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Mathematicians Hunting Prime Numbers Discover Infinite New Pattern

For centuries, prime numbers have captured the imaginations of mathematicians, who continue to search for new patterns that help identify them and the way they’re distributed among other numbers. Primes are whole numbers that are greater than 1 and are divisible by only 1 and themselves. The three smallest prime numbers are 2, 3 and 5. It's easy to find out if small numbers are prime—one simply needs to check what numbers can factor them. When mathematicians consider large numbers, however, the

Samsung Embeds IronSource Spyware App on Phones Across WANA

In recent months, we have received numerous reports from users across West Asia and North Africa (WANA) expressing alarm over a little-known but deeply intrusive bloatware application—AppCloud—pre-installed on Samsung’s A and M series smartphones. Without users’ knowledge or consent, this bloatware collects sensitive personal data, cannot be removed without compromising device security, and offers no clear information about its privacy practices. AppCloud, developed by the controversial Israeli

Yaber T2 Outdoor Projector drops to new record-low price!

Kaitlyn Cimino / Android Authority Are you looking for a good portable projector that won’t break the bank? The Yaber T2 Outdoor Projector is my personal pick. The $349.99 retail price is very reasonable, but discounts are common, and today’s is the best we’ve seen. It’s at a record low price of $233.99! Buy the Yaber T2 Outdoor Projector for just $233.99 ($116 off) This offer is available from Amazon and is a “limited time deal.” Like, very limited. This offer has a timer on it, and according

Proba-3's first artificial solar eclipse

Enabling & Support Proba-3’s first artificial solar eclipse 16/06/2025 24672 views 108 likes Today, the European Space Agency’s Proba-3 mission unveils its first images of the Sun’s outer atmosphere – the solar corona. The mission’s two satellites, able to fly as a single spacecraft thanks to a suite of onboard positioning technologies, have succeeded in creating their first ‘artificial total solar eclipse’ in orbit. The resulting coronal images demonstrate the potential of formation flying tec

Verified dynamic programming with Σ-types in Lean

1. Introduction If you’ve taken an algorithms class, you have likely seen dynamic programming, specifically a technique called memoization. Memoization works to optimize recursive algorithms by caching the solutions to subproblems in a table, and when a subproblem is encountered, it queries the table instead of recomputing the solution. This gives us an exponential performance boost. This blog post will show how to solve a dynamic programming problem using memoization in Lean, and verify its c

Libraries are under-used. LLMs make this problem worse

Libraries are under-used. LLMs make this problem worse. Libraries are under-used. Why? Briefly: Writing code is more fun than reading documentation. Dunning-Kruger effect leads us to understimate the complexity of the problem solved by the library we're considering. Perverse incentives: libraries compete with big internal engineering projects that look good in a promo packet. LLMs make this problem worse. Why? Less briefly: Vibe coding is more fun than reading documentation. Shit, vibe-codin

Apple’s tiny M4 Mac Mini has dropped to its lowest price yet

If you’ve been curious about trying out a Mac for the first time or need a small computer powerful enough to be your home media server, we strongly recommend the latest Mac Mini. Thankfully, the step-up M4 model with 512GB of storage and 16GB of RAM is on sale at Amazon and B&H Photo for $689 ($110 off), which marks its lowest price ever. The entry-level model with 256GB of storage is also on sale at Amazon and B&H Photo for $469 ($130 off) — another all-time low. Former Verge staffer Chris Wel

Verified Dynamic Programming with Σ-types in Lean

1. Introduction If you’ve taken an algorithms class, you have likely seen dynamic programming, specifically a technique called memoization. Memoization works to optimize recursive algorithms by caching the solutions to subproblems in a table, and when a subproblem is encountered, it queries the table instead of recomputing the solution. This gives us an exponential performance boost. This blog post will show how to solve a dynamic programming problem using memoization in Lean, and verify its c

New dating for White Sands footprints confirms controversial theory

The 2009 discovery of footprints (human and animal) left behind in layers of clay and silt at New Mexico’s White Sands National Park sparked a contentious debate about when, exactly, human cultures first developed in North America. Until about a decade ago, it seemed as if the first Americans arrived near the end of the last Ice Age and were part of the Clovis culture, named for the distinctive projectile points they left behind near what’s now Clovis, New Mexico. But various dating methods indi

Chinese Studio Wants to Bring Back Bruce Lee With AI

If you’re a film lover, one of the great things about old classics is that you can always find something to appreciate when you revisit them. If you’re a studio executive, one of the great things about old classics is that you own them and can milk them for every penny their worth. At the Shanghai International Film Festival, several Chinese movie studios announced on Thursday that they would be taking their archive of martial arts classics and AI-ifying them. The government-backed “Kung Fu Mov

