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Prime numbers, the building blocks of mathematics, have fascinated for centuries − now technology is revolutionizing the search for them

Prime numbers, essential in mathematics and history, have been studied since ancient times. They are defined as whole numbers greater than one with only two divisors: one and themselves.

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Last Updated on August 31, 2025 by Daily News Staff

file 20250520 56 lrfedu.png?ixlib=rb 4.1

Prime numbers are numbers that are not products of smaller whole numbers.
Jeremiah Bartz

Jeremiah Bartz, University of North Dakota

A shard of smooth bone etched with irregular marks dating back 20,000 years puzzled archaeologists until they noticed something unique – the etchings, lines like tally marks, may have represented prime numbers. Similarly, a clay tablet from 1800 B.C.E. inscribed with Babylonian numbers describes a number system built on prime numbers.

As the Ishango bone, the Plimpton 322 tablet and other artifacts throughout history display, prime numbers have fascinated and captivated people throughout history. Today, prime numbers and their properties are studied in number theory, a branch of mathematics and active area of research today.

A history of prime numbers

A long, thin shard of bone with small lines scratched into it.
Some scientists guess that the markings on the Ishango bone represent prime numbers.
Joeykentin/Wikimedia Commons, CC BY-SA

Informally, a positive counting number larger than one is prime if that number of dots can be arranged only into a rectangular array with one column or one row. For example, 11 is a prime number since 11 dots form only rectangular arrays of sizes 1 by 11 and 11 by 1. Conversely, 12 is not prime since you can use 12 dots to make an array of 3 by 4 dots, with multiple rows and multiple columns. Math textbooks define a prime number as a whole number greater than one whose only positive divisors are only 1 and itself.

Math historian Peter S. Rudman suggests that Greek mathematicians were likely the first to understand the concept of prime numbers, around 500 B.C.E.

Around 300 B.C.E., the Greek mathematician and logician Euclid proved that there are infinitely many prime numbers. Euclid began by assuming that there is a finite number of primes. Then he came up with a prime that was not on the original list to create a contradiction. Since a fundamental principle of mathematics is being logically consistent with no contradictions, Euclid then concluded that his original assumption must be false. So, there are infinitely many primes.

The argument established the existence of infinitely many primes, however it was not particularly constructive. Euclid had no efficient method to list all the primes in an ascending list.

a diagram showing prime numbers as dots in rows, with composite numbers as dots arranged in rectangles of at least two rows of dots, with the same number of dots in each row.
Prime numbers, when expressed as that number of dots, can be arranged only in a single row or column, rather than a square or rectangle.
David Eppstein/Wikimedia Commons

In the middle ages, Arab mathematicians advanced the Greeks’ theory of prime numbers, referred to as hasam numbers during this time. The Persian mathematician Kamal al-Din al-Farisi formulated the fundamental theorem of arithmetic, which states that any positive integer larger than one can be expressed uniquely as a product of primes.

From this view, prime numbers are the basic building blocks for constructing any positive whole number using multiplication – akin to atoms combining to make molecules in chemistry.

Prime numbers can be sorted into different types. In 1202, Leonardo Fibonacci introduced in his book “Liber Abaci: Book of Calculation” prime numbers of the form (2p – 1) where p is also prime.

Today, primes in this form are called Mersenne primes after the French monk Marin Mersenne. Many of the largest known primes follow this format.

Several early mathematicians believed that a number of the form (2p – 1) is prime whenever p is prime. But in 1536, mathematician Hudalricus Regius noticed that 11 is prime but not (211 – 1), which equals 2047. The number 2047 can be expressed as 23 times 89, disproving the conjecture.

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While not always true, number theorists realized that the (2p – 1) shortcut often produces primes and gives a systematic way to search for large primes.

The search for large primes

The number (2p – 1) is much larger relative to the value of p and provides opportunities to identify large primes.

When the number (2p – 1) becomes sufficiently large, it is much harder to check whether (2p – 1) is prime – that is, if (2p – 1) dots can be arranged only into a rectangular array with one column or one row.

