The Official MathGeek Blog

NEW MERSENNE PRIME FOUND!

Lightning strikes twice. On September 4, 2006, in the same room just a few feet away from their last find, Dr. Curtis Cooper and Dr. Steven Boone's CMSU team broke their own world record, discovering the 44th known Mersenne prime, 2^32,582,657-1. The new prime at 9,808,358 digits is 650,000 digits larger than their previous record prime found last December. However, the new prime falls short of the 10 million digits required for GIMPS to claim the Electronic Frontier Foundation $100,000 award.

With five record primes found in less than 3 years, GIMPS has been on an incredible lucky streak. Never before have Mersenne primes been bunched so closely together. When looking at the exponents, we expect only 1.78 Mersenne primes between powers of two, and prior to 2003, a maximum of 3 Mersenne primes were found between powers of two. The last 5 Mersenne prime exponents all fell between 2²⁴ and 2²⁵ -- and we haven't finished testing all the exponents in that range!

The new prime was independently verified in 6 days by Tony Reix of Bull S.A. in Grenoble, France using 16 Itanium2 1.5 GHz CPUs of a Bull NovaScale 6160 HPC at Bull Grenoble Research Center, running the Glucas program by Guillermo Ballester Valor of Granada, Spain.  More...

Prime Number Posters!

For years Perfectly Scientific Inc. has been producing high quality posters of the largest currently known prime number. Each poster is printed on thick glossy paper and measures 29 inches by 40 inches. Framed and unframed posters dating back to June of 1999 are available for purchase. Prices vary, as each new prime tests the limits of the technology necessary to print these high-resolution posters. The digits are very clear, but unless you have very, very good eyesight, you will need one of their watchmaker's loupes or an equivalent magnifier to read the digits.  More...

Prime Numbers Get Hitched

In their search for patterns, mathematicians have uncovered unlikely connections between prime numbers and quantum physics. Will the subatomic world help reveal the elusive nature of the primes?

In 1972, the physicist Freeman Dyson wrote an article called "Missed Opportunities." In it, he describes how relativity could have been discovered many years before Einstein announced his findings if mathematicians in places like Göttingen had spoken to physicists who were poring over Maxwell's equations describing electromagnetism. The ingredients were there in 1865 to make the breakthrough—only announced by Einstein some 40 years later.

It is striking that Dyson should have written about scientific ships passing in the night. Shortly after he published the piece, he was responsible for an abrupt collision between physics and mathematics that produced one of the most remarkable scientific ideas of the last half century: that quantum physics and prime numbers are inextricably linked.

This unexpected connection with physics has given us a glimpse of the mathematics that might, ultimately, reveal the secret of these enigmatic numbers. At first the link seemed rather tenuous. But the important role played by the number 42 has recently persuaded even the deepest skeptics that the subatomic world might hold the key to one of the greatest unsolved problems in mathematics.  More...

Partitions and Primes

A proof brings closure to a dramatic tale of partitions and primes

In the realm of mathematics, it's hard to imagine anything more basic than the counting numbers: 1, 2, 3, and so on. Yet this set of mathematical objects abounds with beautiful and unexpected patterns. For example, pick any number and double it. You'll always find a prime number—a number divisible only by itself and by 1—between that number and its double. As another case in point, primes that leave a remainder of 1 when divided by 4 can always be expressed as the sum of two squares. Now, a mathematics graduate student has put what may be the final piece into the picture of one of the most surprising patterns of all.  More...

43rd Known Mersenne Prime Found!!

ORLANDO, Florida - December 24, 2005 -- A collaborative effort at Central Missouri State University (CMSU), led by professors Curtis Cooper and Steven Boone, has discovered the largest known prime number as part of the volunteer Great Internet Mersenne Prime Search (GIMPS) project. It is an achievement that also fuels researchers' hopes around the globe that a $100,000 prize is within reach.

The CMSU faculty used idle time on 700 campus lab PCs and free software from www.mersenne.org as part of a world-wide computing grid of tens of thousands of computers working together to make this discovery. The software was developed by GIMPS founder, George Woltman, in Orlando, Florida, and grid computing pioneer Scott Kurowski, in San Diego, California.

The new prime number, known as M30402457, surfaced December 15th on one computer in the Department of Communication lab after running on and off for about 50 days. Dr. Cooper and Dr. Boone have joined together with 21,000 other researchers worldwide participating in GIMPS. In addition to pursuing new prime number discoveries, these individuals also have an opportunity to compete for a cash award offered by the Electronic Frontier Foundation for discovery of the first 10 million digit prime number. If GIMPS claims the $100,000 award, of which $25,000 will go to charity, a large portion will be given to the GIMPS participant that discovers the prime number.

CMSU's research team has come the closest to claiming the award with this discovery of M30402457, or 2 to the 30,402,457th power minus 1, which is a 9,152,052 digit number. It is the largest known prime number, eclipsing GIMPS last discovery of a 7,816,230 digit prime in February 2005. The new prime was independently verified in 5 days by Tony Reix of Bull S.A. in Grenoble, France using 16 Itanium2 1.5 GHz CPUs of a Bull NovaScale 6160 HPC at Bull Grenoble Research Center, running the Glucas program by Guillermo Ballester Valor of Granada, Spain. A second verification was done by Jeff Gilchrist of SHARCNET.

The new prime is the 43rd discovery in a special class of rare prime numbers known as Mersenne primes, named for French monk Marin Mersenne, who studied these numbers more than 350 years ago.