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March 2, 2013
Curtis Cooper, UCM Warrensburg, Missouri, Discovers Largest Prime Number Ever Found, GIMPS
Great Internet Mersenne Prime Search GIMPS Finding World Record Primes Since 1996
WARRENSBURG, MO (Jan. 21, 2016) – A University of Central Missouri professor who has been involved in a 20-year-long continuous research project with a global network of individuals using computer processors, has discovered the world’s largest known prime number. It was found on a computer at UCM - Lee’s Summit.
The new number, identified by researchers in the Great Internet Mersenne Prime Search (GIMPS) as 2^74207281 – 1 or M74207281, has more than 22.3 million digits, almost 5 million digits larger than the previous record Mersenne prime claimed by the same UCM research effort led by Curtis Cooper, professor of computer science, in 2013.
Dr. Curtis Cooper
As GIMPS participants, Cooper and faculty member Steven Boone, professor of chemistry, announced their first record prime in 2005, followed by a second discovery in 2006. The University of California-Los Angeles announced the next discovery in 2008, but UCM has claimed the largest number twice since then, giving UCM a total of four record Mersenne prime discoveries.
A prime number is a positive integer greater than one which can only be evenly divided by itself and the number one. The Great Internet Mersenne Prime Search was formed in January 1996 by George Woltman who developed GIMPS’ Prime95 software to find new world record size Mersenne primes, a special class of prime numbers named for French monk Marin Mersenne, who studied them 350 years ago.
The new prime number - which is 74,207,281 twos multiplied together, minus 1 - is only the 49th known Mersenne prime ever identified, each one increasingly more difficult to find, according to GIMPS. This number was actually reported by a UCM computer to the GIMPS database on Sept. 17, 2015. It went unnoticed, however, until Jan. 7, 2016, after some routine data-mining by Aaron Blosser, the GIMPS system administrator. GIMPS then double-, triple-, and quadruple-checked the number on different hardware and software to verify the result before announcing the find, Cooper said.
The discovery makes UCM eligible for a $3,000 GIMPS research discovery award. As an organization, GIMPS’ major goal is to win $150,000 award administered by the Electronic Frontier Foundation to those who are the first to find a 100 million digit Mersenne prime number.
Asked about what the latest find means to Cooper, he said modestly, “I think it means I am very lucky. And, I am privileged to be a part of in the Great Internet Mersenne Prime Search and to have UCM's support that has allowed me to run the GIMPS software on computers in labs across campus.”
Although the discovery of 2^74207281 - 1 as the current largest known prime number has no known application, he noted that there are some side benefits to the search process.
“It shows that distributed computing projects, like GIMPS, can network computers and work toward a common goal. It also helps improve the architecture and hardware of modern computers since the running of the GIMPS software on a computer provides a good stress test for a computer's hardware, and the GIMPS software has recently detected a flaw in Intel's latest Skylake CPUs,” he said. “Finally, the data collected by GIMPS can be used by number theorists to better understand Mersenne primes and prime numbers in general.”
Cooper credits the support from UCM he receives for the GIMPS project for making his recent discovery possible.
“First of all, I am indebted to UCM's Office of Technology for all of their support over the years, which has greatly contributed to the discovery of this Mersenne prime and for all the other Mersenne primes we have found on campus. In particular, I am grateful to Jeff Greene for helping me set-up the server that manages the GIMPS project at UCM and for all of the technical support people, especially the ones who manage computer labs at UCM. They have put my Mersenne user as an administrator on many of the lab computers across campus, both in Warrensburg and in Lee's Summit. In fact, the computer that discovered M74207281 is prime was Computer Number 5 in Room 143 at the University of Central Missouri - Lee's Summit.”
Cooper doesn’t plan to discontinue his research into Mersenne primes anytime in the near future. As he noted, “I will continue to participate in the GIMPS project. I really enjoy the mathematics related to prime numbers and Mersenne primes and I also enjoy the use of computers to find new primes. My wife jokes, but is halfway serious, saying I can't retire from UCM because then I won't be able to use UCM's computers to search for Mersenne primes.”