Best Internet Providers in Chicago, Illinois

What is the best internet provider in Chicago? CNET’s top recommendation for most households in Chicago is AT&T Fiber due to its ultra-fast symmetrical speeds, straightforward pricing and solid availability. If AT&T Fiber isn’t available in your neighborhood, Xfinity, Verizon 5G Home Internet and Rise Broadband are reliable alternatives. The best internet provider for your home depends on your budget and speed needs. To help you decide, our broadband experts reviewed the top options and found

Leaker doubles down on two key display changes for the iPhone 18 Pro

If you were hoping Apple’s iPhone 18 Pro models would shake up their physical screen sizes, you can extra-officially temper your expectations. But that doesn’t mean the 2026 lineup won’t bring significant shifts in how the front of the iPhone looks. Here’s what may be coming. A new leak from Digital Chat Station on Weibo today says the iPhone 18 Pro and iPhone 18 Pro Max will stick with the same display sizes as the current iPhone 16 Pro series: roughly 6.3 inches and 6.9 inches, respectively.

Why ether ETF inflows have come roaring back from the dead

In this article ETH.CM= Follow your favorite stocks CREATE FREE ACCOUNT Omar Marques | Lightrocket | Getty Images Ether ETFs have finally come to life this year after some started to fear they may be becoming zombie funds. Collectively, the funds tracking the price of spot ether are on pace for their sixth consecutive week of inflows and eight positive week in the last nine, according to SoSoValue. The second largest cryptocurrency has become more attractive to institutions in recent weeks lar

You Can Snag a $200 Amazon Instant Gift Card. Here's How

Zooey Liao/CNET The Prime Visa is easily the best credit card for shopping on Amazon with its high rewards rate and instant Amazon gift card offer. Ahead of the four-day Prime Day event on July 8-11, this card just upped its welcome offer from $150 to $200. It's rare for a credit card to offer a welcome bonus that you don't have to "earn" by spending a certain amount with the card. And while the Prime Visa technically has no annual fee, to get approved for this card, you'll need to be a Prime

Apple’s tiny M4 Mac mini has dropped to its lowest price yet

If you’ve been curious about trying out a Mac for the first time or need a small computer powerful enough to be your home media server, we strongly recommend the latest Mac Mini. Thankfully, the step-up M4 model with 512GB of storage and 16GB of RAM is on sale at Amazon and B&H Photo for $689 ($110 off), which marks its lowest price ever. The entry-level model with 256GB of storage is also on sale at Amazon and B&H Photo for $469 ($130 off) — another all-time low. Former Verge staffer Chris Wel

When will Apple release new AirPods? Here’s what we know

Apple is working on a major revision to AirPods Pro, which could be released as soon as this year. Plus, new AirPods Max are also in the pipeline. Here’s everything we know about when to expect Apple to release new AirPods… Apple’s current AirPods lineup Here is Apple’s AirPods lineup as it stands today: AirPods Pro 3 AirPods Pro 3 are perhaps the most highly anticipated update to the lineup. AirPods Pro 2 were introduced in September 2022 and have undergone significant improvements since th

Topics: airpods apple max new pro

Why I recommend this budget Android phone to most people over Samsung and Google

ZDNET's key takeaways The Nothing Phone 3a Pro offers exceptional value at its $459 sale price. An improved design, camera stack, and charging speed round out this year's upgrades. The lack of wireless charging and IP rating is easy to shoulder, but not the lack of retail presence. View now at Nothing View now at Amazon View now at Walmart more buying choices There's no greater reality check for a tech journalist than when you're at a family gathering, set your phone on the dining table, and

Topics: 3a camera phone pro zdnet

A Python-first data lakehouse

“Good design is actually a lot harder to notice than poor design, in part because good designs fit our needs so well that the design is invisible”. Donald A. Norman, The Design of Everyday Things. Data and ML scientists - A life in the middle Despite AI eating the world and data becoming one of the most important things for every company on the planet, but getting models from prototype to production is still pretty problematic. According to HBR , fewer than 1 in 5 models ever make it into prod

Amazon Offers This i7-Powered Mini PC for Less Than Its Black Friday Price to Clear Out Stock

Sometimes hunting for a great deal on a desktop PC requires beating the weeds a little bit and looking past the giant names that dominate the top of the big-box ads. There’s nothing wrong with sticking to Dell, HP, and Lenovo, but often the real deals are happening outside those brands. Take GMKtec, for instance — the name might not ring a bell, but they’re one of the world’s top mini PC brands, and they’re known for offering incredible deals. See at Amazon Here’s one of the better ones, which

Deals: 48GB M4 Pro MacBook Pro $400 off, M4 Mac mini $150 off, 25W MagSafe charger, AirPods, more

Alongside an ongoing all-time low on the base model M4 Mac mini at $469 and a $150 price drop on the 24GB model, we are also now tracking the mid-range 512GB variant down at the $689 Amazon low. Over to the M4 Pro MacBook Pro lineup, we have this upgraded 48GB 14-inch model at $400 off the list price alongside ongoing deals on AirPods Pro 2, the Apple 25W MagSafe charger at $30, and Journey debuted its new leather VERSA MagSafe Money Clip Wallet with Apple Find My at 20% off. All of that and mor

