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Mathematica 8 Released

Today, Wolfram Research released Mathematica 8, the newest version of its powerful technical computing software.

47th (and Second-Largest) Known Mersenne Prime Announced

Join us for the first annual Wolfram|Alpha Homework Day on Wednesday October 21, 2009. This live, interactive web event will showcase how Wolfram|Alpha is helping students, parents, and educators solve problems and illuminate knowledge. Learn more on http://homeworkday.wolframalpha.com.

47th (and Second-Largest) Known Mersenne Prime Announced

A new Mersenne prime was reported to the GIMPS server in April, but not noticed until now due to a configuration issue on the server. The discovery has now been verified and officially announced as M42643801, which has 12837064 decimal digits, making it the 46th known Mersenne prime ranked by size, and hence only the second largest. The prime was discovered by Norwegian GIMPS participant Odd Magnar Strindmo.

47th Known Mersenne Prime Apparently Discovered

A new Mersenne prime was reported to the GIMPS server in April, but not noticed until now due to a configuration issue on the server. GIMPS organizer Woltman has verified that the last save file is valid, so the reported discovery appears to be real. Verification and announcement of the value will follow shortly.

Mathematica 7 Released

Today, Wolfram Research released Mathematica 7, the newest version of its powerful technical computing software.

45th and 46th Mersenne Primes Discovered

Two years after the 44th known Mersenne prime was reported (MathWorldheadline news, September 11, 2006), the GIMPS project has discovered the 45th and 46th known Mersenne primes: 2^37156667 - 1 and 2^43112609 - 1. The discoveries were made by Edson Smith on August 23, 2008 (for the larger prime) and Hans-Michael Elvenich on September 6, 2008 (for the smaller prime), and announced by GIMPS organizer George Woltman on September 16. The new Mersenne primes have 11,185,272 and 12,978,189 decimal digits, making them not only the largest Mersenne primes known, but also the largest known primes of any type. The first discovered (and largest) of these prime also earns its finders a $100,000 prize from the Electronic Frontier Foundation for the discovery of a prime number with 10 million or more digits.

Two New Mersenne Primes Apparently Discovered

A new Mersenne prime was reported to the GIMPS server on August 23, 2008. This prime was confirmed by Septempber 6, though its value has not yet ben revealed pending independent verification using a different program on a different computer architecture. More amazingly still, during the period required for the first verification of the recently reported new prime a second new Mersenne prime was reported and is currently being verified.

New Mersenne Prime Apparently Discovered

A new Mersenne prime was reported to the GIMPS server on August 23. GIMPS organizer Woltman has asked the finder to send the last save file, so it should very soon be known with more than 99% certainty if the reported discovery is true.

A New Look and New Features for MathWorld

While MathWorld continues to be the most popular and most visited mathematics sites on the internet, and while its mathematical content continues to steadily grow and expand, MathWorld readers will notice more immediate visual changes the next time they visit the site. Design changes and major new pieces of functionality are generally years in the making for large informational websites like MathWorld. The last time the site received a major upgrade to its infrastructure was in July of 2005. On Friday of last week, we introduced a major update of the MathWorld site featuring improved navigation, higher-quality typesetting, and links to interactive demonstrations. I encourage you to visite the updated site and enjoy the beneifts that the new look and associated functionality provide.

NUMB3RS Season 4 Premier to Air Friday, September 28 at 10pm ET on CBS

Wolfram Research is pleased to partner with CBS in promoting math awareness through NUMB3RS. As the world's leading producer of software for mathematical and scientific computation, Wolfram Research is dedicated to spreading our passion for mathematics and computation throughout the globe. Members of Wolfram's R&D staff provide NUMB3RS with real math to support each episode of the show. Just as it is used in so many of today's real-world scientific and technological innovations, our flagship product Mathematica is also used to create the math behind NUMB3RS.

The Wolfram 2,3 Turing Machine Research Prize

A universal Turing machine is powerful enough to emulate any standard computer. The question is: how simple can the rules for a universal Turing machine be? Since the 1960s it has been known that there is a universal 7,4 machine. In A New Kind of Science, Stephen Wolfram found a universal 2,5 machine, and suggested that the particular 2,3 machine that is the subject of this prize might be universal. The prize is for determining whether or not the 2,3 machine is in fact universal.

The Math(ematica) behind Television's Crime Drama NUMB3RS

Viewers of prime time television will likely be quite familiar with police chases, blood-stained bodies, and massive explosions. What they may be less familiar with is a protagonist whose job title is "math professor" and who uses crime investigation techniques that delve deep into mathematical concepts and equations. Nevertheless, that's exactly what viewers are likely to find on the CBS Paramount television crime drama NUMB3RS, which airs at 10 p.m. U.S. Eastern on Fridays. Even before the show first premiered in January 2005, a group of researchers at Wolfram Research has been part of the core group of advisers who assist with all aspects of the the mathematics in the show. NUMB3RS remains one of the most popular programs on television, and its co-creators Nick Falacci and Cheryl Heuton have been the recipients of a number of prestigious awards for science communication to a general audience. Most recently, Nick and Cheryl were honored with a Public Service Award from the National Science Board, presented at the U.S. State Department diplomatic reception rooms in Washington, DC on May 14. We at Wolfram Research count ourselves fortunate to be primary consultants for NUMB3RS, and more fortunate still to have been invited by Cheryl to attend and take part in the award presentation.

