# riemann hypothesis Published articles for riemann hypothesis. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## Searching for RH Counterexamples -- Exploring Data DevFeed: [Searching for RH Counterexamples -- Exploring Data]() Original publisher: [Read original article]() Published: 2021-06-14T08:00:00Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [Data analysis](), [data](), [Amazon Web Services](), [Database](), [Software Engineering]() Tags: [analysis](), [article](), [aws](), [data-analysis](), [data-visualization](), [database](), [databases](), [machine-learning](), [mathematics](), [performance](), [postgres](), [programming](), [python](), [regression](), [riemann-hypothesis](), [superabundant-numbers](), [visualization]() ### AI overview The article examines data from a search for counterexamples to the Riemann Hypothesis. It reports that the search stopped partway through numbers with 136 prime divisors, and that the strongest witness found remained below the value needed to disprove the hypothesis. It also summarizes runtime and AWS costs. ### Source excerpt We're ironically searching for counterexamples to the Riemann Hypothesis. Setting up Pytest Adding a Database Search Strategies Unbounded integers Deploying with Docker Performance Profiling Scaling up Productionizing In the last article we added a menagerie of "production readiness" features like continuous integration tooling (automating test running and static analysis), alerting, and a simple deployment automation. Then I let it loose on AWS, got extremely busy with buying a house, forgot about this program for a few weeks (no alerts means it worked flawlessly! ## Searching for RH Counterexamples -- Scaling Up DevFeed: [Searching for RH Counterexamples -- Scaling Up]() Original publisher: [Read original article]() Published: 2021-02-16T09:00:00Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [Mathematics](), [hashing](), [scaling](), [sha256](), [hash](), [Database]() Tags: [architecture](), [disk-space](), [hashing](), [mathematics](), [performance](), [postgres](), [programming](), [refactor](), [riemann-hypothesis](), [scaling](), [sha256](), [software]() ### AI overview This article describes scaling a search for counterexamples to the Riemann Hypothesis. It focuses on reducing storage by keeping deterministic SHA-256 summaries instead of every witness value and refactoring the application into a worker architecture. ### Source excerpt We're ironically searching for counterexamples to the Riemann Hypothesis. Setting up Pytest Adding a Database Search Strategies Unbounded integers Deploying with Docker Performance Profiling Last time we made the audacious choice to remove primary keys from the RiemannDivisorSums table for performance reasons. To help with that, we will do two things in this post Reduce the storage footprint of the whole application (it was 60 GiB when it crashed, and we got up to 84 prime factors). ## Searching for RH Counterexamples -- Performance Profiling DevFeed: [Searching for RH Counterexamples -- Performance Profiling]() Original publisher: [Read original article]() Published: 2021-02-02T08:00:00Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Computing](), [Docker](), [Amazon EC2](), [Database](), [Linux]() Tags: [cpu](), [database](), [databases](), [debugging](), [docker](), [ec2](), [linux](), [mathematics](), [performance](), [postgres](), [profiling](), [programming](), [riemann-hypothesis](), [software](), [ubuntu]() ### AI overview This tutorial investigates performance problems in a Docker application running on Amazon EC2 while searching for Riemann Hypothesis counterexamples. It describes gathering resource metrics, narrowing the source of delays, isolating computations locally, and measuring divisor-sum blocks. ### Source excerpt We're ironically searching for counterexamples to the Riemann Hypothesis. Setting up Pytest Adding a Database Search Strategies Unbounded integers Deploying with Docker In the last article we ran into some performance issues with our deployed docker application. In this article we'll dig in to see what happened, fix the problem, run into another problem, fix it, and run the search until we rule out RH witness-value-based counterexamples among all numbers with fewer than 85 prime factors. ## Searching for RH Counterexamples -- Deploying with Docker DevFeed: [Searching for RH Counterexamples -- Deploying with Docker]() Original publisher: [Read original article]() Published: 2021-01-04T09:00:00Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Docker](), [Containers](), [reproducibility](), [Database](), [Server]() Tags: [aws](), [containers](), [database](), [docker](), [mathematics](), [programming](), [pytest](), [reproducibility](), [riemann-hypothesis](), [server](), [software]() ### AI overview A tutorial on deploying an application that searches for counterexamples to the Riemann Hypothesis. It explains reproducibility and hermeticity, then uses Docker containers for the database, search application, and planned web server. ### Source excerpt We're ironically searching for counterexamples to the Riemann Hypothesis. Setting up Pytest Adding a Database Search Strategies Unbounded Integers In this article we'll deploy the application on a server, so that it can search for RH counterexamples even when I close my laptop. Servers and containers When deploying applications to servers, reproducibility is crucial. You don't want your application to depend on the details of the computer it's running on. This is a higher-level version of the same principle behind Python virtual environments, but it applies to collections of