Klong: A Simple Array Language

Klong A Simple Array Language The Klong Book Documentation | Download Klong is an array language, like K, but without the ambiguity. If you know K or APL, you may be disappointed by Klong. If you don't know any array languages, it might explode your brain. Use at your own risk! Programming in Klong A Klong program is a set of functions that use various pre-defined operators to manipulate lists (vectors) and (multi-dimensional) arrays. Here is a program that checks whether a number x is pri

How to find the best deals during Amazon’s four-day Prime Day sale

Amazon Prime Day is one of the biggest shopping events of the year outside of Black Friday and Cyber Monday, and in 2025 it’s even longer than usual. It’s running from July 8th through the 11th. The four-day shopping affair will grant Prime members access to some of the best prices of the year on Amazon devices, as well as products from Sony, Sonos, Microsoft, Apple, Withings, and other well-known brands. This applies to items spanning a range of categories, including gaming peripherals, laptops

SoftBank reportedly looking to launch a trillion-dollar AI and robotics industrial complex

In Brief SoftBank is going all in on AI. Just months after announcing its involvement in the $500 billion Stargate AI Infrastructure project, of which SoftBank is rumored to be fronting a cool $19 billion, the Japanese investing conglomerate is reportedly looking to launch its largest AI project yet. The company is looking to team up with Taiwan Semiconductor Manufacturing Company (TSMC) to launch a trillion-dollar industrial complex in Arizona to build AI and robotics, according to reporting

Can users reset their own passwords without sacrificing security?

Like it or not, passwords aren’t going away anytime soon. While many organizations are exploring passwordless authentication, passwords still serve as the main line of defense for most public-facing online services. That said, they come with a heavy management burden. Gartner estimates that 40% of all service desk calls are tied to password issues like expirations, changes, and resets. Some of these issues (like forgotten passwords, routine expirations, or security-driven updates) are unavoidab

Best Internet Providers in Rochester, New York

What is the best internet provider in Rochester? CNET's experts recommend Spectrum as the best internet provider in Rochester for most households. Spectrum has a lot to offer, including extensive coverage in the area, affordable starting prices and lightning-fast speeds. However, you can expect a significant price hike after the first two years. Spectrum maxes out at a respectable 1,000Mbps, but if you're looking for multi-gig speeds, Greenlight is worth checking out. Greenlight's speeds go up

What Big Tech's Band of Execs Will Do in the Army

When I read a tweet about four noted Silicon Valley executives being inducted into a special detachment of the United States Army Reserve, including Meta CTO Andrew “Boz” Bosworth, I questioned its veracity. It’s very hard to discern truth from satire in 2025, in part because of social media sites owned by Bosworth’s company. But it indeed was true. According to an official press release, they’re in the Army now, specifically Detachment 201: the Executive Innovation Corps. Boz is now lieutenant

3 more days to fuel your next big move — and save up to $210 on your TechCrunch All Stage pass

The countdown is on — you have just 3 days left to save on your pass to TechCrunch All Stage, happening July 15 in Boston’s SoWa Power Station. After Sunday, June 22 at 11:59 p.m. PT, prices go up, and this opportunity to lock in savings disappears. If you’re a founder looking to scale, a VC hunting for breakout talent, or an operator ready to level up, this one-day founder summit is built to move you forward — with tactical insights, candid conversations, and high-impact networking from start

Apple's Mac mini M4 drops to a new record-low price

Engadget has been testing and reviewing consumer tech since 2004. Our stories may include affiliate links; if you buy something through a link, we may earn a commission. Read more about how we evaluate products . A new computer is a big purchase, no matter how you slice it. But if you can get your next machine at a discount, all the better. Those looking for a new desktop have a solid deal to consider right now on Apple's M4 Mac mini, which is down to a record-low price of $469. That price wil

Topics: 16gb day deals prime ram

This 50-Inch 4K Smart TV With Alexa Included Is 40% Off, No Need to Wait for Prime Day

Insignia is a Best Buy-owned brand accessible to everyone on Amazon and it has established a reputation for offering quality at a price that’s unexcelled. Produced by well-known manufacturers like LG, Toshiba, or TCL, these TVs deliver good performance and value. If you’re looking for a dependable TV to refurnish a guest room or as an economy choice, there’s a 50-inch model currently on sale that’s a great option. This Insignia 50-inch Class F50 Series LED 4K UHD Smart Fire TV now costs only $1

Cloudflare CEO says people aren't checking AI chatbots' source links

Companies that develop generative AI always make it a point to say that they include links to websites in the answers that their chatbots generate for users. But Cloudflare CEO Matthew Prince has revealed to Axios that search traffic referrals keep plummeting. Publishers are facing an existential threat, he said, because people aren't clicking through those chatbot links and are relying more and more on AI summaries without digging deeper. Prince told Axios that 10 years ago, Google sent a publ