Monthly Archives: January 2019

Finding prefix and repetend length

Posted on January 29, 2019 by Brent

We interrupt your regularly scheduled primality testing to bring you something else fun I’ve been thinking about. It’s well-known that any rational number has a decimal expansion that either terminates, or is eventually periodic—that is, the digits after the decimal … Continue reading →

Posted in number theory, pattern | Tagged , , , | 2 Comments

More on Fermat witnesses and liars

Posted on January 23, 2019 by Brent

In my previous post I stated, without proof, the following theorem: Theorem: if is composite and there exists at least one Fermat witness for , then at least half of the numbers relatively prime to are Fermat witnesses. Were you … Continue reading →

Posted in computation, number theory, primes | Tagged , , , , , | Comments Off on More on Fermat witnesses and liars

Fermat witnesses and liars (some words on PWW #24)

Posted on January 18, 2019 by Brent

Let be a positive integer we want to test for primality, and suppose is some other positive integer with . There are then four possibilities: and could share a common factor. In this case we can find the common factor … Continue reading →

Posted in computation, number theory, posts without words, primes | Tagged , , , , | 1 Comment

Post without words #24

Posted on January 15, 2019 by Brent
Posted in computation, number theory, posts without words, primes | Tagged , , , | 5 Comments