Fortunately, Édouard Lucas developed a prime number test in 1878, later proved by Derrick Henry Lehmer in 1930. Their work resulted in an efficient algorithm for evaluating potential Mersenne primes. Using this algorithm with hand computations on paper, Lucas showed in 1876 that the 39-digit number (2127 – 1) equals 170,141,183,460,469,231,731,687,303,715,884,105,727, and that value is prime.

Also known as M127, this number remains the largest prime verified by hand computations. It held the record for largest known prime for 75 years.

Researchers began using computers in the 1950s, and the pace of discovering new large primes increased. In 1952, Raphael M. Robinson identified five new Mersenne primes using a Standard Western Automatic Computer to carry out the Lucas-Lehmer prime number tests.

As computers improved, the list of Mersenne primes grew, especially with the Cray supercomputer’s arrival in 1964. Although there are infinitely many primes, researchers are unsure how many fit the type (2p – 1) and are Mersenne primes.

By the early 1980s, researchers had accumulated enough data to confidently believe that infinitely many Mersenne primes exist. They could even guess how often these prime numbers appear, on average. Mathematicians have not found proof so far, but new data continues to support these guesses.

George Woltman, a computer scientist, founded the Great Internet Mersenne Prime Search, or GIMPS, in 1996. Through this collaborative program, anyone can download freely available software from the GIMPS website to search for Mersenne prime numbers on their personal computers. The website contains specific instructions on how to participate.

GIMPS has now identified 18 Mersenne primes, primarily on personal computers using Intel chips. The program averages a new discovery about every one to two years.

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The largest known prime

Luke Durant, a retired programmer, discovered the current record for the largest known prime, (2136,279,841 – 1), in October 2024.

Referred to as M136279841, this 41,024,320-digit number was the 52nd Mersenne prime identified and was found by running GIMPS on a publicly available cloud-based computing network.

This network used Nvidia chips and ran across 17 countries and 24 data centers. These advanced chips provide faster computing by handling thousands of calculations simultaneously. The result is shorter run times for algorithms such as prime number testing.

A small rectangle metal chip reading 'nVIDIA'
New and increasingly powerful computer chips have allowed prime-number hunters to find increasingly larger primes.
Fritzchens Fritz/Flickr

The Electronic Frontier Foundation is a civil liberty group that offers cash prizes for identifying large primes. It awarded prizes in 2000 and 2009 for the first verified 1 million-digit and 10 million-digit prime numbers.

Large prime number enthusiasts’ next two challenges are to identify the first 100 million-digit and 1 billion-digit primes. EFF prizes of US$150,000 and $250,000, respectively, await the first successful individual or group.

Eight of the 10 largest known prime numbers are Mersenne primes, so GIMPS and cloud computing are poised to play a prominent role in the search for record-breaking large prime numbers.

Large prime numbers have a vital role in many encryption methods in cybersecurity, so every internet user stands to benefit from the search for large prime numbers. These searches help keep digital communications and sensitive information safe.

This story was updated on May 30, 2025 to correct the name of the Greek mathematician Euclid and to correct the factors of 2047.The Conversation

Jeremiah Bartz, Associate Professor of Mathematics, University of North Dakota

This article is republished from The Conversation under a Creative Commons license. Read the original article.

https://stmdailynews.com/groundbreaking-for-a-sustainable-future-la-metros-southeast-gateway-line-light-rail-project/

https://stmdailynews.com/groundbreaking-for-a-sustainable-future-la-metros-southeast-gateway-line-light-rail-project/

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When your local reflecting pool or pond turns green with algae, don’t reach for chemicals – nature has better solutions

When ponds and reflecting pools turn green with algae, chemical “quick fixes” often fail. Here’s how nature-based solutions like Daphnia and aquatic plants can restore water quality longer-term.

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A man using an underwater vacuum stands knee-deep in the Reflecting Pool with the Washington Monument in the background.
A National Park Service employee uses a vacuum to clean the Lincoln Memorial Reflecting Pool on June 20, 2026. AP Photo/Mark Schiefelbein

Eric Palkovacs, University of California, Santa Cruz

When the Lincoln Memorial Reflecting Pool turned green with algae just days after a US$15 million renovation, the U.S. government scrambled for chemicals and expensive technical solutions to fix the iconic landmark.

