A Mathematician Found a Hidden Pattern That Could Keep Your Biggest Secrets Safe
Here's what you'll learn when you read this story:
Prime numbers are essential for technologies like RSA encryption, which rely on the difficulty of guessing these numerals.
A new paper shows that another area of mathematics called integer partition unlocks 'infinitely many new ways' to detect them beyond divisibility.
The team said that this breakthrough arrived by using decades-old methods to answer mathematical questions no one else thought to ask.
Although prime numbers are a mathematical concept everyone learns about in elementary school, extremely large prime numbers form the backbone of some of the most complex technologies in modern society—especially in the realm of cryptography. But in the burgeoning era of quantum computers, which can solve problems exponentially faster than standard computers (including supercomputers), there's a chance that this kind of previously uncrackable protection could suddenly become very vulnerable.
This has pushed mathematicians—including Ken Ono from the University of Virginia—to continue exploring the frontiers of prime numbers. In September of last year, Ono (along with co-authors William Craig and Jan-Willem van Ittersum) published a paper in the journal Proceedings of the National Academy of Sciences (PNAS) exploring how to find new prime numbers with a novel approach centered around what are called integer partitions. His groundbreaking work scored him recognition for the Cozzarelli Award for originality and creativity, but to understand it, we'll need to take a few steps back.
A prime number (as you likely know) is an integer that is not divisible by any number other than 1 and itself. While there are technically infinite prime numbers, it's difficult to find new ones, as they appear in a number line with no pattern. (Currently, the largest known prime number is more than 41 million digits long.) But Ono and his co-authors discovered a connection between prime numbers and integer partitions, which divvy up numbers into all their possible smaller sums—the number four, for example, can be described as 4, as 3 + 1, as 2 + 2, as 2 + 1 + 1, and as 1 + 1 + 1 + 1.
'The prime numbers, the building blocks of multiplicative number theory, are the solutions of infinitely many special 'Diophantine equations' in well-studied partition functions,' the authors wrote. 'In other words, integer partitions detect the primes in infinitely many natural ways.'
Named for the third-century mathematician Diophantus of Alexandria, these equations can be incredibly complex, but if the resulting answer turns out to be true, that means you're working with a prime number. This essentially devises a new way to investigate prime numbers that has never been explored before.
'This paper, as excited as I am about it, represents theoretical math that could've been done decades ago,' Ono said in a video interview accompanying a press statement. 'What I like about our theorem is that if there was a time machine, I could go back to 1950, explain what we done, and it would generate the same level of excitement […] and the experts at that time would understand what we did.'
Ono is intimately familiar with the security implications of prime number research, as he serves on the advisory board for the National Security Agency (NSA). Technologies like RSA encryption rely on the difficulty of detecting prime numbers to safeguard the world's most sensitive information, so understanding prime numbers from every conceivable angle will be helpful when quantum computers make ferreting out these unfathomably large numbers easier. Speaking with Scientific American, many mathematicians say this work serves as the foundation of a new way of seeing what other mathematical connections can be made using partition functions.
Prime numbers may be elementary, but they remain a fixture of our complex technological future.
You Might Also Like
The Do's and Don'ts of Using Painter's Tape
The Best Portable BBQ Grills for Cooking Anywhere
Can a Smart Watch Prolong Your Life?
Hashtags
Try Our AI Features
Explore what Daily8 AI can do for you:
Comments
No comments yet...
Related Articles
Android Authority
31 minutes ago
- Android Authority
Verizon told to clarify ambiguous advertising claims after T-Mobile complaint
Edgar Cervantes / Android Authority TL;DR The National Advertising Division (NAD) has recommended that Verizon change its marketing language about satellite texting based on a complaint from T-Mobile. T-Mobile has also challenged Verizon's claim of being 'America's largest network,' with the watchdog calling Verizon's advertising 'ambiguous.' Verizon has said that it'll comply with NAD's recommendations. Verizon is once again under the lens for its inconspicuous advertising claims. This time, the Big Red has been pulled up over claims about its satellite texting service and network size following a challenge from rival T-Mobile. The National Advertising Division (NAD), an industry watchdog under BBB National Programs, found some of Verizon's claims to be supported but recommended that the carrier make its advertising clearer for the benefit of consumers. NAD said Verizon's slogan 'conquering dead zones with satellite' is not misleading on its own, but warned that Verizon must improve its disclosures. Specifically, the NAD says Verizon failed to clarify that the satellite texting service only works on select new phone models and under certain conditions. Moreover, T-Mobile also took issue with Verizon's 'America's largest network' claim. While Verizon has based that claim on the number of postpaid subscribers, T-Mobile said the phrase could mislead consumers into thinking it refers to coverage area or geographic reach. NAD recommended Verizon clarify what Verizon means by 'largest.' 'NAD found the phrase 'largest network' to be ambiguous, potentially conveying different messages to consumers. NAD also determined that the term 'postpaid phone connections' may not clearly communicate that it refers to Verizon subscribers,' the organization wrote in a press release shared with Android Authority. NAD made similar recommendations to those of Verizon last year and asked the carrier to discontinue or modify its satellite texting claims based on a previous complaint by T-Mobile. Verizon stated it would comply with the NAD's recommendations. While the NAD does not have the power to enforce changes, companies often follow its guidance to avoid legal or regulatory issues. For customers, the ruling means Verizon ads may soon become more transparent, especially regarding satellite texting and what its 'largest network' claims really mean.
