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When you lose your health insurance, you may also lose your primary doctor – and that hurts your health

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theconversation.com – Jane Tavares, Senior Research Fellow and Lecturer of Gerontology, UMass Boston – 2025-06-17 07:36:00


Losing health insurance or switching to plans with limited preventive care disrupts the critical bond with primary care providers, leading to missed checkups, late diagnoses, worsening health, and higher medical expenses. Research shows that consistent care improves health, lowers costs, and ensures timely preventive services. Millions risk losing Medicaid coverage amid congressional budget debates, threatening these vital connections for low-income and disabled Americans. Uninsured individuals postpone care, leading to emergencies that raise costs across the health system. Medicaid acts as a health lifeline, enabling ongoing care and preventing crisis-driven treatment. Cutting funding could fracture care relationships, harming health outcomes and increasing system-wide costs.

Seeing the same doctor on a regular basis is good for your health.
Morsa Images/DigitalVision via Getty Images

Jane Tavares, UMass Boston and Marc Cohen, UMass Boston

When you lose your health insurance or switch to a plan that skimps on preventive care, something critical breaks.

The connection to your primary care provider, usually a doctor, gets severed. You stop getting routine checkups. Warning signs get missed. Medical problems that could have been caught early become emergencies. And because emergencies are both dangerous and expensive, your health gets worse while your medical bills climb.

As gerontology researchers who study health and financial well-being in later life, we’ve analyzed how someone’s ties to the health care system strengthen or unravel depending on whether they have insurance coverage. What we’ve found is simple: Staying connected to a trusted doctor keeps you healthier and saves the system money. Breaking that link does just the opposite.

And that’s exactly what has us worried right now. Members of Congress are debating whether to make major cuts to Medicaid and other social safety net programs. If the Senate passes its own version of the tax-and-spending package that the House approved in May 2025, millions of Americans will soon face exactly this kind of disruption – with big consequences for their health and well-being.

How people end up uninsured

Someone can lose their health insurance for a number of reasons. For many Americans, coverage is tied to employment. Being fired, retiring before you turn 65 and become eligible to enroll in the Medicare program, or even getting a new job can mean losing insurance. Others wind up uninsured due to a different array of changes: moving to a different state, getting divorced or aging out of a parent’s plan after their 26th birthday.

And those who buy their own coverage may find that they can no longer afford the premiums. In 2024, average premiums on the individual market exceeded more than US$600 per month for many adults, even with subsidies.

Government-sponsored insurance programs can also leave you vulnerable to this predicament. The Senate is currently considering its own version of a tax-and-spending bill the House of Representatives passed in May that would make cuts and changes to Medicaid. If the provisions in the House bill are enacted, millions of Americans who get health insurance through Medicaid – a health insurance program jointly run by the federal government and the states that is mainly for people who have low incomes or disabilities – would lose their coverage, according to the nonpartisan Congressional Budget Office.

Medicaid was established in the 1960s, explains a scholar of the program’s history.

Consequences of becoming uninsured

Health insurance is more than a way to pay medical bills; it’s a doorway into the health care system itself. It connects people to health care providers who come to know their medical history, their medications and their personal circumstances.

When that door closes, the effects are immediate. Uninsured people are much less likely to have a usual source of care – typically a doctor or another primary care provider or clinic you know and trust. That relationship acts as a foundation for managing chronic conditions, staying current with preventive screenings and getting guidance when new symptoms arise.

Researchers have found that adults who go uninsured for even six months become significantly more likely to postpone care or forgo it altogether to save money. In practical terms, this means they’re less likely to be examined by someone who knows their medical history and can spot red flags early.

The Affordable Care Act, the landmark health care law enacted during the Obama administration, made the number of Americans without insurance plummet. The share of people without insurance fell from 16% in 2010 to 7.7% in 2023.

The people who got insurance coverage, particularly those who were middle age, saw big improvements in their health.

Researching the results

In research that looked at data collected from 2014 to 2020, we followed what happened to 12,000 adults who were 50 or older and lived across the nation.

Our research team analyzed how their experiences changed when they lost, and sometimes later regained, a regular source of care during those six years.

Many of the participants in this study had multiple chronic conditions like diabetes, hypertension and heart disease.

The results were striking.