Trying to kill algae with chemicals is a common response when community ponds or other water features go green. But as a scientist who studies freshwater ecology, I can tell you there are better solutions that cost far less, last longer and carry less risk of harm to pets and wildlife.

Rather than battling against nature, these alternatives work with nature for long-term solutions. https://www.youtube.com/embed/nkqBQ1r0Kto?wmode=transparent&start=0 If you need to treat a slimy, green, algae-filled body of water, you shouldn’t drain and refill the water, which resets the entire ecosystem. Instead, one solution is quite simple and relies on nature, not chemicals.

What went wrong on the National Mall

The algal bloom that turned the Reflecting Pool a vibrant green shouldn’t have been a surprise.

The pool is big, more than a third of a mile long and around 165 feet wide. But it’s shallow, meaning it warms up quickly in the sun. When it was repainted “American flag blue” during the renovations in spring 2026, the new color darkened the pool, and darker colors absorb more heat.

On top of those conditions, the pool was refilled with water from the nutrient-rich tidal basin of the Potomac River. The combination of warm water and nutrients created prime conditions for algae to bloom, turning the water pea soup green.

A tube into the Reflecting Pool, with the Jefferson Memorial in the background, puts out white bubbles.
In addition to hydrogen peroxide and vacuums, the government ordered nanobubble ozone technology to break up the algae. The nanobubbler contract was for $1.7 million. AP Photo/Jacquelyn Martin

As the national conversation over the Reflecting Pool shifts to political finger-pointing, an important environmental question deserves careful scrutiny: What is the best approach to maintain water quality in a case like this, whether for a national monument or a community water feature or pond?

Trying to chemically or mechanically remove algae can damage the structure of a water feature and may harm species in the water that could actually help solve the problem.

Importantly, chemical and mechanical solutions are only temporary fixes. When the Reflecting Pool is drained and filled again, there’s a good chance that algae will bloom again.

Natural algae control

Limnologists – scientists like me who study inland water bodies – have spent many decades learning why lakes and ponds turn green and how to clear them up.

Often, nutrient-rich waters fueled by fertilizer runoff from farm fields or sewage from cities are the sources that stimulate algal growth.

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However, natural ponds also host grazing zooplankton, which eat algae. For example, a type of zooplankton called Daphnia, known as water fleas because of the way these tiny crustaceans swim, can control algae by consuming it before it becomes a pea soup nuisance. Thus, a thriving Daphnia population can help maintain good water quality in a lake, pond or community water feature, even when nutrient levels spike.

A close-up image of a see-through water creature with eggs inside.
Daphnia are a genus of hundreds of species of tiny, see-through crustaceans that happen to be voracious algae eaters. A female Daphnia magna’s eggs are visible in this magnified image. Hajime Watanabe, PLoS Genetics, March 2011, CC BY

In addition to being highly effective grazers, Daphnia have another superpower – they can evolve rapidly. Urban waterbodies are often harsh environments with a variety of challenges, including high temperatures, low levels of dissolved oxygen, and pollutants. Daphnia can adapt to tough conditions, making these creatures an ideal source of algae control in many urban ponds.

Rooted aquatic plants are also useful for algae control in ponds because they absorb nutrients. Thus, shallow ponds with thick beds of aquatic plants can often resist algal blooms when nutrient levels rise.

Why draining might not be the best solution

One downside to draining and refilling a pond or urban water feature to try to clean it is that doing so resets the aquatic ecosystem, erasing the signature of any past evolution that has taken place.

Imagine Daphnia in a shallow pond that experiences periodic heat waves throughout the summer. Through repeated exposure to high temperatures, natural selection favors heat-resistant genotypes that can thrive in an urban pond.

Daphnia and other grazing zooplankton can also evolve resistance to some types of cyanobacteria, also known as blue-green algae, which produce compounds that are toxic to people and pets. Daphnia that evolve resistance to those toxins can help control harmful cyanobacterial blooms.