programs, possibly written in different languages and running on different computers. ## Searching for RH Counterexamples -- Unbounded Integers DevFeed: [Searching for RH Counterexamples -- Unbounded Integers]() Original publisher: [Read original article]() Published: 2020-10-13T09:00:00Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [Database](), [Python](), [Software Engineering](), [Numba](), [Sorting]() Tags: [arbitrary-precision-arithmetic](), [database](), [databases](), [mathematics](), [numba](), [number-theory](), [open-closed](), [postgres](), [python](), [riemann-hypothesis](), [software](), [software-engineering](), [sorting](), [superabundant-numbers]() ### AI overview This article examines how searching for Riemann Hypothesis counterexamples reaches the limits of 64-bit integers. It explains unbounded integer arithmetic and considers database and performance alternatives for storing and processing the search results. ### Source excerpt We're ironically searching for counterexamples to the Riemann Hypothesis. Setting up Pytest Adding a Database Search strategies In the last article, we improved our naive search from "try all positive integers" to enumerate a subset of integers (superabundant numbers), which RH counterexamples are guaranteed to be among. These numbers grow large, fast, and we quickly reached the limit of what 64 bit integers can store. Unbounded integer arithmetic is possible on computers, but it requires a special software implementation. ## Searching for RH Counterexamples -- Search Strategies DevFeed: [Searching for RH Counterexamples -- Search Strategies]() Original publisher: [Read original article]() Published: 2020-09-28T20:48:00Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Software Engineering](), [Algorithm](), [Code](), [implementation](), [Testing]() Tags: [code](), [engineering](), [git](), [implementation](), [interface](), [riemann-hypothesis](), [software](), [software-engineering](), [superabundant-numbers](), [testing]() ### AI overview A tutorial episode that uses a search for counterexamples to the Riemann Hypothesis to teach software engineering. It develops a more efficient enumeration strategy based on superabundant numbers, prime exponents, and integer partitions, while connecting the implementation to testing, interfaces, and repository commits. ### Source excerpt We're glibly searching for counterexamples to the Riemann Hypothesis, to trick you into learning about software engineering principles. In the first two articles we configured a testing framework and showed how to hide implementation choices behind an interface. Next, we'll improve the algorithm's core routine. As before, I'll link to specific git commits in the final code repository to show how the project evolves. Superabundant numbers A superabundant number $ n$ is one which has "maximal relative divisor sums" in the following sense: for all $ m < n$, ## Searching for RH Counterexamples -- Adding a Database DevFeed: [Searching for RH Counterexamples -- Adding a Database]() Original publisher: [Read original article]() Published: 2020-09-11T18:53:48Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Database](), [Software Engineering](), [Code](), [interface](), [Testing](), [Git]() Tags: [code](), [database](), [databases](), [dependency](), [git](), [interface](), [mathematics](), [number-theory](), [oeis](), [programming](), [riemann-hypothesis](), [software](), [software-design](), [sql](), [testing]() ### AI overview This tutorial extends a Python application that computes divisor sums related to attempts to disprove the Riemann Hypothesis by adding a database dependency. It advocates defining and testing a minimal interface before choosing a database, so the dependency can change as the application evolves. ### Source excerpt In the last article we set up pytest for a simple application that computes divisor sums $ \sigma(n)$ and tries to disprove the Riemann Hypothesis. In this post we'll show how to extend the application as we add a database dependency. The database stores the computed sums so we can analyze them after our application finishes. As in the previous post, I'll link to specific git commits in the final code repository to show how the project evolves. ## Searching for RH Counterexamples -- Setting up Pytest DevFeed: [Searching for RH Counterexamples -- Setting up Pytest]() Original publisher: [Read original article]() Published: 2020-09-11T15:51:48Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Pytest](), [Python](), [Testing](), [Code](), [Development]() Tags: [development-environment](), [git](), [github](), [mathematics](), [number-theory](), [programming](), [project-organization](), [pytest](), [python](), [riemann-hypothesis](), [setup](), [shell](), [software](), [testing]() ### AI overview A hands-on tutorial that sets up a Python 3.8 project with pytest and Git, using a search for counterexamples related to the Riemann Hypothesis as the example problem. It explains terminal-based project setup, testing, organization, and how design evolves during development. ### Source excerpt Some mathy-programmy people tell me they want to test their code, but struggle to get set up with a testing framework. I suspect it's due to a mix of: There are too many choices with a blank slate. Making slightly wrong choices early on causes things to fail in unexpected ways. I suspect the same concerns apply to general project organization and architecture. Because Python is popular for mathy-programmies, I'll build a Python project that shows how I organize my projects and and test my code, and how that shapes the design and evolution of my software.