Critical Fallibilism, Evolution and Digital Error Correction [CF Article]

[lmf]

@Elliot

The basic purpose of primes is to understand and use numbers better. E.g. prime factorization is helpful to understand for people who care about arithmetic.

@ingracke

Prime numbers are really useful and should be explicitly taught as part of basic math, before algebra.

Being able to use & understand prime factorization is helpful with basic arithmetic (multiplication & division). And understanding and being able to use prime numbers helps a lot with understanding divisibility rules and using them efficiently. Primes, prime factorizations, and divisibility rules all help a lot with working with basic fractions (e.g. simplification and arithmetic with fractions), which helps with understanding decimals, ratios, and percentages, which helps with understanding statistics and a lot of real-world math. Being able to do prime factorizations & cancellations is also really helpful with algebra. And mental math in general would be a lot easier if people understood prime numbers and prime factorizations better. When I have recommended that people go back and learn math better, this (prime numbers & prime factorization) is the kind of stuff I think they should be focussing on.

Prime numbers are also useful for basic counting problems that would have existed before modern math: it is useful to know that there are some quantities that you are not going to be able to break up into equally sized groups or arrange into rectangles (except groups of one or rectangles by one). It is useful to know that there are plenty of ways to break up 48 potatoes equally, but no ways to break up 47 potatoes equally (without cutting some of the potatoes). Or that you can arrange 48 people into a rectangle, but you cannot arrange 47. (Arranging people into rectangles is currently used for things like desks in a classroom, and in the past was used for arranging military troops.) These are useful things that people could have noticed just trying to solve real-life problems.

You’re right. I don’t know how I was able to blank out the fact that primes are essential for all these basic algorithms of arithmetic.