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Tag Archives: algorithm
Post without words #23
Posted in pattern, pictures, posts without words
Tagged algorithm, CalkinWilf, Euclidean, tree
11 Comments
Quickly recognizing primes less than 1000: memorizing exceptional composites
In my previous post I wrote about a procedure for testing the primality of any number less than : Test for divisibility by all primes up to , and also . (In practice I test for 2 and 5 first, … Continue reading
Quickly recognizing primes less than 1000: divisibility tests
I took a little hiatus from writing here since I attended the International Conference on Functional Programming, and since then have been catching up on teaching stuff and writing a bit on my other blog. I gave a talk at … Continue reading
Modular exponentiation by repeated squaring
In my last post we saw how to quickly compute powers of the form by repeatedly squaring: ; then ; and so on. This is much more efficient than computing powers by repeated multiplication: for example, we need only three … Continue reading
Posted in computation, number theory
Tagged algorithm, exponentiation, logarithmic, modular, primality, repeated, squaring, test
4 Comments
More on sums of palindromes
In my previous post I reported on a recent proof that every positive integer can be written as the sum of three palindromes. The first thing to report in this followup post is that Lewis Baxter sent me the Python … Continue reading
Every positive integer is a sum of three palindromes
I recently learned from John Cook about a new paper by Javier Cilleruelo, Florian Luca, and Lewis Baxter proving that every positive integer can be written as a sum of three palindromes. A palindrome is a number that is the … Continue reading
Posted in arithmetic, computation, links
Tagged algorithm, constructive, news, palindromes, proof, sum
14 Comments
Fast and slow machines
In my previous post, I presented three hypothetical machines which take a positive integer as input and give us something else as output: a factorization machine gives us the complete prime factorization of ; a factor machine gives us one … Continue reading
Posted in computation, number theory, primes
Tagged algorithm, division, efficiency, exponential, factor, factorization, machine, polynomial, primality, testing, trial
1 Comment
From primitive roots to Euclid’s orchard
Commenter Snowball pointed out the similarity between Euclid’s Orchard… …and this picture of primitive roots I made a year ago: At first I didn’t see the connection, but Snowball was absolutely right. Once I understood it, I made this little … Continue reading