Those who didn’t see the same provider on a regular basis were far less likely to feel heard or respected by health care professionals. They had fewer medical appointments, filled fewer prescriptions and were less likely to follow through with recommended treatments.

Their health also deteriorated considerably over the six years. Their blood pressure and blood sugar levels rose, and they had more elevated indicators of kidney impairment compared with their counterparts who had regular care providers.

The longer they went without consistent health care, the worse these clinical markers became.

Warning signs

Preventive care is one of the best tools that both patients and their health care providers have to head off major health problems. This care includes screenings like cholesterol and blood pressure checks, mammograms, PAP smears and prostate exams, as well as routine vaccinations. But most people only get preventive care when they stay engaged with the health care system.

And that’s far more likely when you have stable and comprehensive health insurance coverage.

Our research team also examined what happened to preventive care based on whether the participants had a regular doctor. We found that those who kept seeing the same providers were almost three times more likely to get basic preventive services than those who did not.

Over time, these missed preventive care opportunities can add up to a big problem. They can turn what could have been a manageable issue into an emergency room visit or a long, expensive hospital stay.

For example, imagine a man in his 50s who no longer gets cholesterol screenings after losing insurance coverage. Over several years, his undiagnosed high cholesterol leads to a heart attack that could have been prevented with early medication. Or a woman who skips mammograms because of out-of-pocket costs, only to face a late-stage cancer diagnosis that might have been caught years earlier.

People in scrubs work and mill about in a hospital emergency room.
Waiting too long to deal with a health condition can mean you make a trip to the emergency room, increasing the cost of care for you and others.
FS Productions/Tetra images via Getty Images

Shifting the costs

Patients whose conditions take too long to be diagnosed aren’t the only ones who pay the price.

We also studied how stable care relationships affect health care spending. To do this, we linked Medicare claims cost data to our original study and tracked the medical costs of the same adults age 50 and older from 2014 to 2020. One of our key findings is that people with regular care providers were 38% less likely to incur above-average health care costs.

These savings aren’t just for patients – they ripple through the entire health care system. Primary care stability lowers costs for both public and private health insurers and, ultimately, for taxpayers.

But when people lose their health care coverage, those savings disappear.

Emergency rooms see more uninsured patients seeking care that could have been handled earlier and more cheaply in a clinic or doctor’s office. While hospitals are legally required to provide emergency care regardless of a patient’s ability to pay, much of the resulting cost goes unreimbursed.

Hospitals foot the bill for about two-thirds of those losses. They pass the other third along to private insurance companies through higher hospital fees. Those insurers, in turn, raise their customers’ premiums. Larger taxpayer subsidies can then be required to keep hospitals open.

Seeing Medicaid as a lifeline

For the nearly 80 million Americans enrolled in Medicaid, the program provides more than coverage.

It contributes to the health care stability our research shows is critical for good health. Medicaid makes it possible for many Americans with serious medical conditions to have a regular doctor, get routine preventive services and have someone to turn to when symptoms arise – even when they have low incomes. It helps prevent health care from becoming purely crisis-driven.

As Congress considers cutting Medicaid funding by hundreds of billions of dollars, we believe that lawmakers should realize that scaling back coverage would break the fragile links between millions of patients and the providers who know them best.The Conversation

Jane Tavares, Senior Research Fellow and Lecturer of Gerontology, UMass Boston and Marc Cohen, Professor of Gerontology, UMass Boston

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

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Note: The following A.I. based commentary is not part of the original article, reproduced above, but is offered in the hopes that it will promote greater media literacy and critical thinking, by making any potential bias more visible to the reader –Staff Editor.

Political Bias Rating: Left-Leaning

This article presents a strong case in favor of maintaining or expanding government-funded health insurance programs like Medicaid, using empirical research to emphasize the benefits of continuous coverage and the harms of potential cuts. While it relies on data and expert opinion, the framing consistently warns against proposed Republican-led cuts to Medicaid, characterizing them as harmful and disruptive. The language portrays these policy shifts in a negative light, without presenting counterarguments or alternative fiscal perspectives, which contributes to a left-leaning tone in support of social safety nets and expansive health care coverage.

