The Greek mathematician Euclid may very well have proved, circa 300 BCE, that there are infinitely many prime numbers. But it was the British mathematician Christian Lawson-Perfect who, more recently, devised the computer game “Is this prime?”
Launched five years ago, the game surpassed three million tries on July 16—or, more to the point, it hit run 2,999,999—after a Hacker News post generated a surge of about 100,000 attempts.
The aim of the game is to sort as many numbers as possible into “prime” or “not prime” in 60 seconds (as Lawson-Perfect originally described it on The Aperiodical, a mathematics blog of which he’s a founder and editor).
A prime number is a whole number with precisely two divisors, 1 and itself.
“It’s very simple, but infuriatingly difficult,” says Lawson-Perfect, who works in the e-learning unit in Newcastle University’s School of Mathematics and Statistics. He created the game in his spare time, but it’s proved useful on the job: Lawson-Perfect writes e-assessment software (systems that evaluate learning). “The system I make is designed to randomly generate a maths question, and take an answer from the student, which it automatically marks and gives feedback on,” he says. “You could view the primes game as a kind of assessment”—he’s used it when doing outreach sessions in schools.
He made the game slightly easier with keyboard shortcuts—the y and n keys click the corresponding yes-no buttons on the screen—in order to save mouse-moving time.
Give it a whirl:
Prime numbers have practical utility in computing—such as with error-correcting codes and encryption. But while prime factorization is hard (hence its value in encryption), primality checking is easier, if tricky. The Fields Medal–winning German mathematician Alexander Grothendieck infamously mistook 57 for prime (the “Grothendieck prime”). When Lawson-Perfect analyzed data from the game, he found that various numbers exhibited a certain “Grothendieckyness.” The number most often mistaken for a prime was 51, followed by 57, 87, 91, 119, and 133—Lawson-Perfect’s nemesis (he also devised a handy primality-checking service: https://isthisprime.com/2).
The most minimalistic algorithm for checking a number’s primeness is trial division—divide the number by every number up to its square root (the product of two numbers greater than the square root would be greater than the number in question).
However, this naïve method is not very efficient, and neither are some other techniques devised over the centuries—as the German mathematician Carl Friedrich Gauss observed in 1801, they “require intolerable labor even for the most indefatigable calculator.”
The algorithm Lawson-Perfect coded up for the game is called the Miller-Rabin primality test (which builds on a very efficient but not ironclad 17th-century method, “Fermat’s little theorem”). The Miller-Rabin test works surprisingly well. As far as Lawson-Perfect is concerned, it’s “basically magic”—“I don’t really understand how it works, but I’m confident I could if I spent the time to look at it more deeply,” he says.
Since the test uses randomness, it produces a probabilistic result. Which means that sometimes the test lies. “There is a chance of uncovering an imposter, a composite number that is trying to pass as prime,” says Carl Pomerance, a mathematician at Dartmouth College and coauthor of the book Prime Numbers: A Computational Perspective. The chances of an imposter slipping through the algorithm’s clever checking mechanism are maybe one in a trillion, though, so the test is “pretty safe.”
But as far as clever primality checking algorithms go, the Miller-Rabin test is “the tip of the iceberg,” says Pomerance. Notably, 19 years ago, three computer scientists—Manindra Agrawal, Neeraj Kayal, and Nitin Saxena, all at the Indian Institute of Technology Kanpur—announced the AKS primality test (again building upon Fermat’s method), which finally provided a test for unequivocally proving that a number is prime, with no randomization and (theoretically, at least) with impressive speed. Alas, fast in theory doesn’t always translate to fast in real life, so the AKS test isn’t useful for practical purposes.
The unofficial world record
But practicality isn’t always the point. Occasionally Lawson-Perfect receives email from people keen to share their high scores in the game. Recently a player reported 60 primes in 60 seconds, but the record is more likely 127. (Lawson-Perfect doesn’t track high scores; he knows there are some cheaters, with computer-aided attempts that produce spikes in the data.)
The 127 score was achieved by Ravi Fernando, a mathematics graduate student at the University of California, Berkeley, who posted the result in July 2020. It’s still his personal best and, he reckons, the “unofficial world record.”
Since last summer, Fernando hasn’t played the game much with the default settings, but he has tried with customized settings, selecting for larger numbers and allowing longer time limits—he scored 240 with a five-minute limit. “Which took a lot of guesswork, because the numbers got into the high four-digit range and I’ve only ever memorized primes up to the low 3,000s,” he says. “I suppose some would argue even that is excessive.”
Fernando’s research is in algebraic geometry, which involves primes to some extent. But, he says, “my research has more to do with why I stopped playing the game than why I started” (he started his PhD in 2014). Plus, he figures 127 would be very hard to beat. And, he says, “it just feels right to stop at a prime-number record.”