Painting by Justus van Gent [Public domain], via Wikimedia Commons
Prime numbers—integers that are divisible only by themselves and 1—are the easiest path into understanding both rigor and mysticism in mathematics. Euclid's proof that there is an infinite number of prime numbers is both one of the simplest mathematical proofs and one of the oldest. Late last month, Curtis Cooper of the University of Central Missouri moved one small step closer to Euclid’s infinity, when he announced that 257,885,161-1 is prime. This is now the largest known prime number, eclipsing the previous record-holder, which had been discovered at UCLA in 2008. The new number has 17,425,170 digits—just writing them down makes for a 22.45-megabyte text file. The UCLA number had knocked an earlier number of Cooper's, from 2006, out of the record books. With apologies to the Magnetic Fields, the book of primes is long and boring, but an addition to that book is a good chance to look for the music within it. Cooper and a group at UCLA have been swapping records as part of a common effort called GIMPS, the Great Internet Mersenne Prime Search. Mersenne primes are numbers like 3=22-1 , 7=23-1 or 31=25-1 that are 1 less than a power of 2. The vast majority of such numbers are not prime, but they are good candidates to check for primality nonetheless. All of the 10 largest known primes are Mersenne.
Though mathematicians don't know whether a given large number is prime until they check, the statistical distribution of primes is well understood. It was one of the central problems of 19th-century mathematics. Many giants of mathematical history—Euler, Legendre, Dirichlet, Gauss, and Riemann among them—worked toward a result describing that distribution, which would become known as the Prime Number Theorem. The remarkable thing about many of these efforts is that they created extremely surprising links between discrete questions—how integers behave—and analytic questions—how continuous functions of real numbers act.
Riemann's paper On the Number of Prime Numbers Less Than a Given Quantityis often cited by mathematicians as one of the most significant in the history of the field. (For a lovely and readable popular history of Riemann and his mathematical ideas, pick up a copy ofPrime Obsession; I interviewed the book’s author here.) But Riemann didn't prove the Prime Number Theorem, which places rigorous bounds on where large primes can be found. The proof took until 1896, when Jacques Hadamard and Charles Jean de la Vallée-Poussin, French and Belgian mathematicians respectively, independently proved it.
For decades, the behavior of prime numbers was among the central intellectual and aesthetic questions of mathematics, but not one with great practical import. That changed in the last several decades, after Ron Rivest, Adi Shamir, and Leonard Adelman, a trio of young MIT professors, published a paper describing a new cryptographic algorithm in 1977. Their idea was revolutionary (though it was provoked by an earlier paper of Whitfield Diffie and Martin Hellman, at Stanford). The RSA algorithm (after the initials of Rivest, Shamir, and Adelman) was the first system of public-key cryptography, which makes it easy to encrypt messages, and hard to decrypt them, and is the underpinning of modern e-commerce. It depends on knowledge of large prime numbers. As a practical matter, the numbers used are not normally nearly so large as Cooper's behemoth, which took his computer 39 days to verify as prime, though 3 independent subsequent confirmations took only 3.6, 4.5, and 7.7 days—all still too long to buy something on the Web.
The mathematical fascination with primes comes from how they reveal the hidden structure of the world. Riemann’s paper on primes discussed how their distribution is connected to something that came to be called the Riemann zeta function, which is the subject of Riemann’s hypothesis, probably the most important outstanding problem in mathematics, and the subject of Prime Obsession.
The lure of Riemann’s hypothesis (and of mathematics more generally) is not that solving it would create jobs, or better lasers or computer algorithms. As G.H. Hardy, a British mathematician, wrote, “very little of mathematics is useful practically.” What Hardy, and other mathematicians, are chasing after is a “very high degree of unexpectedness, combined with inevitability and economy.” Or as Hardy also put it: “truth plays odd pranks.” When those pranks, as in the case of RSA, end up being useful, it’s gravy.