If a Daphnia population that evolved to tolerate warm temperatures, low oxygen levels or cyanotoxins is removed, the new population likely won’t be ready to handle those local challenges. This evolutionarily naive population will perform poorly in its new environment, reducing its effectiveness at controlling algal blooms.

As a result, traditional mechanical and chemical approaches may actually work against the goal of minimizing algae in ponds and other water features.

Nature-based solutions

The use of Daphnia to control algal blooms is just one example of solving environmental challenges with nature-based solutions.

Growing urban forests to provide cooling and improve air quality to help reduce the need for more energy-intensive air conditioning is another example. Maintaining urban wetlands can help reduce flooding, protect property and recharge groundwater more effectively and for less money than building and maintaining levees. Coastal marshes similarly reduce erosion, buffer storm surges and support fisheries.

All these urban ecosystems protect biodiversity and support human health and well-being.

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From national landmarks to city parks and backyard ponds, projects of all sizes can take advantage of nature-based solutions. While each specific project is unique, some general principles apply.

Ecosystems are most resilient when they are diverse and connected. So, it is beneficial to use a variety of species and genotypes and provide corridors that support the movement of organisms and their beneficial genes.

Urban climates are changing rapidly, so it helps to use species and genotypes that will thrive under future conditions, including rising temperatures.

Not every solution has to be engineered

The hubbub over the Reflecting Pool holds a mirror up to assumptions about how to solve pressing environmental challenges. The idea of just engineering one’s way out of any environmental crisis has limits.

Understanding ecology and nature’s mechanisms of ecosystem resilience can achieve sustainable solutions that benefit both nature and people.

Eric Palkovacs, Professor of Ecology and Evolutionary Biology, University of California, Santa Cruz

This article is republished from The Conversation under a Creative Commons license. Read the original article.

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Terminal Island: The Untold Story of Los Angeles Harbor’s Forgotten Community and Industrial Giant

Discover the remarkable history of Terminal Island in Los Angeles Harbor—from its thriving Japanese American fishing village to World War II shipbuilding and today’s global shipping hub.

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Terminal Island in the background, and Mormon Island in the foreground, sometime before 1942. Image Credit: U.S. National Archives and Records Administration
Terminal Island in the background, and Mormon Island in the foreground, sometime before 1942. Image Credit: U.S. National Archives and Records Administration

Whenever I think about Terminal Island, my mind immediately goes back to childhood trips with my parents to San Pedro’s Fisherman’s Wharf. Those visits were some of my favorite family outings. We’d walk along the waterfront while my parents picked up fresh crab, shrimp, fish, and occasionally shellfish. The smells of the ocean, the sound of fishing boats, and the towering presence of the Vincent Thomas Bridge left a lasting impression on me long before I understood the incredible history hidden just beyond the docks.

As a child, I simply saw ships, cranes, and bridges. It wasn’t until years later that I learned Terminal Island had once been home to one of Southern California’s most vibrant immigrant communities—and that much of it disappeared almost overnight during World War II.

Today, Terminal Island stands at the crossroads of history, commerce, and remembrance.

From Sandbar to Strategic Harbor

Terminal Island wasn’t always an island as we know it today. Originally a marshy stretch of land in San Pedro Bay, it was reshaped through decades of dredging and engineering projects that transformed Los Angeles Harbor into one of the world’s busiest ports.

As railroads arrived in the late 1800s, the island became a gateway for commerce. Warehouses, rail terminals, and docks expanded rapidly, laying the foundation for the economic powerhouse that would eventually emerge.

The Village That Built an Industry

In the early 1900s, Japanese immigrants established a thriving fishing village along Fish Harbor.

Families built homes, schools, churches, markets, and businesses while creating a close-knit community unlike any other in Southern California. Many residents came from Japan’s Wakayama Prefecture, bringing generations of fishing knowledge with them.

Their expertise helped build California’s tuna fishing industry into one of the largest in the nation. Long before canned tuna became a pantry staple across America, many of the fishermen of Terminal Island were helping shape the industry that made it possible.

