Questions tagged [prime-numbers]
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How can we explain intuitively the convergence and divergence of these two series?
It is known that $\displaystyle\sum_1^{\infty} \frac{1}{n^{1.000001}}$ converges while $\displaystyle\sum_{n\text{ is a prime number}}\frac{1}{n}$ diverges. Though we can logically prove these results,...
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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 ...
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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 $\mathbb{Z}$ ...
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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 ...
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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 ...
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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 ...
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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 ...
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