Same for all primes)
Bases are pretty much just different notation to write the same numbers. The number ten is equal to ten whatever base you write it in.
So long as you can communicate [a quantity of (number)] with them you can get the meaning across. 2 blobs, 3 blobs, 5 blobs, etc.
Base 10 is just a way we represent numbers. The numbers themselves are just that… numbers. 92 in base 10 is 10 in base 92, but physically it is still 92 objects. Prime numbers are dependent on the absolute numbers, not their representation, and hence are the same irrespective of the base you use.
Think of playing cards, a five of diamonds has thr symbol “5” and shows five diamonds on it. If we used base 2 (binary), the “5” symbol would change to “101”, but there would still be the same number of diamonds displayed on the card.
Since prime numbers are just an amount, the symbol used isn’t the important bit. We probably wouldn’t be able to communicate with aliens using any symbol representing an amount since aliens wouldnt know our alphabet. The symbols would have to be a literal depiction of the amount eg you could use dots or a tally system, like the way we display the numbers on playing cards or dice.
Bases are a way of representing numbers but they don’t affect the underlying arithmetic. It’s like how you get the same result whether you express it as two plus three equals five (English) or dos plus tres equals cinco (Spanish).
To get back to numbers, imagine you have two apples in front of you and then you add three more to wind up with five apples. You can represent that as 2+3=5 or 10+11=101 (binary) but the result has to be the same because the number of apples doesn’t depend on the “language” we describe it in.
The fact that we can do the same math in different bases is very handy because computers think in binary so they can compute in binary (or any other system) and then just translate back to base ten at the end.
Numbers are prime when they can only be divided by themselves and one. Since what divides them doesn’t depend on the base (since arithmetic doesn’t change), primes are the same in every base.
Answer: the base number we use is base 10 but in any base, it would only change how the number *looks*, not how it *acts*. Remember that prime numbers are numbers that are only divisible by themselves and 1!
Being a prime number is just answering the question “given that many objects, can you make a rectangle out of them”.
For exemple, if you have 12 apples, you can make a 3×4 rectangle. If you have 9 apples, you can make a 3×3 rectangle (which is a square).
But if you have 11 apples, you can’t make a rectangle out of them. Well, you can put them in a long line, but we don’t allow that here.
And numbers that are not “rectangle numbers” are called “prime numbers”.
But as you saw, it is something who has to deal with real life objects. While things like “base 10” is a question of “how things are named”.
Imagine taking 6 marbles. You can split that into 2 equal piles of 3. That tells you that 6 is not prime. It is 2×3. Now imagine taking 7 marbles. You can’t split this into equal piles of anything except 7 piles of 1. So 7 is prime. This is true regardless of the number system. Whether base 2 or 10 or 60. The number in each marble pile is equal or it’s not.
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