Primes

Prime Factorization of a Number (Advanced)

Last time we looked at basic methods for finding the prime factorization of a number. Here we will look at some special techniques for large numbers, demonstrating them for not-too-large numbers. This takes us a step beyond previous tests that told us whether a number was composite, without actually factoring them.

Prime Factorization of a Number (Basics)

I’ll close this series on prime numbers by looking at how to find the prime factorization of a number, starting with the most basic ideas applicable to relatively small numbers, and then (next week) looking at some advanced methods for larger numbers.

Prime Numbers: Making a List

We’ve looked at what prime numbers are, and how the concept extends (or doesn’t) to 0, 1, and negative integers. The next question many students have is, how can I make a list of prime numbers (or write a computer program to do so)? We’ll learn about the Sieve of Eratosthenes, and list all the …

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Prime Numbers: What About Negatives?

We’ve looked at the basic idea of primes, then at where 0 and 1 fit in. But what about negative integers? Can they be prime? If so, how does that affect the definition? And can you factorize a negative number if you don’t have negative primes?

Prime Numbers: What About 0 and 1?

Last week we looked at the definitions of prime and composite numbers, and saw that 1 is neither. The same is true of 0. What, then, are they? That raises some deep questions that we’ll look at here.

Prime Numbers: What and Why

I’ll begin a short series of posts on prime numbers with several questions on the basics: What are prime (and composite) numbers, and why do they matter?