48th Known Mersenne Prime Found!

[NeoGen]

GIMPS Project Discovers
Largest Known Prime Number, 2^57,885,161-1

ORLANDO, Florida -- On January 25th at 23:30:26 UTC, the largest known prime number, 2^57,885,161-1, was discovered on Great Internet Mersenne Prime Search (GIMPS) volunteer Curtis Cooper's computer. The new prime number, 2 multiplied by itself 57,885,161 times, less one, has 17,425,170 digits. With 360,000 CPUs peaking at 150 trillion calculations per second, 17th-year GIMPS is the longest continuously-running global "grassroots supercomputing"[1] project in Internet history.

Dr. Cooper is a professor at the University of Central Missouri. This is the third record prime for Dr. Cooper and his University. Their first record prime was discovered in 2005, eclipsed by their second record in 2006. Computers at UCLA broke that record in 2008 with a 12,978,189 digit prime number. UCLA held the record until University of Central Missouri reclaimed the world record with this discovery. The new primality proof took 39 days of non-stop computing on one of the university's PCs. Dr. Cooper and the University of Central Missouri are the largest individual contributors to the project. The discovery is eligible for a $3,000 GIMPS research discovery award.

The new prime number is a member of a special class of extremely rare prime numbers known as Mersenne primes. It is only the 48th known Mersenne prime ever discovered, each increasingly difficult to find. Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. GIMPS, founded in 1996, has discovered all 14 of the largest known Mersenne primes. Volunteers download a free program to search for these primes with a cash award offered to anyone lucky enough to compute a new prime. Chris Caldwell maintains an authoritative web site on the largest known primes as well as the history of Mersenne primes.

To prove there were no errors in the prime discovery process, the new prime was independently verified using different programs running on different hardware. Serge Batalov ran Ernst Mayer's MLucas software on a 32-core server in 6 days (resource donated by Novartis[2] IT group) to verify the new prime. Jerry Hallett verified the prime using the CUDALucas software running on a NVidia GPU in 3.6 days. Finally, Dr. Jeff Gilchrist verified the find using the GIMPS software on an Intel i7 CPU in 4.5 days and the CUDALucas program on a NVidia GTX 560 Ti in 7.7 days.

GIMPS software was developed by founder, George Woltman, in Orlando, Florida. Scott Kurowski, in San Diego, California, wrote and maintains the PrimeNet system that coordinates all the GIMPS clients. Volunteers have a chance to earn research discovery awards of $3,000 or $50,000 if their computer discovers a new Mersenne prime. GIMPS' next major goal is to win the $150,000 award administered by the Electronic Frontier Foundation offered for finding a 100 million digit prime number.

Credit for GIMPS' prime discoveries goes not only to Dr. Cooper for running the software on his University's computers, Woltman and Kurowski for authoring the software and running the project, but also the thousands of GIMPS volunteers that sifted through millions of non-prime candidates. Therefore, official credit for this discovery shall go to "C. Cooper, G. Woltman, S. Kurowski, et al."


(press release here: http://www.mersenne.org/various/57885161.htm)

[vaughan]

WASHINGTON: Prime numbers - integers that are divisible only by themselves and 1 - are the easiest path into understanding both rigour 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 2 to the 57,885,161th minus 1 is prime.

This is now the largest known prime number, eclipsing the previous record-holder, which had been discovered at UCLA in 2008.
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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=2 to the second minus 1 , 7=2 to the third minus 1 or 31=2 to the fifth minus 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 Quantity is 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 of Prime Obsession).

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 Valle-Poussin, French and Belgian mathematicians respectively, independently proved it.

For decades, the behavioUr 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. 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.

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.

Read more: http://www.smh.com.au/technology/tec...#ixzz2KMu0kL8v

[Brucifer]

That is a *huge* prime number!!! Sure eclipes any of the ones that I have found! :-) So while I'm not famous, lol, at least I've found a few -- which doesn't change the price of coffee but it was fun. :-)