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12-30-2005, 07:17 AM

Largest Known Prime Number Discovered at CMSU,

Giving Hope that $100,000 Award is Within Grasp

WARRENSBURG, MO (Dec. 24, 2005) - A collaborative effort at Central Missouri State University has led to the discovery of the largest known prime number. It is an achievement that also fuels researchers' hopes across the globe that a $100,000 prize is within reach.

The discovery of the new number known as M30402457 was made in December by CMSU faculty members who have joined about 21,000 other researchers worldwide to participate in the Great Internet Mersenne Prime Search (GIMPS). In addition to pursuing new prime number discoveries, these individuals also have an opportunity to compete for a monetary award offered by the Electronic Frontier Foundation. The award, of which $25,000 will go to charity and a portion for prime number research, will be given to the first GIMPS participant to discover a

10 million-digit prime.

CMSU's research team, led by professors Curtis Cooper, computer science, and Steven Boone, chemistry, has come the closest to claiming the award with the discovery of a 9.1 million-digit number expressed as M30402457 or, otherwise, 2 to the 30,402,457th power minus 1. It is the largest known prime number that has been found since the discovery of a 7.8 million-digit prime by GIMPS in February 2005. CMSU's discovery was made in the Department of Communication computer lab Dec. 15, using a free GIMPS software program that ran on and off for about 50 days.

The number discovered at CMSU 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 300 years ago. A prime number is a positive integer that can only be evenly divided by itself or the number 1. The prime number, 13, for example, can only be divided by two positive integer factors, 1 and 13.

George Woltman, who founded GIMPS in 1996, said Mersenne primes today are most relevant to number theory. He added, however, most GIMPS participants study them for the fun of having a role in real research and the chance of finding a new Mersenne prime.

"While we think we understand the frequency and distribution of Mersenne primes, it has not been proven. Finds such as this one give us 'another piece of the puzzle' in confirming our theories," Woltman said.

He noted that in the past Mersenne prime searches have led to important advances in Fast Fourier Transforms (used in countless applications) as well as discovering computer hardware problems via rigorous stress testing.

"The research project also promotes interest in math by capturing the imagination of younger participants," Woltman said.

CMSU President Aaron Podolefsky praised the collaborative spirit that has contributed to the discovery of the new prime number. He noted that the discovery of M30402457 demonstrates how a regional university can contribute to national research at the same level as some more well-known research colleges and universities.

Involvement in this worldwide research project is enormous. The 700 computers involved on campus are part of an international grid of about 70,000 networked computers in virtually every time zone of the world. All are using the free software that is provided via the Internet by Woltman and Scott Kurowski, who developed the PrimeNet system that runs GIMPS from San Diego.

PrimeNet pulls together hundreds of thousands of computers in parallel to create a virtual supercomputer running at 18 trillion calculations per second, or 'teraflops.' This greatly accelerates the GIMPS research. A study that would have taken 4,500 years on a single PC can be completed in a matter of months.

"We've worked with Information Services to make sure we are not compromising the campus computing infrastructure," said Cooper, who got interested in this project about 10 years ago with colleague Vince Edmondson. Edmondson, professor of mathematics, was instrumental in the campus effort until he passed away in 2003.

"We owe a lot to all of the people on campus who have helped with this project," Boone added.

Ed Davenport, chair of CMSU's Department of Mathematics and Computer Science, recalled how the campus honored Edmondson's work on the project by planting three trees in front of the W.C. Morris Science Building. Three is the first Mersenne prime.

"I don't know if the university can handle planting the number of trees to denote this Mersenne prime," he said jokingly.

More information about CMSU's GIMPS team can be found on the web at http://www.math-cs.cmsu.edu/~gimps/. People who want to know more about the Mersenne prime can also check out http://mersenne.org.

Giving Hope that $100,000 Award is Within Grasp

WARRENSBURG, MO (Dec. 24, 2005) - A collaborative effort at Central Missouri State University has led to the discovery of the largest known prime number. It is an achievement that also fuels researchers' hopes across the globe that a $100,000 prize is within reach.

The discovery of the new number known as M30402457 was made in December by CMSU faculty members who have joined about 21,000 other researchers worldwide to participate in the Great Internet Mersenne Prime Search (GIMPS). In addition to pursuing new prime number discoveries, these individuals also have an opportunity to compete for a monetary award offered by the Electronic Frontier Foundation. The award, of which $25,000 will go to charity and a portion for prime number research, will be given to the first GIMPS participant to discover a

10 million-digit prime.

CMSU's research team, led by professors Curtis Cooper, computer science, and Steven Boone, chemistry, has come the closest to claiming the award with the discovery of a 9.1 million-digit number expressed as M30402457 or, otherwise, 2 to the 30,402,457th power minus 1. It is the largest known prime number that has been found since the discovery of a 7.8 million-digit prime by GIMPS in February 2005. CMSU's discovery was made in the Department of Communication computer lab Dec. 15, using a free GIMPS software program that ran on and off for about 50 days.

The number discovered at CMSU 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 300 years ago. A prime number is a positive integer that can only be evenly divided by itself or the number 1. The prime number, 13, for example, can only be divided by two positive integer factors, 1 and 13.

George Woltman, who founded GIMPS in 1996, said Mersenne primes today are most relevant to number theory. He added, however, most GIMPS participants study them for the fun of having a role in real research and the chance of finding a new Mersenne prime.

"While we think we understand the frequency and distribution of Mersenne primes, it has not been proven. Finds such as this one give us 'another piece of the puzzle' in confirming our theories," Woltman said.

He noted that in the past Mersenne prime searches have led to important advances in Fast Fourier Transforms (used in countless applications) as well as discovering computer hardware problems via rigorous stress testing.

"The research project also promotes interest in math by capturing the imagination of younger participants," Woltman said.

CMSU President Aaron Podolefsky praised the collaborative spirit that has contributed to the discovery of the new prime number. He noted that the discovery of M30402457 demonstrates how a regional university can contribute to national research at the same level as some more well-known research colleges and universities.

Involvement in this worldwide research project is enormous. The 700 computers involved on campus are part of an international grid of about 70,000 networked computers in virtually every time zone of the world. All are using the free software that is provided via the Internet by Woltman and Scott Kurowski, who developed the PrimeNet system that runs GIMPS from San Diego.

PrimeNet pulls together hundreds of thousands of computers in parallel to create a virtual supercomputer running at 18 trillion calculations per second, or 'teraflops.' This greatly accelerates the GIMPS research. A study that would have taken 4,500 years on a single PC can be completed in a matter of months.

"We've worked with Information Services to make sure we are not compromising the campus computing infrastructure," said Cooper, who got interested in this project about 10 years ago with colleague Vince Edmondson. Edmondson, professor of mathematics, was instrumental in the campus effort until he passed away in 2003.

"We owe a lot to all of the people on campus who have helped with this project," Boone added.

Ed Davenport, chair of CMSU's Department of Mathematics and Computer Science, recalled how the campus honored Edmondson's work on the project by planting three trees in front of the W.C. Morris Science Building. Three is the first Mersenne prime.

"I don't know if the university can handle planting the number of trees to denote this Mersenne prime," he said jokingly.

More information about CMSU's GIMPS team can be found on the web at http://www.math-cs.cmsu.edu/~gimps/. People who want to know more about the Mersenne prime can also check out http://mersenne.org.