What Are Prime Numbers For?
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- Опубликовано: 17 окт 2023
- What exactly defines a prime number? While many might rush to describe them as numbers that can only be expressed as themselves times one, this definition leaves out nuances that make the subject far more intriguing.
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In this video, we delve into the intricacies of prime numbers. We'll address why numbers like 1 and -1, which can also be expressed as themselves times one, aren't considered prime. By exploring the true definition of primes as positive integers with exactly two factors, we'll bridge the connection to the fundamental theorem of arithmetic and reveal the genuine significance of prime numbers in mathematical theory.
🔍 YOUR THOUGHTS: After watching, do you believe there's a more intuitive way to describe prime numbers or is the two-factor definition truly optimal? Share your perspective in the comments.
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I always wondered why prime numbers were even a thing. This makes a lot more sense. A lot of math teachers would rejoice in such a simple yet effective explanation.
Brilliant explanation of a basic concept that often gets overlooked or taken for granted. Thanks!
You’re very kind, thank you!
i had never thought of the 30*1 repeating example everything makes more sense now 😅👍
As a 6th grade math teacher I taught my students that prime numbers are numbers with exactly 2 factors.
One thing that is fascinating about prime numbers is that they are all either one more or one less than a multiple of six.
Why is this the case?
Has this ever been proven?
Some modular arithmetic might help you think about such results, but basically there are six options for the remainder when dividing by 6 (notice that a remainder of 5 is the same one less than a multiple of 6). By inspection, the other four possible remainders: 0, 2, 3, 4 will allow you to factor out a number, e.g. 6k + 2 = 2(3k + 1).