The community even developed its own distinctive blend of Japanese and English known as “Terminal Island lingo,” reflecting the unique culture that flourished there.

A Community Lost

Everything changed after the attack on Pearl Harbor on December 7, 1941.

Within weeks, Terminal Island became the first Japanese American community in the United States to be forcibly removed.

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Residents were given little time to leave their homes.

Many men were arrested first under suspicion simply because of their ancestry. Families were separated. Businesses were abandoned. Eventually, nearly every house in the village was demolished.

For many residents, there was nothing to return to after the war.

Today, the story of Terminal Island serves as a powerful reminder of how fear and prejudice can overwhelm constitutional rights during times of national crisis.

Building Victory

As one community disappeared, another chapter began.

Terminal Island became one of America’s great wartime industrial centers.

Shipyards worked around the clock constructing destroyers, cargo ships, and support vessels for the Allied war effort. Thousands of workers—including many African Americans who had migrated west seeking defense jobs—helped build and repair ships that crossed the Pacific.

The island became a symbol of American industrial strength, contributing directly to victory during World War II.

The Bridge That Became an Icon

In 1963, the opening of the Vincent Thomas Bridge forever changed the harbor skyline.

The graceful green suspension bridge connected San Pedro with Terminal Island, replacing ferry service and improving access to the growing port.

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For many Southern Californians—including myself—the bridge became more than just a transportation link. It was a landmark that signaled you were entering one of the hardest-working waterfronts in America.

Every crossing offered sweeping views of ships arriving from around the world, reminding visitors that Los Angeles Harbor is one of the nation’s most important economic engines.

Terminal Island Today

Modern Terminal Island bears little resemblance to the fishing village that once stood there.

Today it is home to massive container terminals, rail yards, ship repair facilities, Coast Guard operations, federal facilities, and the Federal Correctional Institution. Together with the neighboring Port of Long Beach, the Port of Los Angeles moves millions of cargo containers every year, supporting jobs and businesses across the United States.

The island remains essential to global trade while quietly preserving memories of the people who first called it home.

Remembering the Whole Story

Terminal Island is more than an industrial center.

It represents the American dream of immigrants who built thriving businesses through hard work.

It reminds us of the injustice experienced by Japanese American families during World War II.

It showcases the extraordinary industrial effort that helped win a global conflict.

And it demonstrates how one small piece of land helped shape the economy of Southern California and the nation.

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The next time you cross the Vincent Thomas Bridge or see the towering cranes along the harbor, remember that beneath today’s shipping terminals lies a story of resilience, sacrifice, innovation, and hope.

Sometimes the most important history isn’t found in famous landmarks—it lives in the places we pass every day without realizing what came before.

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From Hand Signals to Smart Crosswalks: The Evolution of the Modern Pedestrian Signal

Discover the history of the modern pedestrian signal, from Garrett A. Morgan’s groundbreaking traffic signal to today’s smart, accessible crosswalks.

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Last Updated on July 12, 2026 by Daily News Staff

The Evolution of the Modern Pedestrian Signal

Every day, millions of people rely on pedestrian signals to cross busy street safely. A glowing white walking figure, an orange-red hand, and a countdown timer have become familiar sights around the world. While these signals may seem like simple pieces of infrastructure, they are the result of more than a century of innovation, engineering, and public safety improvements.

The modern pedestrian signal did not appear overnight. Instead, it evolved through the contributions of inventors, engineers, city planners, and transportation officials who continually refined traffic control systems as cities grew and automobiles became more common.

The Early Days of Traffic Control

Before electric traffic signals, intersections were controlled by police officers, railway-style semaphores, or even hand signals. As horse-drawn wagons gave way to automobiles in the early 1900s, traffic congestion and accidents increased dramatically, creating an urgent need for better traffic management.

One of the earliest electric traffic lights was installed in Cleveland, Ohio, in 1914. It used red and green lights and was manually operated. While it improved vehicle movement, pedestrians still had to judge for themselves when it was safe to cross.

