Questions tagged [prime-numbers]

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24
votes
7answers
3k views

A Non-Unique Factorization of Integers!

I'm going to introduce my students to the fundamental theorem of arithmetic (uniqueness of integer factorization to prime factors), and I don't want them to take the uniqueness for granted! To make my ...
22
votes
15answers
6k views

Explaining why (or whether) zero and one are prime, composite or neither to younger children

There are lots of discussions out there about whether $1$ is a prime number (such as this one) and even about zero (such as this question, though note zero does generate a prime ideal in $\mathbb{Z}$ ...
11
votes
4answers
786 views

How to arrive at infinitude of primes proof?

I know Euclid's proof of there being infinite number of primes. I want to let my brother (age 15) arrive at that proof by himself. He knows definition of a prime number (number divisible only by 1 and ...
10
votes
3answers
312 views

Planning high school workshop on Goldbach Conjecture

So I'm doing a mathematics education extension for my current undergraduate maths course, and for one bit of the final assessment we're asked to create a detailed lesson plan on the (strong) Goldbach ...
9
votes
6answers
2k views

Student Project about Prime Numbers: How to Continue?

I know a talented, enthusiastic, and very very hard-wroking 7th grade student, who began working on a research project about prime numbers a month ago. He has written numerous Pascal programs to ...
-4
votes
2answers
301 views

Missing Step in Most Proofs of the Irrationality of $\sqrt{2}$ [closed]

Numerous online resources parrot the usual proof by contradiction of the irrationality of $\sqrt{2}$. These all rely upon the assumption that the rational form (say, $a/b$) is in its simplest ...