How the idea of a “transgender contagion” went viral—and caused untold harm
The ROGD paper was not funded by anti-trans zealots. But it arrived at exactly the time people with bad intentions were looking for science to buoy their opinions.
The results were in line with what one might expect given those sources: 76.5% of parents surveyed “believed their child was incorrect in their belief of being transgender.” More than 85% said their child had increased their internet use and/or had trans friends before identifying as trans. The youths themselves had no say in the study, and there’s no telling if they had simply kept their parents in the dark for months or years before coming out. (Littman acknowledges that “parent-child conflict may also explain some of the findings.”)
Arjee Restar, now an assistant professor of epidemiology at the University of Washington, didn’t mince words in her 2020 methodological critique of the paper. Restar noted that Littman chose to describe the “social and peer contagion” hypothesis in the consent document she shared with parents, opening the door for biases in who chose to respond to the survey and how they did so. She also highlighted that Littman asked parents to offer “diagnoses” of their child’s gender dysphoria, which they were unqualified to do without professional training. It’s even possible that Littman’s data could contain multiple responses from the same parent, Restar wrote. Littman told MIT Technology Review that “targeted recruitment [to studies] is a really common practice.” She also called attention to the corrected ROGD paper, which notes that a pro-gender-affirming parents’ Facebook group with 8,000 members posted the study’s recruitment information on its page—although Littman’s study was not designed to be able to discern whether any of them responded.
But politics is blind to nuances in methodology. And the paper was quickly seized by those who were already pushing back against increasing acceptance of trans people. In 2014, a few years before Littman published her ROGD paper, Time magazine had put Laverne Cox, the trans actress from Orange Is the New Black, on its cover and declared a “transgender tipping point.” By 2016, bills across the country that aimed to bar trans people from bathrooms that fit their gender identity failed, and one that succeeded, in North Carolina, cost its Republican governor, Pat McCrory, his job.
Yet by 2018 a renewed backlash was well underway—one that zeroed in on trans youth. The debate about trans youth competing in sports went national, as did a heavily publicized Texas custody battle between a mother who supported her trans child and a father who didn’t. Groups working to further marginalize trans people, like the Alliance Defending Freedom and the Family Research Council, began “printing off bills and introducing them to state legislators,” says Gillian Branstetter, a communications strategist at the American Civil Liberties Union.
The ROGD paper was not funded by anti-trans zealots. But it arrived at exactly the time people with bad intentions were looking for science to buoy their opinions. The paper “laundered what had previously been the rantings of online conspiracy theorists and gave it the resemblance of serious scientific study,” Branstetter says. She believes that if Littman’s paper had not been published, a similar argument would have been made by someone else. Despite its limitations, it has become a crucial weapon in the fight against trans people, largely through online dissemination. “It is astonishing that such a blatantly bad-faith effort has been taken so seriously,” Branstetter says.
Littman plainly rejects that characterization, saying her goal was simply to “find out what’s going on.” “This was a very good-faith attempt,” she says. “As a person I am liberal; I’m pro-LGBT. I saw a phenomenon with my own eyes and I investigated, found that it was different than what was in the scientific literature.”
One reason for the success of Littman’s paper is that it validates the idea that trans kids are new. But Jules Gill-Peterson, an associate professor of history at Johns Hopkins and author of Histories of the Transgender Child, says that is “empirically untrue.” Trans children have only recently started to be discussed in mainstream media, so people assume they weren’t around before, she says, but “there have been children transitioning for as long as there has been transition-related medical technology,” and children were socially transitioning—living as a different gender without any medical or legal interventions—long before that.
Many trans people are young children when they first observe a dissonance between how they are identified and how they identify. The process of transitioning is never simple, but the explanation of their identity might be.
Inside the software that will become the next battle front in US-China chip war
EDA software is a small but mighty part of the semiconductor supply chain, and it’s mostly controlled by three Western companies. That gives the US a powerful point of leverage, similar to the way it wanted to restrict access to lithography machines—another crucial tool for chipmaking—last month. So how has the industry become so American-centric, and why can’t China just develop its own alternative software?
What is EDA?
Electronic design automation (also known as electronic computer-aided design, or ECAD) is the specialized software used in chipmaking. It’s like the CAD software that architects use, except it’s more sophisticated, since it deals with billions of minuscule transistors on an integrated circuit.
There’s no single dominant software program that represents the best in the industry. Instead, a series of software modules are often used throughout the whole design flow: logic design, debugging, component placement, wire routing, optimization of time and power consumption, verification, and more. Because modern-day chips are so complex, each step requires a different software tool.
How important is EDA to chipmaking?
Although the global EDA market was valued at only around $10 billion in 2021, making it a small fraction of the $595 billion semiconductor market, it’s of unique importance to the entire supply chain.