New York Times
an hour ago
- New York Times
Can You Choose an A.I. Model That Harms the Planet Less?
From uninvited results at the top of your search engine queries to offering to write your emails and helping students do homework, generative A.I. is quickly becoming part of daily life as tech giants race to develop the most advanced models and attract users. All those prompts come with an environmental cost: A report last year from the Energy Department found A.I. could help increase the portion of the nation's electricity supply consumed by data centers from 4.4 percent to 12 percent by 2028. To meet this demand, some power plants are expected to burn more coal and natural gas. And some chatbots are linked to more greenhouse gas emissions than others. A study published Thursday in the journal Frontiers in Communication analyzed different generative A.I. chatbots' capabilities and the planet-warming emissions generated from running them. Researchers found that chatbots with bigger 'brains' used exponentially more energy and also answered questions more accurately — up until a point. 'We don't always need the biggest, most heavily trained model, to answer simple questions. Smaller models are also capable of doing specific things well,' said Maximilian Dauner, a Ph.D. student at the Munich University of Applied Sciences and lead author of the paper. 'The goal should be to pick the right model for the right task.' The study evaluated 14 large language models, a common form of generative A.I. often referred to by the acronym LLMs, by asking each a set of 500 multiple choice and 500 free response questions across five different subjects. Mr. Dauner then measured the energy used to run each model and converted the results into carbon dioxide equivalents based on global most of the models tested, questions in logic-based subjects, like abstract algebra, produced the longest answers — which likely means they used more energy to generate compared with fact-based subjects, like history, Mr. Dauner said. A.I. chatbots that show their step-by-step reasoning while responding tend to use far more energy per question than chatbots that don't. The five reasoning models tested in the study did not answer questions much more accurately than the nine other studied models. The model that emitted the most, DeepSeek-R1, offered answers of comparable accuracy to those that generated a fourth of the amount of emissions. Source: Dauner and Socher, 2025 Note: A.I. models answered 500 free-response questions By Harry Stevens/The New York Times Grams of CO2 emitted per answer Source: Dauner and Socher, 2025 Note: A.I. models answered 100 free-response questions in each category By Harry Stevens/The New York Times Want all of The Times? Subscribe.
Yahoo
an hour ago
- Yahoo
Tech accounts for half of US M&A spending so far in 2025
There has been less dealmaking in 2025 than there was the year prior, but the 2025 deals total more than the mergers and acquisitions (M&A) in the first six months of 2024. Yahoo Finance Senior Banking Reporter David Hollerith outlines what this signals about the dealmaking landscape and what's to come in the second half of the year. To watch more expert insights and analysis on the latest market action, check out more Asking for a Trend here. With the first half of the year coming to a close, we're taking a look at the M&A landscape. New data from PWC highlight that about 30% of companies are pausing or revisiting pending deals due to tariffs. We're bringing in Yahoo Finance banking reporter, David Hollerith. David. Hey Josh. So, um, you know, it's kind of a mixed picture with the deals market right now. We're seeing that the number of deals year to date compared to last year is actually, um, down, but total volume or in dollar amount, the amount of dollars going into deals so far this year is actually up. So it's fairly confusing, and we have two big trends that are sort of shaping this market. The first is tariffs or sort of companies' reaction to tariffs, and that goes back to the PWC stat that you just put out, um, which is just that, um, you know, they're having to rethink their models and uh, you know, whether or not they can actually, um, do a deal without, uh, you know, taking some sort of impact from tariffs that they didn't think. And that's just if they're in an industry that might be sort of resistant to tariffs or exposed to tariffs, excuse me. Um, and then we have AI, and AI is a huge one, obviously, because, um, tech at this point makes up 50% of, uh, uh, US M&A so far year to date, and that's up from about 41% from, uh, the same period last year. And within tech, um, AI is kind of taking over in these few big deals that we're seeing. Um, OpenAI, uh, the investment from, uh, SoftBank, as well as, uh, Salesforce, um, purchasing Informatica, uh, Meta's, uh, purchase of Scale AI. I could sort of go on with that. But so it's a market where a lot of the smaller players aren't really making decisions yet, but it looks not too bad in dollar amount just because we've seen all these big players do these AI plays effectively. All right, David. Thank you for that setup. Appreciate it. Error while retrieving data Sign in to access your portfolio Error while retrieving data Error while retrieving data Error while retrieving data Error while retrieving data
