Monthly Archives: January 2018

Orthogonal polygons

It’s time to say more about PWW #21, in which I exhibited things like this: Quite a few commenters figured out what was going on, and mentioned several nice (equivalent) ways to think about it. Primarily, the idea is to … Continue reading

Posted in combinatorics, geometry | Tagged , , | 5 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 , , , , , , , , , , | 1 Comment

New Mersenne prime

With impeccable timing, just in the middle of my series about primality testing, a new Mersenne prime has been announced, a little under two years after the previous one. In particular, it has been shown that is prime; this is … Continue reading

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A tale of three machines

The Fundamental Theorem of Arithmetic tells us that any positive integer can be factored into a product of prime factors.1 Given a positive integer , this leads naturally to several questions: What is the prime factorization of ? This is … Continue reading

Posted in computation, number theory, primes | Tagged , , , , | 11 Comments