Mathematica 6 and The Wolfram Demonstrations Project Launched

As many of you have probably noticed on the pages of MathWorld, a number of exciting new things have happened in the last few days that may be of special interest to you. The first is the long-awaited release of Mathematica 6. For MathWorld readers who may not need to harness the full computational power of Mathematica themselves but may still be interested in the computations and visualizations it can produce, the new Wolfram Demonstrations Project (http://demonstrations.wolfram.com), unveiled in conjunction with the release of Mathematica 6, contains more than a thousand interactive Demonstrations built with Mathematica.

Record Twin Prime Discovered

The largest known twin prime pair found to date was discovered today through the Twin Internet Prime Search and PrimeGrid distributed computation projects. The new twins are 2003,663,613 2^195000 +/- 1, each of which has 58711 decimal digits.

44th Mersenne Prime Found

Less than a year after the 43rd known Mersenne prime was reported (MathWorldheadline news, December 25, 2005), the GIMPS project has discovered the 44th known Mersenne prime: 2^32582657 - 1. The discovery was made by Dr. Curtis Cooper and Dr. Steven Boone on September 4, tentatively announced by GIMPS organizer George Woltman on September 4, and independently verified by Tony Reix on September 11. The new Mersenne prime has 9808358 decimal digits, making it not only the largest Mersenne prime known, but also the largest known prime of any type.

44th Mersenne Prime (Probably) Found

Less than a year after the 43rd known Mersenne prime was reported (MathWorld headline news, December 25, 2005), GIMPS project organizer George Woltman is reporting in an email message that a new Mersenne prime has been reported to the GIMPS server. A verification run on the number has been started, and more details will be made public when verification of the discovery has been completed.

Lennart Carleson Receives 2006 Abel Prize

The Norwegian Academy of Science and Letters has awarded the 2006 Abel Prize to Lennart Carleson of Royal Institute of Technology, Sweden. Carleson received the Abel Prize for his contributions to harmonic analysis and the theory of smooth dynamical systems. King Harald of Norway will present the Abel Prize to Lennart Carleson at an award ceremony in Oslo on May 23.

43rd Mersenne Prime Found

Less than a year after the 42nd known Mersenne prime was reported (MathWorld headline news, February 26, 2005), the GIMPS project has discovered the 43rd known Mersenne prime: 2^30402457 - 1. The discovery was made by Drs. Curtis Cooper and Steven Boone, professors at Central Missouri State University on December 15, tentatively announced by GIMPS organizer George Woltman on December 19, and independently verified by Tony Reix on December 25. The new Mersenne prime has 9,152,052 decimal digits, making it not only the largest Mersenne prime known, but also the largest known prime of any type.

43rd Mersenne Prime (Probably) Found

Less than a year after the 42nd known Mersenne prime was reported (MathWorld headline news, February 26, 2005), GIMPS project organizer George Woltman is reporting in an email message that a new Mersenne prime has been reported to the GIMPS server. A verification run on the number has been started, and will take a week or two to complete. The potential prime was identified by an experienced GIMPS participant and no errors were reported during the run, so it seems likely that a new Mersenne prime has indeed been found. While the exponent of the potential prime has not yet been revealed, it has has fewer than ten million digits.

RSA-640 Factored

A team at the German Federal Agency for Information Technology Security (BSI) recently announced the factorization of the 193-digit number known as RSA-640. The team responsible for this factorization is the same one that previously factored the 174-digit number known as RSA-576 and the 200-digit number known as RSA-200. While RSA-640 has slightly fewer digits than the previously factored RSA-200, its factorization carries the additional benefit of a cash reward of $20,000 awarded by RSA Laboratories as part of RSA's program to encourage research into computational number theory and the practical difficulty of factoring large integers.

Springer Publishes The Mathematica GuideBooks

After a nearly 15-year wait, the complete 4-volume set of Michael Trott's definitive Mathematica GuideBooks> is now available. Described as a unique tour de force by prominent mathematicians, physicists, and visualization experts, the GuideBooks deal with educational, current research, and recreational problems from mathematics, computer science, computer graphics, and physics. The Mathematica GuideBooks are true mathematical gems. Overflowing with beautiful results, extensive literature references, and stunning graphics, these books provide a fascinating glimpse into the power of computational mathematics.

WolframTones Launched by Wolfram Research

A new system of computer-generated music known as WolframTones has been launched by Wolfram Research. WolframTones works by taking simple programs in the form of cellular automata and using music theory and Mathematica algorithms to render them as music. Each program can be viewed as defining a virtual world and WolframTones captures that computational world as a musical composition.

