# superabundant numbers

Published articles for superabundant numbers.

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## Searching for RH Counterexamples -- Exploring Data

DevFeed: [Searching for RH Counterexamples -- Exploring Data](<https://devfeed.tech/articles/searching-for-rh-counterexamples-exploring-data-40447.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2021/06/14/searching-for-rh-counterexamples-exploring-data/>)

Published: 2021-06-14T08:00:00Z

Content type: article

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Data analysis](<https://devfeed.tech/topics/data-analysis.md>), [data](<https://devfeed.tech/topics/data.md>), [Amazon Web Services](<https://devfeed.tech/topics/aws.md>), [Database](<https://devfeed.tech/topics/database.md>), [Software Engineering](<https://devfeed.tech/topics/software-engineering.md>)

Tags: [analysis](<https://devfeed.tech/tags/analysis.md>), [article](<https://devfeed.tech/tags/article.md>), [aws](<https://devfeed.tech/tags/aws.md>), [data-analysis](<https://devfeed.tech/tags/data-analysis.md>), [data-visualization](<https://devfeed.tech/tags/data-visualization.md>), [database](<https://devfeed.tech/tags/database.md>), [databases](<https://devfeed.tech/tags/databases.md>), [machine-learning](<https://devfeed.tech/tags/machine-learning.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [performance](<https://devfeed.tech/tags/performance.md>), [postgres](<https://devfeed.tech/tags/postgres.md>), [programming](<https://devfeed.tech/tags/programming.md>), [python](<https://devfeed.tech/tags/python.md>), [regression](<https://devfeed.tech/tags/regression.md>), [riemann-hypothesis](<https://devfeed.tech/tags/riemann-hypothesis.md>), [superabundant-numbers](<https://devfeed.tech/tags/superabundant-numbers.md>), [visualization](<https://devfeed.tech/tags/visualization.md>)

### 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 -- Unbounded Integers

DevFeed: [Searching for RH Counterexamples -- Unbounded Integers](<https://devfeed.tech/articles/searching-for-rh-counterexamples-unbounded-integers-40440.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2020/10/13/searching-for-rh-counterexamples-unbounded-integers/>)

Published: 2020-10-13T09:00:00Z

Content type: article

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Database](<https://devfeed.tech/topics/database.md>), [Python](<https://devfeed.tech/topics/python.md>), [Software Engineering](<https://devfeed.tech/topics/software-engineering.md>), [Numba](<https://devfeed.tech/topics/numba.md>), [Sorting](<https://devfeed.tech/topics/sorting.md>)

Tags: [arbitrary-precision-arithmetic](<https://devfeed.tech/tags/arbitrary-precision-arithmetic.md>), [database](<https://devfeed.tech/tags/database.md>), [databases](<https://devfeed.tech/tags/databases.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [numba](<https://devfeed.tech/tags/numba.md>), [number-theory](<https://devfeed.tech/tags/number-theory.md>), [open-closed](<https://devfeed.tech/tags/open-closed.md>), [postgres](<https://devfeed.tech/tags/postgres.md>), [python](<https://devfeed.tech/tags/python.md>), [riemann-hypothesis](<https://devfeed.tech/tags/riemann-hypothesis.md>), [software](<https://devfeed.tech/tags/software.md>), [software-engineering](<https://devfeed.tech/tags/software-engineering.md>), [sorting](<https://devfeed.tech/tags/sorting.md>), [superabundant-numbers](<https://devfeed.tech/tags/superabundant-numbers.md>)

### 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](<https://devfeed.tech/articles/searching-for-rh-counterexamples-search-strategies-40439.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2020/09/28/searching-for-rh-counterexamples-search-strategies/>)

Published: 2020-09-28T20:48:00Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Software Engineering](<https://devfeed.tech/topics/software-engineering.md>), [Algorithm](<https://devfeed.tech/topics/algorithm.md>), [Code](<https://devfeed.tech/topics/code.md>), [implementation](<https://devfeed.tech/topics/implementation.md>), [Testing](<https://devfeed.tech/topics/testing.md>)

Tags: [code](<https://devfeed.tech/tags/code.md>), [engineering](<https://devfeed.tech/tags/engineering.md>), [git](<https://devfeed.tech/tags/git.md>), [implementation](<https://devfeed.tech/tags/implementation.md>), [interface](<https://devfeed.tech/tags/interface.md>), [riemann-hypothesis](<https://devfeed.tech/tags/riemann-hypothesis.md>), [software](<https://devfeed.tech/tags/software.md>), [software-engineering](<https://devfeed.tech/tags/software-engineering.md>), [superabundant-numbers](<https://devfeed.tech/tags/superabundant-numbers.md>), [testing](<https://devfeed.tech/tags/testing.md>)

### 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$,