Recent Posts

Generating many prime numbers Today, a fellow student claimed that it would take much time to check the first 1,000,000 numbers for primes. I claimed that it would be a matter of seconds to do so for the first 1,000,000,000 numbers. So, lets prove my claim. Trivial approach #include … Read More »

The Collatz sequence The goal of this post is to show you some tools that allow you to visualize data. And I also want to analyze some basic characteristics of the Collatz sequence. The Collatz sequences $(c^n_i)$ of a number $n \in \mathbb{N}_{> 0}$ is defined like this: $$f:\mathbb … Read More »

Project Euler: Problem 35 The task in Problem 35 of Project Euler is: The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime. There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and … Read More »

Project Euler: Problem 33 The task in Problem 33 of Project Euler is: The fraction $\frac{49}{98}$ is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that $\frac{49}{98} = \frac{4}{8}$, which is correct, is obtained by cancelling the 9s. We shall consider fractions … Read More »

Project Euler: Problem 32 The task in Problem 32 of Project Euler is: We shall say that an $n$-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital. The product 7254 is unusual, as the … Read More »

Project Euler: Problem 26 The task in Problem 26 of Project Euler is: Find the value of d < 1000 for which $\frac{1}{d}$ contains the longest recurring cycle in its decimal fraction part. How to solve Think about how you divide with pen and paper. How do you recognize that you have a … Read More »

Python one-liners for Project Euler Today, I've been trying to get used to Pythons functional programming tools by solving Project-Euler tasks. To make them more interesting, I've solved them in one line. But I realized, that it is difficult to read online as only about 70 characters get displayed without a scrollbar. So I made … Read More »

Project Euler: Problem 142 Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems. The motivation for … Read More »

Challenge Websites Challenge websites are websites which offer many tasks to solve and a ranking system. If you solve the challenges, you get points and your rank increases. You don't get anything else. No money, no price. Only the knowledge and the ranking. Which is enough in my opinion. It might sound … Read More »