If you change the prime number 13 to base 7 you get 16. How can 16 be a prime number? Is it that 16 base 7 is a prime number in base 7 math? Can you give an example of how this could be true?
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Think of it in higher bases and it might make more sense.
Base 10: 11
Base 13: B
Now ask the question, how can B be prime?
Think of it in higher bases and it might make more sense.
Base 10: 11
Base 13: B
Now ask the question, how can B be prime?
The base used to express a number is simply a language, whereas being prime is an inherent property of a number.
Think about the object you see every day that has four wheels, a hood and front compartment, a rear compartment, and a space in the middle for ~5 people to sit. In English we call this a car, but Spanish calls it el auto. German calls it das auto. Japanese, Chinese, Russian, each language has their own word for this object. But what language you speak doesn’t change the fact that it is a car.
The base used to express a number is simply a language, whereas being prime is an inherent property of a number.
Think about the object you see every day that has four wheels, a hood and front compartment, a rear compartment, and a space in the middle for ~5 people to sit. In English we call this a car, but Spanish calls it el auto. German calls it das auto. Japanese, Chinese, Russian, each language has their own word for this object. But what language you speak doesn’t change the fact that it is a car.
How we “spell” the numbers has nothing to do with properties like primality – it’s still the exact same number. The number seven is prime whether you’re French and call it “sept”, or German and call it “sieben”. Similarly, primality doesn’t change because you write a number in a different base.
How we “spell” the numbers has nothing to do with properties like primality – it’s still the exact same number. The number seven is prime whether you’re French and call it “sept”, or German and call it “sieben”. Similarly, primality doesn’t change because you write a number in a different base.
The “base” just determines the specific kinds of written symbols you use to represent a number. It does not change any of the fundamental properties of that number.
Even/Odd numbers are still even/odd.
Negative/Positive numbers are still negative/positive.
Prime/composite numbers are still prime/composite.
Rational/Irrational numbers are still rational/irrational.
And so on.
The “base” just determines the specific kinds of written symbols you use to represent a number. It does not change any of the fundamental properties of that number.
Even/Odd numbers are still even/odd.
Negative/Positive numbers are still negative/positive.
Prime/composite numbers are still prime/composite.
Rational/Irrational numbers are still rational/irrational.
And so on.
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