# number Published articles for number. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## How big are factorials? DevFeed: [How big are factorials?]() Original publisher: [Read original article]() Author: Eli Bendersky Published: 2026-08-28T01:52:00Z Content type: tutorial Language: en Sources: [Eli Bendersky]() Topics: [math](), [function]() Tags: [function](), [gamma](), [math](), [misc](), [number]() ### AI overview This tutorial explains how to estimate the number of digits in factorials, using 52! as an example. It introduces the Gamma function and outlines Stirling's approximation and its derivation using Laplace's method. ### Source excerpt The other day, I found myself wondering how big 52! (52 factorial) is, and that led me to ponder how these could be estimated without a calculator or a computer. It turns out there's some fairly interesting math behind being able to estimate the size (number of digits) of ... ## Five Minutes of Prime Time DevFeed: [Five Minutes of Prime Time]() Original publisher: [Read original article]() Published: 2026-05-16T00:00:00Z Content type: opinion Language: en Sources: [Susam Pal]() Topics: [Mathematics]() Tags: [games](), [mathematics](), [mobile](), [number](), [puzzles](), [rsa]() ### AI overview A personal story about nerd culture at RSA, including mathematics and physics forums, monthly team challenges, and a five-minute contest to write as many prime numbers between 1 and 1000 as possible. ### Source excerpt Let me share a very silly story from roughly 18 years ago! In 2008, I joined RSA, the network security company named after the initials of the inventors of the RSA algorithm, Rivest, Shamir and Adleman, who were also the founders of RSA, the company. There was a bit of a nerd culture in the workplace where topics like prime numbers, combinatorics, probability theory, etc. were discussed fervently. A prime-number employee number was considered a lucky charm. I had a rather nice large five-digit prime number as my employee number, which I remember being quite pleased about. There were internal forums for almost all kinds of topics. A few I remember fondly were a mathematics forum where colleagues would challenge each other with mathematical puzzles and a similar physics forum where, for some reason, crafting contrived paradoxes using special and general relativity and putting them up for debate was a common activity. The participants would analyse each paradox to determine if it truly was one or if it could be resolved into something that was no longer a paradox. I loved hanging out on those forums and made many friends there. The mathematics forum, in particular, gave me plenty of fun problems to think about. In fact, my Langford Pairing (2011) post was the result of a question I had stumbled upon there. The human resources (HR) department used to organise afternoon games once every month where people would self-organise into teams and solve a small challenge. There was a cash prize for the winning team each time. The HR folks were very well aware of the nerd culture and the fascination with prime numbers, but they probably did not know enough about exactly what type of problems we were fascinated with. So in one of the monthly game events, the HR team gave us this challenge. Write as many prime numbers between 1 and 1000 as you can in 5 minutes. The 5-minute timer started immediately. Really, that was the challenge. We all looked at each other in surprise, wondering ## Powershell Users Like To Vomit DevFeed: [Powershell Users Like To Vomit]() Original publisher: [Read original article]() Published: 2025-01-05T00:00:00Z Content type: opinion Language: en Sources: [Tim Kellogg]() Topics: [PowerShell](), [data](), [Bash](), [Bluesky]() Tags: [bash](), [bias](), [data](), [number](), [powershell](), [quotes](), [social-media]() ### AI overview This satirical commentary examines how a small, biased Bluesky poll can produce misleading conclusions about PowerShell and Bash users. It argues that data should be questioned, especially when samples are non-random and quotes are taken out of context. ### Source excerpt In a stunning new study, PowerShell users insist that they like to vomit. How can this be? It's all about the data, and why you absolutely should question the data. ## TLD Domain Count Stats DevFeed: [TLD Domain Count Stats]() Original publisher: [Read original article]() Published: 2023-08-11T22:05:34Z Content type: article Language: en Sources: [Signs of Triviality]() Topics: [domain]() Tags: [domain](), [number]() ### AI overview The article presents counts of domain names grouped by top-level domain (TLD). ### Source excerpt I got tired of not finding a good source of domain name stats, so I put together counts of all TLDs by number of domain names in them myself. ## Basic values in Kotlin DevFeed: [Basic values in Kotlin]() Original publisher: [Read original article]() Published: 2023-02-27T00:01:00Z