The Conversation

Robots run out of energy long before they run out of work to do − feeding them could change that

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theconversation.com – James Pikul, Associate Professor of Mechanical Engineering, University of Wisconsin-Madison – 2025-06-02 07:45:00


Earlier this year, a robot completed a half-marathon in just under 2 hours 40 minutes, showcasing impressive agility but limited endurance. Unlike animals that store energy in dense fat, robots rely on lithium-ion batteries, which offer far less energy density and require frequent recharging, limiting operational time. Current robots like Boston Dynamics’ Spot function for around 90 minutes per charge, far less than biological endurance. New battery chemistries and fast-charging technologies may help, but challenges remain. Researchers are exploring bioinspired “robotic metabolism” systems, where robots “digest” fuels and circulate energy like blood, promising enhanced endurance, adaptability, and resilience beyond current limitations.

Robots can run, but they can’t go the distance.
AP Photo/Ng Han Guan

James Pikul, University of Wisconsin-Madison

Earlier this year, a robot completed a half-marathon in Beijing in just under 2 hours and 40 minutes. That’s slower than the human winner, who clocked in at just over an hour – but it’s still a remarkable feat. Many recreational runners would be proud of that time. The robot kept its pace for more than 13 miles (21 kilometers).

But it didn’t do so on a single charge. Along the way, the robot had to stop and have its batteries swapped three times. That detail, while easy to overlook, speaks volumes about a deeper challenge in robotics: energy.

Modern robots can move with incredible agility, mimicking animal locomotion and executing complex tasks with mechanical precision. In many ways, they rival biology in coordination and efficiency. But when it comes to endurance, robots still fall short. They don’t tire from exertion – they simply run out of power.

As a robotics researcher focused on energy systems, I study this challenge closely. How can researchers give robots the staying power of living creatures – and why are we still so far from that goal? Though most robotics research into the energy problem has focused on better batteries, there is another possibility: Build robots that eat.

Robots move well but run out of steam

Modern robots are remarkably good at moving. Thanks to decades of research in biomechanics, motor control and actuation, machines such as Boston Dynamics’ Spot and Atlas can walk, run and climb with an agility that once seemed out of reach. In some cases, their motors are even more efficient than animal muscles.

But endurance is another matter. Spot, for example, can operate for just 90 minutes on a full charge. After that, it needs nearly an hour to recharge. These runtimes are a far cry from the eight- to 12-hour shifts expected of human workers – or the multiday endurance of sled dogs.

The issue isn’t how robots move – it’s how they store energy. Most mobile robots today use lithium-ion batteries, the same type found in smartphones and electric cars. These batteries are reliable and widely available, but their performance improves at a slow pace: Each year new lithium-ion batteries are about 7% better than the previous generation. At that rate, it would take a full decade to merely double a robot’s runtime.

Robots such as Boston Dynamic’s Atlas are remarkably capable – for relatively short amounts of time.

Animals store energy in fat, which is extraordinarily energy dense: nearly 9 kilowatt-hours per kilogram. That’s about 68 kWh total in a sled dog, similar to the energy in a fully charged Tesla Model 3. Lithium-ion batteries, by contrast, store just a fraction of that, about 0.25 kilowatt-hours per kilogram. Even with highly efficient motors, a robot like Spot would need a battery dozens of times more powerful than today’s to match the endurance of a sled dog.

And recharging isn’t always an option. In disaster zones, remote fields or on long-duration missions, a wall outlet or a spare battery might be nowhere in sight.

In some cases, robot designers can add more batteries. But more batteries mean more weight, which increases the energy required to move. In highly mobile robots, there’s a careful balance between payload, performance and endurance. For Spot, for example, the battery already makes up 16% of its weight.

Some robots have used solar panels, and in theory these could extend runtime, especially for low-power tasks or in bright, sunny environments. But in practice, solar power delivers very little power relative to what mobile robots need to walk, run or fly at practical speeds. That’s why energy harvesting like solar panels remains a niche solution today, better suited for stationary or ultra-low-power robots.

Why it matters

These aren’t just technical limitations. They define what robots can do.

A rescue robot with a 45-minute battery might not last long enough to complete a search. A farm robot that pauses to recharge every hour can’t harvest crops in time. Even in warehouses or hospitals, short runtimes add complexity and cost.

If robots are to play meaningful roles in society assisting the elderly, exploring hazardous environments and working alongside humans, they need the endurance to stay active for hours, not minutes.