The zeta function plays very odd pranks indeed, for example echoing the behavior of large random matrices in ways that leave mathematicians in disbelief. It’s hard to render that disbelief to people who don’t speak mathematics, but it’s something like watching a running back find an elusive line through his opponents’ entire defense to score a touchdown on a long run. But rather than a fugitive moment of aesthetic perfection, the mathematical connections revealed are not a consequence of elaborate rules made by people, but are universal and permanent.
Just finding one large prime number is a fun puzzle to have solved, but it doesn't say anything basic about how the world works. The patterns behind the primes, however, both proven patterns and ones only suspected, are the lens through which humanity can apprehend deep and unfamiliar truths about how reality is structured.
Largest Prime Number Known Is 17-Million Digits Long, Mathematician Says
Curtis Cooper, University of Central Missouri, Prime Number Hunter!
Published: 02/05/2013 11:57 AM EST on LiveScience
The largest prime number yet has been discovered — and it's 17,425,170 digits long. The new prime number crushes the last one discovered in 2008, which was a paltry 12,978,189 digits long.
The number — 2 raised to the 57,885,161 power minus 1 — was discovered by University of Central Missouri mathematician Curtis Cooper as part of a giant network of volunteer computers devoted to finding primes, similar to projects like SETI@Home, which downloads and analyzes radio telescope data in the Search for Extraterrestrial Intelligence (SETI). The network, called the Great Internet Mersenne Prime Search (GIMPS) harnesses about 360,000 processors operating at 150 trillion calculations per second. This is the third prime number discovered by Cooper.
"It's analogous to climbing Mt. Everest," said George Woltman, the retired, Orlando, Fla.-based computer scientist who created GIMPS. "People enjoy it for the challenge of the discovery of finding something that's never been known before."
In addition, the number is the 48th example of a rare class of primes called Mersenne Primes. Mersenne primes take the form of 2 raised to the power of a prime number minus 1. Since they were first described by French monk Marin Mersenne 350 years ago, only 48 of these elusive numbers have been found, including the most recent discovery. [The Most Massive Numbers in the Universe]
After the prime was discovered, it was double-checked by several other researchers using other computers.
While the intuitive way to search for primes would be to divide every potential candidate by every single number smaller than itself, that would be extremely time-consuming, Woltman told LiveScience. "If you were to do it that way it would take longer than theage of the universe," he said.
Instead, mathematicians have devised a much cleverer strategy that dramatically reduces the time to find primes.
The new discovery makes Cooper elligible for a $3,000 GIMPS research discovery award.
Copyright 2013 LiveScience, a TechMediaNetwork company. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.
The newly discovered largest prime number on record has 4,446,981 more digits than its predecessor.
Using an arrangement of powerful computers running trillions of calculations every second, mathematicians have discovered the largest prime number yet. (In case you missed math class: A prime number can only be divided by 1 and itself. So the roster of prime numbers includes 2, 3, 5, 7, 11, 13, 17, and on and on.)
In this case, the behemoth prime number contains 17,425,170 digits and is much too long to repost for the purposes of this article. (You can, however, download the entire 22MB text filehere.)
The number — which is equivalent to 2 multiplied by itself 57,885,161 times, minus 1 — is the first prime number discovered in four years. It belongs to a rare class of numbers called Mersenne primes, which are 2 raised to the power of a prime number minus 1. They were first discovered by a French monk named Marin Mersenne 350 years ago. So far, only 48 of these rare numbers have ever been discovered.
Scientists at the University of Central Missouri, led by mathematician Curtis Cooper, used a powerful network called the Great Internet Mersenne Prime Search (GIMPS), which tapped into 360,000 processors to crunch 150 trillion calculations per second. The GIMPS project is directly responsible for discovering all 14 of the large Mersenne primes we know about.
So what does this new number's discovery mean for mathematics? Well, practically speaking, not much, admit researchers. "It's analogous to climbing Mt. Everest," George Woltman, the retired computer scientist who created GIMPS, tells LiveScience. "People enjoy it for the challenge of the discovery of finding something that's never been known before."
