The largest known prime number is now almost 5 million digits longer than the previous record-holder.
In a computer laboratory at a satellite campus of the University of Central Missouri, an otherwise nondescript desktop computer, machine No. 5 in room 143, multiplied 74,207,281 by itself and subtracted 1. It then checked that this number was not divisible by any positive integer except 1 and itself — the definition of a prime number.
This immense number can only be practically written down in mathematical notation using exponents: 74,207,2812-1.
The previous largest was 57,885,1612-1, which has a mere 17 million or so digits.
It is the 15th prime number found by the Great Internet Mersenne Prime Search (GIMPS), a volunteer project that has been running for 20 years.
“I’ve always been interested in prime numbers,” said George Woltman, who founded GIMPS after he retired. “I had a lot of time on my hands.”
Mersenne primes are those that can be written in the form n2-1, where n is an integer. They are named after Marin Mersenne, a French theologian and mathematician who studied them in the early 17th century.
For example, 3 is a Mersenne prime. Plug in 2 for n and you find 22-1=3.
However, not all integers plugged into the expression generate a prime number. Put in 4 and the result is 15, which is not a prime number, because 15 is divisible by 3 and 5.
As integers get bigger, prime numbers become rarer, but there is always a bigger prime number to be found. It is just much harder to find. In total, only 49 Mersenne primes are known.
GIMPS takes advantage of otherwise idle computers. Volunteers download free software that runs unobtrusively when no one is using the computer.
At the University of Central Missouri, math professor Curtis Cooper was one of the early enthusiasts, joining GIMPS in 1997. He has the program installed on 800 PCs on the university’s two campuses. Cooper does research in the mathematical realm of number theory and teaches computer science classes.
“This kind of marries the two fields together,” he said.
The university’s computers had previously turned up three other Mersenne primes, most recently in 2013.
PC No. 5 in room 143 churned for 31 days before completing its calculation that 74,207,2812-1 is a prime. It dutifully reported the result on Sept. 17 last year to a computer server in Seattle that coordinates the worldwide GIMPS effort.
No one noticed.
Because of a glitch on the server, e-mails that should have been sent to Cooper and GIMPS administrators were never sent. The discovery remained unknown until Jan. 7, when Aaron Blosser, the administrator of the server, came across it during routine maintenance. He verified it on a much faster computer and notified Cooper two days later.
After further checking, the new finding was announced publicly on Tuesday.
Prime numbers are crucial to fields such as cryptography, but this one is so big that it has no practical use, at least not anytime soon.
The GIMPS software does have a practical use. It played a key role in uncovering a flaw in Intel’s latest Skylake processors.
How big is this new prime number? If you had enough paper and ink — and made the impossible assumption that your hand could maintain the pace — it would take me more than three months to write down the 22,338,618 digits of 74,207,2812-1.
Printing it out could fill 6,000 to 7,000 sheets of paper, depending on the font size.
Cooper said that the PC would be set aside for posterity.
“It’s kind of a dumb computer,” he said. “It doesn’t know it’s so popular.”
Nearly half of China’s major cities are suffering “moderate to severe” levels of subsidence, putting millions of people at risk of flooding, especially as sea levels rise, according to a study of nationwide satellite data released yesterday. The authors of the paper, published by the journal Science, found that 45 percent of China’s urban land was sinking faster than 3mm per year, with 16 percent at more than 10mm per year, driven not only by declining water tables, but also the sheer weight of the built environment. With China’s urban population already in excess of 900 million people, “even a small portion
UNSETTLING IMAGES: The scene took place in front of TV crews covering the Trump trial, with a CNN anchor calling it an ‘emotional and unbelievably disturbing moment’ A man who doused himself in an accelerant and set himself on fire outside the courthouse where former US president Donald Trump is on trial has died, police said yesterday. The New York City Police Department (NYPD) said the man was declared dead by staff at an area hospital. The man was in Collect Pond Park at about 1:30pm on Friday when he took out pamphlets espousing conspiracy theories, tossed them around, then doused himself in an accelerant and set himself on fire, officials and witnesses said. A large number of police officers were nearby when it happened. Some officers and bystanders rushed
HYPOCRISY? The Chinese Ministry of Foreign Affairs yesterday asked whether Biden was talking about China or the US when he used the word ‘xenophobic’ US President Joe Biden on Wednesday called for a hike in steel tariffs on China, accusing Beijing of cheating as he spoke at a campaign event in Pennsylvania. Biden accused China of xenophobia, too, in a speech to union members in Pittsburgh. “They’re not competing, they’re cheating. They’re cheating and we’ve seen the damage here in America,” Biden said. Chinese steel companies “don’t need to worry about making a profit because the Chinese government is subsidizing them so heavily,” he said. Biden said he had called for the US Trade Representative to triple the tariff rates for Chinese steel and aluminum if Beijing was
Beijing is continuing to commit genocide and crimes against humanity against Uyghurs and other Muslim minorities in its western Xinjiang province, U.S. Secretary of State Antony Blinken said in a report published on Monday, ahead of his planned visit to China this week. The State Department’s annual human rights report, which documents abuses recorded all over the world during the previous calendar year, repeated language from previous years on the treatment of Muslims in Xinjiang, but the publication raises the issue ahead of delicate talks, including on the war in Ukraine and global trade, between the top U.S. diplomat and Chinese