The semiconductor ecosystem today can be seen as a triangle, says Mike Demler, a consultant who has been in the chip design and EDA industry for over 40 years. On one corner are the foundries, or chip manufacturers like TSMC; on another corner are intellectual-property companies like ARM, which make and sell reusable design units or layouts; and on the third corner are the EDA tools. All three together make sure the supply chain moves smoothly.
From the name, it may sound as if EDA tools are only important to chip design firms, but they are also used by chip manufacturers to verify that a design is feasible before production. There’s no way for a foundry to make a single chip as a prototype; it has to invest in months of time and production, and each time, hundreds of chips are fabricated on the same semiconductor base. It would be an enormous waste if they were found to have design flaws. Therefore, manufacturers rely on a special type of EDA tool to do their own validation.
What are the leading companies in the EDA industry?
There are only a few companies that sell software for each step of the chipmaking process, and they have dominated this market for decades. The top three companies—Cadence (American), Synopsys (American), and Mentor Graphics (American but acquired by the German company Siemens in 2017)—control about 70% of the global EDA market. Their dominance is so strong that many EDA startups specialize in one niche use and then sell themselves to one of these three companies, further cementing the oligopoly.
What is the US government doing to restrict EDA exports to China?
US companies’ outsize influence on the EDA industry makes it easy for the US government to squeeze China’s access. In its latest announcement, it pledged to add certain EDA tools to its list of technologies banned from export. The US will coordinate with 41 other countries, including Germany, to implement these restrictions.
Bright LEDs could spell the end of dark skies
Specifications in the current proposal provide a starting point for planning, including a color temperature cutoff of 3,000 K in line with Pittsburgh’s dark-sky ordinance, which passed last fall. However, Martinez says that is the maximum, and as they look for consultants, they’ll be taking into account which ones show dark-sky expertise. The city is also considering—budget and infrastructure permitting—a “network lighting management system,” a kind of “smart” lighting that would allow them to control lighting levels and know when there is an outage.
Martinez says there will be citywide engagement and updates on the status as critical milestones are reached. “We’re in the evaluation period right now,” she says, adding that the next milestone is authorization of a new contract. She acknowledges there is some “passionate interest in street lighting,” and that she too is anxious to see the project come to fruition: “Just because things seem to go quiet doesn’t mean work is not being done.”
While they aren’t meeting with light pollution experts right now, Martinez says the ones they met with during the last proposal round—Stephen Quick and Diane Turnshek of CMU— were “instrumental” in adopting the dark-sky ordinance.
In recent months, Zielinska-Dabkowska says, her “baby” has been the first Responsible Outdoor Light at Night Conference, an international gathering of more than 300 lighting professionals and light pollution researchers held virtually in May. Barentine was among the speakers. “It’s a sign that all of this is really coming along, both as a research subject but also something that attracts the interest of practitioners in outdoor lighting,” he says of the conference.
There is more work to be done, though. The IDA recently released a report summarizing the current state of light pollution research. The 18-page report includes a list of knowledge gaps to be addressed in several areas, including the overall effectiveness of government policies on light pollution. Another is how much light pollution comes from sources other than city streetlights, which a 2020 study found accounted for only 13% of Tucson’s light pollution. It is not clear what makes up the rest, but Barentine suspects the next biggest source in the US and Europe is commercial lighting, such as flashy outdoor LED signs and parking lot lighting.
Working with companies to reduce light emissions can be challenging, says Clayton Trevillyan, Tucson’s chief building officer. “If there is a source of light inside the building, technically it’s not regulated by the outdoor lighting code, even if it is emitting light outside,” Trevillyan says. In some cases, he says, in order to get around the city’s restrictions, businesses have suspended illuminated signs inside buildings but aimed them outside.
Light pollution experts generally say there is no substantial evidence that more light amounts to greater safety.
For cities trying to implement a lighting ordinance, Trevillyan says, the biggest roadblocks they’ll face are “irrelevant” arguments, specifically claims that reducing the brightness of outdoor lighting will cut down on advertising revenue and make the city more vulnerable to crime. The key to successfully enforcing the dark-sky rules, he says, is to educate the public and refuse to give in to people seeking exceptions or exploiting loopholes.
Light pollution experts generally say there is no substantial evidence that more light amounts to greater safety. In Tucson, for example, Barentine says, neither traffic accidents nor crime appeared to increase after the city started dimming its streetlights at night and restricting outdoor lighting in 2017. Last year, researchers at the University of Pennsylvania analyzed crime rates alongside 300,000 streetlight outages over an eight-year period. They concluded there is “little evidence” of any impact on crime rates on the affected streets—in fact, perpetrators seemed to seek out better-lit adjacent streets. Barentine says there is some evidence that “strategically placed lighting” can help decrease traffic collisions. “Beyond that, things get murky pretty quickly,” he says.