New battery chemistries such as lithium-sulfur and metal-air offer a more promising path forward. These systems have much higher theoretical energy densities than today’s lithium-ion cells. Some approach levels seen in animal fat. When paired with actuators that efficiently convert electrical energy from the battery to mechanical work, they could enable robots to match or even exceed the endurance of animals with low body fat. But even these next-generation batteries have limitations. Many are difficult to recharge, degrade over time or face engineering hurdles in real-world systems.

Fast charging can help reduce downtime. Some emerging batteries can recharge in minutes rather than hours. But there are trade-offs. Fast charging strains battery life, increases heat and often requires heavy, high-power charging infrastructure. Even with improvements, a fast-charging robot still needs to stop frequently. In environments without access to grid power, this doesn’t solve the core problem of limited onboard energy. That’s why researchers are exploring alternatives such as “refueling” robots with metal or chemical fuels – much like animals eat – to bypass the limits of electrical charging altogether.

illustration off a humanoid robot putting a metal nut into its mouth
Robots could one day harvest energy from high-energy-density materials such as aluminum through synthetic digestive and vascular systems.
Yichao Shi and James Pikul

An alternative: Robotic metabolism

In nature, animals don’t recharge, they eat. Food is converted into energy through digestion, circulation and respiration. Fat stores that energy, blood moves it and muscles use it. Future robots could follow a similar blueprint with synthetic metabolisms.

Some researchers are building systems that let robots “digest” metal or chemical fuels and breathe oxygen. For example, synthetic, stomachlike chemical reactors could convert high-energy materials such as aluminum into electricity.

This builds on the many advances in robot autonomy, where robots can sense objects in a room and navigate to pick them up, but here they would be picking up energy sources.

Other researchers are developing fluid-based energy systems that circulate like blood. One early example, a robotic fish, tripled its energy density by using a multifunctional fluid instead of a standard lithium-ion battery. That single design shift delivered the equivalent of 16 years of battery improvements, not through new chemistry but through a more bioinspired approach. These systems could allow robots to operate for much longer stretches of time, drawing energy from materials that store far more energy than today’s batteries.

In animals, the energy system does more than just provide energy. Blood helps regulate temperature, deliver hormones, fight infections and repair wounds. Synthetic metabolisms could do the same. Future robots might manage heat using circulating fluids or heal themselves using stored or digested materials. Instead of a central battery pack, energy could be stored throughout the body in limbs, joints and soft, tissuelike components.

This approach could lead to machines that aren’t just longer-lasting but more adaptable, resilient and lifelike.

The bottom line

Today’s robots can leap and sprint like animals, but they can’t go the distance.

Their bodies are fast, their minds are improving, but their energy systems haven’t caught up. If robots are going to work alongside humans in meaningful ways, we’ll need to give them more than intelligence and agility. We’ll need to give them endurance.The Conversation

James Pikul, Associate Professor of Mechanical Engineering, University of Wisconsin-Madison

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

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Note: The following A.I. based commentary is not part of the original article, reproduced above, but is offered in the hopes that it will promote greater media literacy and critical thinking, by making any potential bias more visible to the reader –Staff Editor.

Political Bias Rating: Centrist

This article presents a factual, science- and technology-focused discussion about the challenges of energy storage in robotics. It reports on current limitations and future research directions without advocating any political ideology or policy stance. The tone is neutral and informative, emphasizing technical innovation and potential benefits without framing the topic in a partisan context. There is no language or framing that suggests a left- or right-leaning bias; instead, it adheres to objective reporting of scientific progress and challenges.

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Our trans health study was terminated by the government – the effects of abrupt NIH grant cuts ripple across science and society

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theconversation.com – Jae A. Puckett, Associate Professor of Psychology, Michigan State University – 2025-06-02 07:44:00


The Trump administration abruptly terminated federally funded research on transgender and nonbinary health, including a four-year NIH-supported study on resilience in these communities. This termination, based on ideological grounds, undermines decades of scientific progress, dismissing valid research and harming both the scientific workforce and community trust. The project had collected extensive data and developed new resilience measures, but funding cuts jeopardize the careers of researchers and reduce future training opportunities. The loss wastes millions of taxpayer dollars and halts valuable insights into improving trans health, while government reports contradict established science on gender-affirming care, promoting misinformation instead.