The number was double-checked several times by other researchers not involved in the project. For his discovery, Cooper will be awarded $3,000 by the Electronic Frontier Foundation, which is also offering a $150,000 reward to whoever finds a prime number with 100 million digits, and $250,000 to whoever can crack the billion-digit mark.
It could be a never-ending race, this Great Internet Mersenne Prime Search, known as GIMPS. But as of Wednesday a professor at the University of Central Missouri in Warrensburg has the lead.
Curtis Cooper, a professor of computer science there, has made the most recent discovery of the world’s largest known prime number, it was announced Wednesday.
The new number, 2 multiplied by itself 57,885,161 times, minus 1, has 17,425,170 digits. Primes are numbers that can only be divided by themselves and 1, such as 2, 3, 5, 7 and 11
The latest discovery was made by one of more than 1,000 computers running for 39 days across the campus in Warrensburg. The actual prime number was found by Computer 22, and the university is eligible for a $3,000 GIMPS research discovery award.
In the last seven years the University of Central Missouri has found the largest prime number in the world three times. Cooper and a colleague, Steven Boone, a professor of chemistry, announced their first discovery in 2005 and a second in 2006. The University of California, Los Angeles made the next discovery in 2008.
UCLA got kudos for having found the largest prime for four years until this latest announcement by the University of Central Missouri. It has been the longest period between prime discoveries since the launch of GIMPS, a computing project that has involved tens of thousands of machines since 1996.
Cooper, who was being inundated with telephone calls Wednesday from curious media and congratulatory colleagues, said the new prime number is in a special class of “extremely rare prime numbers known as Mersenne primes.” His is only the 48th known Mersenne prime ever discovered. The GIMPS project has found the last 14 Mersenne primes.
Cooper said that as the primes found get larger, it will take mathematicians longer to discover new ones.
Mathematician: Finding 17M-digit prime number like climbing Everest
Computer that discovered latest Mersenne prime did 57M calculations over 39 days
The mathematician who found the largest known prime number said the discovery last month was like climbing Mount Everest or landing on the moon.
The prime number, which is more than 17 million digits long, won't make computers run faster or help scientists develop better rockets. However, searching for the number was an exhilarating journey for Curtis Cooper, a mathematician at the University of Central Missouri.
If this prime number --2 57,885,161minus 1, or 2 to the power of 57,885,161 minus 1 - was typed out in a standard Times Roman 12-point font, it would span more than 30 miles. It also would fill more than six Bibles.
It is the third prime number discovery he has made, and Cooper said the discovery isn't any less exciting. He said the feat, for a mathematician, was like climbing Mount Everest, because it was a goal he set out to achieve because he wanted to, not because he needed to.
"We've been working on this for years," Cooper told Computerworld. "We probably finish 50, 60 or 70 numbers per day, and for years we didn't find anything. Then on Jan. 25 we hit the jackpot. It's truly like looking for a needle in a haystack."
The Great Internet Mersenne Prime Search (GIMPS), a 16-year-old project that uses a grid of computers provided by volunteers to find large prime numbers, announced Tuesday that Cooper discovered the 48th known Mersenne prime.
A prime number is a whole number that can be divided only by one and itself. A Mersenne prime number is a class of primes named after Marin Mersenne, a 17th century French monk who studied the rare numbers more than 350 years ago.
Mersenne primes are extremely rare. With this discovery, only 48 are known. Each Mersenne prime is increasingly difficult to find.
Mersenne Primes are 2 raised to the x power, minus 1. For instance, the number 3 is a Mersenne prime number because it can be written as 2 squared, minus one. Number 7 is also a Mersenne prime number because it's 2 cubed, minus one.
To find this new Mersenne prime, Cooper used 1,000 computers on his university campus in Warrensburg, Mo. Each computer checked individual numbers. Dual-core machines could check two numbers at once.
The computer that discovered this 17 million-digit prime is a Dell desktop running an Intel dual-core processor. Sitting in the university's modern language lab, the computer spent 39 days running 57 million calculations to test the number.