MathWorld Introduces New Interactive Features for Teachers and Students

Wolfram Research and the MathWorld team are pleased to announce the unveiling of a number of exciting new features on the MathWorld website. These innovative features--including the new MathWorld Classroom, interactive entries, a streamlined comment system, and improved equation formatting--represent a major update of the site that enhance the usability, interactivity, and navigability of the website. We hope you enjoy these new features, and also that you continue to use and rely on MathWorld as an important resource in your mathematical explorations.

RSA-200 Factored

A team at the German Federal Agency for Information Technology Security (BIS) has announced the factorization of the 200-digit number known as RSA-200. The team responsible for this factorization is the same one that previously factored the 174-digit number known as RSA-576 (MathWorld headline news, December 5, 2003). While RSA-200 is a much smaller number than the 7,816,230-digit monster Mersenne prime known as M42 (the largest prime number known), its factorization is significant because the RSA-numbers serve as benchmarks for users of the RSA public-key cryptography algorithm in choosing suitable key lengths that provide an appropriate level of security for data encryption.

Peter Lax Receives 2005 Abel Prize

The 2005 Abel Prize in mathematics has been awarded to Peter D. Lax for his groundbreaking contributions to the theory and application of partial differential equations and the computation of solitons. The Abel prize is a mathematics prize of the Norwegian Academy of Science and Letters that is modeled after the Nobel Prize and has been awarded annually beginning in the year 2003.

42nd Mersenne Prime Found

Less than a year after the 41st known Mersenne prime was reported (MathWorld headline news, June 1, 2004), the GIMPS project has discovered the 42nd known Mersenne prime: 2^2596495 - 1. The discovery was tentatively announced by GIMPS organizer George Woltman on February 18, independently verified by Tony Reix on February 25, and the exponent was reported on February 26. The new Mersenne prime has 7,816,230 decimal digits, making it not only the largest Mersenne prime known, but also the largest known prime of any type.

42nd Mersenne Prime (Probably) Discovered

Less than a year after the 41st known Mersenne prime was reported (MathWorld headline news, June 1, 2004), GIMPS project organizer George Woltman is reporting in an email message that a new Mersenne prime has been reported to the GIMPS server. Addendum: As of February 25, the new Mersenne prime has been verified. More details will be provided as they become available.

The Mathematics of Tsunamis

The recent tragic events following the December 2004 magnitude 9.0 earthquake in the Indian Ocean have reminded us of the need for scientific understanding and modeling of complicated physical phenomena in order to prevent unnecessary loss of life from natural disasters. Here we model and visualize a tsunami by solving the shallow water wave equations using Mathematica.

Seven Mathematical Tidbits

While the last several months have not been filled with any particularly earth-shattering new mathematical results, a number of interesting events, findings, and mathematical books have recently appeared. Here is a recap of some of them, including a birthday, some very odd numbers, a whole lot of nothing, two new books, and major milestones for two mathematical websites.

Mathematica's Google Aptitude

Google makes use of unusual mathematically oriented recruiting techniques. These techniques have received additional coverage in the last few weeks and months following the erection of a mathematical billboard in Silicon Valley in July. Google followed their unusual billboard with a math-intensive Google Labs Aptitude Test. Mathematica clearly shows its extremely high mathematical aptitude by easily solving most of these questions, especially when guided by a little research on MathWorld.

Show Your Math Savvy with a MathWorld T-Shirt

You can now sport an elegant, mathematical look by donning a T-shirt bearing the MathWorld logo. The new MathWorld shirt is a short-sleeve white T-shirt made of 100% cotton adorned with attractive mathematical graphics. The T-shirts come in medium, large, X-large, and youth medium sizes, and are available for purchase from the Wolfram Worldwide Web Store (http://store.wolfram.com/view/misc/). In other news, Ed Pegg, Jr. has recently joined the MathWorld team, and a new RSS newsfeed is now in place for more convenient reading of MathWorld Headline News.

Wolfram Technology Conference 2004 to Be Held October 21-23 in Champaign, Illinois

The 2004 Wolfram Technology Conference invites authors, students, educators, and developers who use Mathematica and other Wolfram products to participate. This year's conference will include contributed talks, a new student presentation forum, an art gallery, tutorials, hands-on workshops, and problem-solving clinics.

Twin Prime Proof Proffered

A May 26 preprint by Vanderbilt University mathematician R. F. Arenstorf appears to come close to settling the long-standing question of the infinitude of twin primes. While a hole has recently been found in the proof, mathematicians remain hopeful that the proof can be corrected.

Riemann Hypothesis "Proof" Much Ado About Nothing

A June 8 Purdue University news release reports a proof of the Riemann Hypothesis by L. de Branges. However, both the 23-page preprint (from 2003) cited in the original release and a 124-page preprint (from 2004) cited in a back-dated modified release seem to lack an actual proof. Furthermore, a counterexample to de Branges's approach by Conrey and Li has been known since 1998. The media coverage therefore appears to be much ado about nothing.

41st Mersenne Prime Announced

Josh Findley, a participant in the Great Internet Mersenne Prime Search (GIMPS), identified the 41st known Mersenne Prime on the morning of May 15. The discovery was confirmed on May 29, making 2^24036583 - 1 the largest known Mersenne prime, as well as the largest prime number known.