Funding cuts to trans health research are part of the Trump administration’s broader efforts to medically and legally restrict trans rights.
AP Photo/Lindsey Wasson

Jae A. Puckett, Michigan State University and Paz Galupo, Washington University in St. Louis

Given the Trump administration’s systematic attempts to medically and legally disenfranchise trans people, and its abrupt termination of grants focused on LGBTQ+ health, we can’t say that the notice of termination we received regarding our federally funded research on transgender and nonbinary people’s health was unexpected.

As researchers who study the experiences of trans and nonbinary people, we have collectively dedicated nearly 50 years of our scientific careers to developing ways to address the health disparities negatively affecting these communities. The National Institutes of Health had placed a call for projects on this topic, and we had successfully applied for their support for our four-year study on resilience in trans communities.

However, our project on trans health became one of the hundreds of grants that have been terminated on ideological grounds. The termination notice stated that the grant no longer fit agency priorities and claimed that this work was not based on scientific research.

Screenshot of email
Termination notice sent to the authors from the National Institutes of Health.
Jae A. Puckett and Paz Galupo, CC BY-ND

These grant terminations undermine decades of science on gender diversity by dismissing research findings and purging data. During Trump’s current term, the NIH’s Sexual and Gender Minority Research Office was dismantled, references to LGBTQ+ people were removed from health-related websites, and datasets were removed from public access.

The effects of ending research on trans health ripple throughout the scientific community, the communities served by this work and the U.S. economy.

Studying resilience

Research focused on the mental health of trans and nonbinary people has grown substantially in recent years. Over time, this work has expanded beyond understanding the hardships these communities face to also study their resilience and positive life experiences.

Resilience is often understood as an ability to bounce back from challenges. For trans and nonbinary people experiencing gender-based stigma and discrimination, resilience can take several forms. This might look like simply continuing to survive in a transphobic climate, or it might take the form of being a role model for other trans and nonbinary people.

As a result of gender-based stigma and discrimination, trans and nonbinary people experience a range of health disparities, from elevated rates of psychological distress to heightened risk for chronic health conditions and poor physical health. In the face of these challenges and growing anti-trans legislation in the U.S., we believe that studying resilience in these communities can provide insights into how to offset the harms of these stresses.

Studies show anti-trans legislation is harming the mental health of LGBTQ+ youth.

With the support of the NIH, we began our work in earnest in 2022. The project was built on many years of research from our teams preceding the grant. From the beginning, we collaborated with trans and nonbinary community members to ensure our research would be attuned to the needs of the community.

At the time our grant was terminated, we were nearing completion of Year 3 of our four-year project. We had collected data from over 600 trans and nonbinary participants across the U.S. and started to follow their progress over time. We had developed a new way to measure resilience among trans and nonbinary people and were about to publish a second measure specifically tailored to people of color.

The termination of our grant and others like it harms our immediate research team, the communities we worked with and the field more broadly.

Loss of scientific workforce

For many researchers in trans health, the losses from these cuts go beyond employment.

Our project had served as a training opportunity for the students and early career professionals involved in the study, providing them with the research experience and mentorship necessary to advance their careers. But with the termination of our funding, two full-time researchers and at least three students will lose their positions. The three lead scientists have lost parts of their salaries and dedicated research time.

These NIH cuts will likely result in the loss of much of the next generation of trans researchers and the contributions they would have made to science and society. Our team and other labs in similar situations will be less likely to work with graduate students due to a lack of available funding to pay and support them. This changes the landscape for future scientists, as it means there will be fewer opportunities for individuals interested in these areas of research to enter graduate training programs.

Building with Harvard insignia banners hanging between pillars, a student in a cap and gown walking past
The Trump administration has directly penalized universities across the country for ‘ideological overreach.’
Zhu Ziyu/VCG via Getty Images

As universities struggle to address federal funding cuts, junior academics will be less likely to gain tenure, and faculty in grant-funded positions may lose their jobs. Universities may also become hesitant to hire people who work in these areas because their research has essentially been banned from federal funding options.

Loss of community trust

Trans and nonbinary people have often been studied under opportunistic and demeaning circumstances. This includes when researchers collect data for their own gains but return little to the communities they work with, or when they do research that perpetuates theories that pathologize those communities. As a result, many are often reluctant to participate in research.

To overcome this reluctance, we grounded our study on community input. We involved an advisory board composed of local trans and nonbinary community members who helped to inform how we conducted our study and measured our findings.

Our work on resilience has been inspired by feedback we received from previous research participants who said that “[trans people] matter even when not in pain.”