In 1997, when Cooper and the university first began searching for Mersenne primes, he only had four computers in the project.
"We didn't have a server so I had to watch each machine," he said. "I thought that four computers was about all I could handle. But as we got a server, and a lot of the work was automated and the software got better, we were able to add so many more computers. I really like the process of having a goal in mind and working for that goal. Every morning I wake up and check our machines and see how they're doing. I really just love the process."
To verify the new Mersenne prime number, it was independently tested using different programs running on different hardware, according to the GIMPS organization. One verification test, which lasted 3.6 days, used an Nvidia GPU, and another used an Intel Core i7 CPU and ran for 4.5 days.
Cooper discovered his first record-breaking prime number in 2005. He found the second in 2006.
Mathematicians at UCLA broke Cooper's record in 2008. That record Mersenne prime number held until Cooper and the University of Central Missouri reclaimed it with this latest discovery.
The GIMPS organization will award $3,000 to Cooper, who is donating the money to the university since it provided the computers for his project.
Correction: Due to a production error, the prime number discovered by mathematician Curtis Cooper was incorrectly posted. The number appeared as 257,885,161 minus 1, but should be 257,885,161 minus 1, or 2 to the power of 57,885,161 minus 1. The story has been changed to correct the error.
Sharon Gaudin covers the Internet and Web 2.0, emerging technologies, and desktop and laptop chips for Computerworld. Follow Sharon on is email@example.com.
UCM Professor Discovers World's Largest Known Prime Number
Contact: Mike Greife WARRENSBURG, MO (Feb. 6, 2013) – Curtis Cooper, professor of computer science at the University of Central Missouri, has made the most recent discovery of the world’s largest known prime number, according to information released by the Great Internet Mersenne Prime Number Search, also known as GIMPS.
Curtis Cooper, professor of computer science at the University of Central Missouri, with the computer that made the discovery of the world’s largest known prime number.
The new number, 2 multiplied by itself 57,885, 161 times, minus 1, has 17,425,170 digits. The discovery was made by one of the more than 1,000 computers running for 39 days across the UCM campus. The actual prime number was found by Computer #22 in a computer lab in Wood 210 on the UCM campus at 11:30 p.m. Jan. 25. Following an extensive verification process completed by GIMPS, the newest known prime number was announced Feb. 5. The discovery is eligible for a $3,000 GIMPS research discovery award.
This is the third discovery for Cooper and UCM in the ongoing search for the largest prime number. Cooper and UCM colleague Steven Boone, professor of chemistry, announced their first discovery in 2005, followed by a second in 2006. The University of California-Los Angeles made the next discovery in 2008, followed by UCM’s most recent discovery.
“There are a lot of people on campus to thank,” Curtis said. “I’ve had great support from my department and my department chair, Xiadong Yue, and Dean Alice Greife of the College of Health, Science, and Technology, as well as the technical support from Technology Services and technology coordinators from departments and colleges across the campus. That support is what allowed us to use more than 1,000 computers to make the discovery possible.”
The new prime number is in a special class of extremely rare prime numbers known as Mersenne primes. It is only the 48th known Mersenne prime ever discovered, with each discovery become more difficult to find than the previous one. GIMPS has discovered the last 14 Meresenne primes.
GIMPS was formed in 1996 by George Woltman to discover the new world-record size Mersenne prime numbers. In 1997 Scott Kurowski enabled GIMPS to harness the power of hundreds of thousands of ordinary computers to complete the extraordinary search. Woltman developed the software that allows the massive network of computers to make the search and automatically report findings to GIMPS.
“When we first started working with the project in 1997, we had four computers on campus that we had to monitor individually, and we had to report our findings to GIMPS by email,” Cooper said. “Current technology allows us to undertake the search, and because the numbers are becoming larger with each discovery, it is anticipated that future discoveries will take longer.”
Learn more about the GIMPS and the world’s largest prime number search at www.mersenne.org.
Read more here: http://www.kansascity.com/2013/02/06/4052510/central-missouri-claims-largest.html#storylink=cpy