Content type: tutorial Language: en Sources: [Kt. Academy]() Topics: [Kotlin](), [Compiler]() Tags: [compiler](), [floating-point](), [format](), [kotlin](), [literals](), [number](), [operations](), [precision](), [readability](), [types](), [values](), [workshop-learning-programming]() ### AI overview This tutorial introduces Kotlin's basic value types and literals, including numbers, booleans, characters, strings, and arrays. It explains Kotlin's object model, compiler optimization of some types, numeric ranges and precision, explicit type conversions, and underscore formatting in number literals. ### Source excerpt Learn about the basic Kotlin values, types and operations. ## Operator overloading in Kotlin DevFeed: [Operator overloading in Kotlin]() Original publisher: [Read original article]() Published: 2023-01-23T00:01:00Z Content type: tutorial Language: en Sources: [Kt. Academy]() Topics: [Kotlin](), [Code](), [class](), [function](), [Compiler](), [Math and Logic]() Tags: [arithmetic](), [class](), [code](), [compiler](), [complex-numbers](), [engineering](), [extension-function](), [function](), [kotlin](), [number](), [numbers](), [operations](), [operator-overloading](), [physics](), [type](), [types](), [workshop-learning-programming]() ### AI overview A tutorial on Kotlin operator overloading. It explains Kotlin's predefined operators, how operator methods are declared for custom classes, and how arithmetic and range operators are handled, using complex numbers as an example. ### Source excerpt How are operators defined for types in Kotlin, and how can we define our own operators. ## A random number you already have: The stack address DevFeed: [A random number you already have: The stack address]() Original publisher: [Read original article]() Author: Graham King Published: 2022-06-05T23:19:39Z Content type: article Language: en Sources: [Graham King]() Topics: [Linux](), [Rust](), [Python](), [macOS](), [Security](), [Go]() Tags: [go](), [linux](), [macos](), [number](), [performance](), [python](), [random](), [rust](), [security](), [software](), [stack]() ### AI overview This article explains how Address Space Layout Randomization can make a stack variable's memory address serve as a low-cost source of random bits. It describes address-bit handling in Rust and CPython, notes that the approach does not work the same way in Go, and connects the technique to hash-table randomization and denial-of-service resistance. ### Source excerpt Thanks to Address Space Layout Randomization you can use the address of a stack variable as a zero-cost random number. ## Creating Optimized Images in Craft CMS DevFeed: [Creating Optimized Images in Craft CMS]() Original publisher: [Read original article]() Author: andrew@nystudio107.com (Andrew Welch) Published: 2016-12-01T09:13:00Z Content type: tutorial Language: en Sources: [nystudio107 | Articles on modern web development.]() Topics: [Content Management System](), [Website](), [User Experience](), [Mobile]() Tags: [cloudinary](), [cms](), [craft](), [create](), [here-s](), [images](), [insights](), [number](), [optimize](), [optimized](), [performance](), [speedy](), [thing](), [website]() ### AI overview This tutorial explains how to optimize client-uploaded images in Craft CMS to improve website performance across desktop and mobile devices. It also recommends Cloudinary's Image Analysis Tool for estimating image sizes and potential savings. ### Source excerpt The number one thing you can do to create a speedy website is to optimize the images. Here's how to do it in Craft CMS ## Weak Learning, Boosting, and the AdaBoost algorithm DevFeed: [Weak Learning, Boosting, and the AdaBoost algorithm]() Original publisher: [Read original article]() Published: 2015-05-18T09:00:00Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Algorithm](), [Learning]() Tags: [algorithm](), [better](), [boosting](), [classification](), [distribution](), [efficiently](), [function](), [learner](), [learning](), [models](), [number](), [pac-learning](), [re](), [runtime]() ### AI overview This article introduces learning models in the context of Probably Approximately Correct (PAC) learning and compares the usual PAC model with weak PAC learning. It explains that weak learning requires accuracy only slightly better than random guessing and states that weak and strong learning are equivalent. ### Source excerpt When addressing the question of what it means for an algorithm to learn, one can imagine many different models, and there are quite a few. This invariably raises the question of which models are "the same" and which are "different," along with a precise description of how we're comparing models. We've seen one learning model so far, called Probably Approximately Correct (PAC), which espouses the following answer to the learning question: ## There are Infinitely Many Primes (Erdős) DevFeed: [There are Infinitely Many Primes (Erdős)]() Original publisher: [Read original article]() Published: 2012-11-10T13:48:52Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [primes]() Tags: [limits](), [lower-bounds](), [number](), [primes](), [product](), [square]() ### AI overview A proof by Paul Erdős establishes that infinitely many primes exist by bounding the number of factorizations of integers as a square-free number times a square. This yields π(n) >= 1/2 log(n), which grows without bound. ### Source excerpt Problem: Prove there are infinitely many primes Solution: Denote by $ \pi(n)$ the number of primes less than or equal to $ n$. We will give a lower bound on $ \pi(n)$ which increases without bound as $ n \to \infty$. Note that every number $ n$ can be factored as the product of a square free number $ r$ (a number which no square divides) and a square $ s^2$. ## New Developer Contract DevFeed: [New Developer Contract]() Original publisher: [Read original article]() Published: 2012-09-07T00:00:00Z Content type: release Language: en Sources: [Front Page on ReactOS Website]() Topics: [ReactOS](), [win32](), [Development]() Tags: [added](), [announce](), [bugs](), [developer](), [development](), [features](), [free](), [instead](), [new-features](), [number](), [open-source](), [os](), [period](), [project](), [react](), [reactos](), [reduce](), [summary](), [time](), [win32](), [winapi]() ### AI overview The ReactOS Project announced a one-month development contract with James Tabor focused on fixing longstanding bugs in the Win32 subsystem. The contract covers 120 hours and is intended to address an initial list of bugs, with additional bugs added if time permits. ### Source excerpt The ReactOS Project is pleased to announce a new development contract with James Tabor, a long time ReactOS developer that has worked extensively on the Win32 subsystem. Jim intends to tackle many of the longstanding bugs and hopefully significantly reduce the number of outstanding issues in the Win32 subsystem. This particular contract will have a heavy emphasis on bugfixing instead of attempting to introduce new features. Time: 120 hours ## Number Theory--A Primer DevFeed: [Number Theory--A Primer]() Original publisher: [Read original article]() Published: 2011-07-30T15:03:38Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [primes](), [Cryptography](), [Encryption]() Tags: [arithmetic](), [encryption](), [factoring](), [gcd](), [mathematics](), [number](), [number-theory](), [primer](), [primes](), [programming](), [rsa]() ### AI overview A primer on elementary number theory covering integers, divisibility, composite and prime numbers, prime factorization, and the greatest common divisor. It provides background for a separate post on RSA encryption. ### Source excerpt This primer exists for the background necessary to read our post on RSA encryption, but it also serves as a general primer to number theory. Oh, Numbers, Numbers, Numbers We start with some easy definitions. Definition: The set of integers, denoted $ \mathbb{Z}$, is the set $ \left \{ \dots -2, -1, 0, 1, 2, \dots \right \}$. Definition: Let $ a,b$ be integers, then $ a$ divides $ b$, denoted $ a \mid b$, if there exists an integer $ n$ such that $ na = b$. ## Number of Games in a Tournament DevFeed: [Number of Games in a Tournament]() Original publisher: [Read original article]() Published: 2011-06-23T16:04:47Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Math and Logic]() Tags: [logic](), [mathematics](), [number]() ### AI overview A tournament with 1,000 players requires 999 games. The article proves the general result that a single-elimination tournament with n players has n−1 games by pairing each game with the player who loses it. ### Source excerpt Problem: 1000 players compete in a tournament. In each round, players are matched with opponents, and the winner proceeds to the next round. If there are an odd number of players in a round, one player chosen at random sits out of that round. What is the total number of games are played in the tournament? Solution: 999. Each player loses exactly one game, except for the winner of the tournament. ## The Odds of Finding a Set in The Card Game SET DevFeed: [The Odds of Finding a Set in The Card Game SET]() Original publisher: [Read original article]() Published: 2010-04-28T00:00:00Z Content type: article Language: en Sources: [Peter Norvig]() Topics: [math](), [Simulation]() Tags: [card](), [color](), [game](), [number](), [results](), [set](), [simulation]() ### AI overview An analysis of why the odds of finding no SET in the card game SET change during play. A simulation shows that the chances differ substantially between a freshly dealt layout and layouts reached after SETs are repeatedly removed and replaced, suggesting the instruction booklet's odds do not describe the course of an actual game. ### Source excerpt Correcting an error in the instruction booklet for the card game SET