Abruptly terminating projects like these can break down trust between researchers and the populations they study.

Loss of scientific knowledge

Research that focuses on the strengths of trans and nonbinary communities is in its infancy. The termination of our grant has led to the loss of the insights our study would have provided on ways to improve health among trans and nonbinary people and future work that would have built off our findings. Resilience is a process that takes time to unfold, and we had not finished the longitudinal data collection in our study – nor will we have the protected time to publish and share other findings from this work.

Meanwhile, the Department of Health and Human Services released a May 2025 report stating that there is not enough evidence to support gender-affirming care for young people, contradicting decades of scientific research. Scientists, researchers and medical professional organizations have widely criticized the report as misrepresenting study findings, dismissing research showing benefits to gender-affirming care, and promoting misinformation rejected by major medical associations. Instead, the report recommends “exploratory therapy,” which experts have likened to discredited conversion therapy.

Hands clapping beside a small trans flag on top of a pile of signs, one reading 'WE'RE STILL HERE,'
Transgender and nonbinary people continue to exist, regardless of legislation.
Kayla Bartkowski/Getty Images

Despite claims that there is insufficient research on gender-affirming care and more data is needed on the health of trans and nonbinary people, the government has chosen to divest from actual scientific research about trans and nonbinary people’s lives.

Loss of taxpayer dollars

The termination of our grant means we are no longer able to achieve the aims of the project, which depended on the collection and analysis of data over time. This wastes the three years of NIH funding already spent on the project.

Scientists and experts who participated in the review of our NIH grant proposal rated our project more highly than 96% of the projects we competed against. Even so, the government made the unscientific choice to override these decisions and terminate our work.

Millions of taxpayer dollars have already been invested in these grants to improve the health of not only trans and nonbinary people, but also American society as a whole. With the termination of these grants, few will get to see the benefits of this investment.The Conversation

Jae A. Puckett, Associate Professor of Psychology, Michigan State University and Paz Galupo, Professor of Sexual Health and Education, Washington University in St. Louis

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

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The post Our trans health study was terminated by the government – the effects of abrupt NIH grant cuts ripple across science and society appeared first on theconversation.com



Note: The following A.I. based commentary is not part of the original article, reproduced above, but is offered in the hopes that it will promote greater media literacy and critical thinking, by making any potential bias more visible to the reader –Staff Editor.

Political Bias Rating: Left-Leaning

This content strongly critiques actions taken by the Trump administration and associated federal agencies, particularly regarding the termination of funding for transgender and nonbinary health research. It emphasizes harm caused to LGBTQ+ communities, highlights scientific consensus supporting gender-affirming care, and portrays the policy decisions as ideologically driven and detrimental to both communities and scientific progress. The language and framing align with perspectives commonly found on the political left, especially those advocating for LGBTQ+ rights and inclusion, while opposing conservative policies perceived as hostile to these groups.

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

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theconversation.com – Jeremiah Bartz, Associate Professor of Mathematics, University of North Dakota – 2025-05-30 07:47:00


Prime numbers, numbers greater than one divisible only by one and themselves, have fascinated humanity for millennia, evidenced by artifacts like the 20,000-year-old Ishango bone and the Babylonian Plimpton 322 tablet. Greek mathematicians around 500 B.C.E. first understood primes, while Euler proved their infinitude circa 300 B.C.E. Arab scholars advanced prime theory, including the fundamental theorem of arithmetic. Mersenne primes, of form (2^p – 1), offer a key to finding large primes. The Lucas-Lehmer test enables efficient identification, enhanced by computers since the 1950s. Collaborative efforts like GIMPS have discovered many large primes, with the current largest prime found in 2024, critical for encryption and cybersecurity.

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.

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.

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.

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Note: The following A.I. based commentary is not part of the original article, reproduced above, but is offered in the hopes that it will promote greater media literacy and critical thinking, by making any potential bias more visible to the reader –Staff Editor.

Political Bias Rating: Centrist

The article presents a factual, educational overview of the history and significance of prime numbers, focusing on mathematics and technological advancements without promoting any political or ideological stance. Its tone is neutral and informative, aimed at explaining mathematical concepts and recent developments in prime number research. The content does not include partisan language or viewpoints and remains centered on scientific progress and historical context, making it a balanced, non-partisan piece.

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