How the Modern Pedestrian Signal Changed the Way We Cross Streets

Garrett A. Morgan’s Breakthrough

One of the most important milestones came in 1923 when inventor and entrepreneur Garrett Augustus Morgan received U.S. Patent No. 1,475,024 for an improved traffic signal.

Morgan’s design introduced a third position in addition to “Stop” and “Go.” This intermediate phase temporarily stopped traffic in every direction before allowing vehicles to proceed. The brief pause reduced confusion at intersections and provided additional time for pedestrians to cross safely.

Morgan reportedly developed his design after witnessing a serious traffic accident. His invention demonstrated how thoughtful engineering could improve public safety while making increasingly busy streets more efficient.

Although Morgan did not invent the illuminated “WALK” and “DON’T WALK” pedestrian signal used today, his three-position signal became a foundational step in the evolution of modern traffic control.

The Birth of Dedicated Pedestrian Signals

As cities expanded after World War II, pedestrian safety became an even greater concern. More people were walking in increasingly crowded downtown districts, and separating pedestrian movements from vehicle traffic became a priority.

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During the early 1950s, several American cities began experimenting with dedicated pedestrian signals. New York City became one of the first major municipalities to install illuminated “WALK” and “DON’T WALK” signs at busy intersections.

These early systems gave pedestrians their own designated crossing phase, reducing conflicts with turning vehicles and improving safety at some of the nation’s busiest intersections.

Standardization Across America

By the 1960s and 1970s, traffic engineers recognized the importance of creating consistent traffic control devices nationwide.

The Manual on Uniform Traffic Control Devices (MUTCD) established national standards for traffic signs, pavement markings, and pedestrian signals. Standardized designs helped ensure that pedestrians could understand crossing signals regardless of where they traveled in the United States.

Eventually, words gave way to internationally recognized symbols—a walking person to indicate it was safe to cross and an upraised hand to indicate pedestrians should wait. These symbols transcended language barriers and improved accessibility for visitors and non-English speakers.

The Countdown Era

One of the most significant modern improvements arrived with pedestrian countdown timers.

Rather than simply flashing a warning, countdown displays show exactly how many seconds remain before the crossing phase ends. Research has shown that countdown timers help pedestrians make better crossing decisions and improve compliance with traffic signals.

Today, countdown timers have become standard equipment at intersections across much of the United States.

Accessibility Takes Center Stage

Modern pedestrian signals are designed to serve everyone.

Accessible Pedestrian Signals (APS) now provide audible tones, spoken messages, vibrating push buttons, and locator sounds that assist pedestrians who are blind or have low vision. These features allow more people to navigate intersections independently and safely.

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The continued development of accessible technology reflects a broader commitment to making transportation systems inclusive for all users.

The Future of Pedestrian Safety

Pedestrian signals continue to evolve.

Many cities now use smart traffic systems that detect pedestrians waiting to cross, automatically adjust signal timing based on traffic conditions, and prioritize people walking during busy periods.

Researchers are exploring artificial intelligence, connected vehicle technology, and sensor-based systems capable of communicating directly with autonomous vehicles. Future pedestrian crossings may adapt in real time to weather conditions, crowd sizes, emergency vehicles, and even the needs of older adults or individuals with disabilities.

A Legacy Built by Many Innovators

The pedestrian signal we know today is the product of more than a century of collaboration and innovation.

Early traffic engineers created the first electric traffic lights. Garrett A. Morgan improved intersection safety with his groundbreaking three-position traffic signal. Transportation agencies standardized traffic control devices, while engineers continued refining pedestrian technology through countdown timers, accessible features, and intelligent traffic systems.

Every safe crossing today reflects the work of countless inventors, planners, researchers, and public officials dedicated to protecting lives.

As cities continue to grow and transportation technology advances, the humble pedestrian signal remains one of the most effective—and often overlooked—public safety innovations ever developed.

At STM Daily News, we celebrate the inventors, engineers, and visionaries whose everyday innovations quietly improve life for millions of people. Sometimes the most important inventions aren’t the ones that grab headlines—they’re the ones we depend on every single day without giving them a second thought.

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