High School Number Theory Archives - Page 3 of 11

The Polynomials that Generate Prime Numbers

January 12, 2013 GB High School Mathematics, High School Number Theory

The search for primes started thousands of years ago. Mathematicians since antiquity tried to find ways to look for primes. They also searched for methods to test if a number is prime or not. Others tried to find polynomials to generate primes.

The Sieve of Eratosthenes

One of the ancient methods of listing prime numbers is the Sieve of Eratosthenes. The Sieve consists of a finite list of numbers, where the multiples of each number are crossed out starting from 2 and increasing each time the list is exhausted. » Read more

10 comments example of prime generating polynomials, formula to generate prime numbers, polynomial generating prime numbers, prime generating polynomials, sieve of Eratosthenes

Are all fractions rational numbers?

January 6, 2013 GB High School Mathematics, High School Number Theory, Question and Answer

No.

A rational number can be expressed in the form $\displaystyle\frac{a}{b}$ where $a$ and $b$ are integers and $b \neq 0$ . In other words, it is a fraction whose denominator is not zero, and both the denominator and numerator are integers.

$fractions$

Some fractions, however, may contain a numerator or denominator that is not an integer. Some examples of such fractions are

$\displaystyle\frac{\sqrt{3}}{2}$ , $\displaystyle\frac{\pi}{4}$ and $\displaystyle\frac{e}{2}$ .

A rational number may be represented in many ways, but it can always be expressed as a fraction. For instance, $10^{-1}$ is a rational number because we can express it as $\frac{1}{10}$ . Also, the number $0.333 \cdots$ , a repeating decimal, is a rational number because we can also express it as fraction $\frac{1}{3}$ .

5 comments are all rational fractions, area all fractions rational, fractions, rational number examples, rational numbers, repeating decimals

Guest Post: An Interesting Property of Prime Numbers

September 8, 2012 GB College Mathematics, High School Mathematics, High School Number Theory, Number Theory

Although I have already discussed modulo division, I believe that this proof is beyond the reach of average high school students. To explain further, I made additional notes on Patrick’s proof . I hope these explanations would be able to help students who want to delve on the proof.

***

I’ve got a prime number trick for you today.

Choose any prime number $p > 3$ .
Square it.
Add 5.
Divide by 8.

Having no idea which prime number you chose, I can tell you this:

The remainder of your result is 6. » Read more

4 comments modulo division, prime number divided by 4, prime trick, prime trick proof, property of prime numbers, remainder of prime number over 4

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