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Science News
April 24, 2004
Ivars Peterson |
Progressive Primes In one step toward elucidating certain primal mysteries, two mathematicians have now apparently proved that the population of primes contains an infinite collection of arithmetic progressions.   |
Science News
June 2, 2001
Ivars Peterson |
Prime Twins Although most mathematicians believe that there are infinitely many twin primes, no one has yet proved this conjecture to be true. Indeed, the twin prime conjecture is considered one of the major unsolved problems in number theory... |
Science News
July 16, 2005
Ivars Peterson |
Closing the Gap on Twin Primes Euclid proved that the set of primes is infinite in size more than 2000 years ago, but no one has yet proved whether there is an infinite number of twin primes, or pairs of primes that have a difference of two. There's now hope that that matter will finally be resolved. |
Science News
March 20, 2004
Ivars Peterson |
Deriving the Structure of Numbers The study of prime numbers has long been a central part of number theory, a field traditionally pursued for its own sake and for the mathematical beauty of its results. |
Science News
August 27, 2005
Ivars Peterson |
Primes, Palindromes, and Pyramids Many questions about palidromic prime pyramids remain open. Is there a better way than exhaustive search for finding the tallest pyramids with fixed step sizes? Can you prove that fixed step size pyramids are finite? |
Science News
August 6, 2005
Ivars Peterson |
Playing with Ruth-Aaron Pairs Mathematicians have taken the home run records of Hank Aaron and Babe Ruth and made the fascinating discovery that the numbers have more in common than just baseball. |
Science News
January 4, 2003
Ivars Peterson |
Sound-Byte Math Music Swedish composer Daniel Cummerow has created mathematical sound bytes belonging to a category known as algorithmic music. Each musical fragment is determined by a mathematical recipe -- a formula that links digits with musical notes and their duration... |
Science News
June 24, 2006
Ivars Peterson |
Counting Franklin's Magic Squares One mathematician finds that Benjamin Franklin's remarkable magic squares are just three of more than 1 million possibilities. |
Science News
August 28, 2004
Ivars Peterson |
More Progressive Primes In July, Markus Frind, Paul Jobling, and Paul Underwood announced that they had discovered the first sequence consisting of 23 prime numbers in arithmetic progression. This surpasses the previous record of 22 primes in arithmetic progression, set in 1993. |
Science News
January 11, 2003
Ivars Peterson |
A Remarkable Dearth of Primes The pursuit of prime numbers -- integers evenly divisible only by themselves and 1 -- can lead to all sorts of curious results and unexpected patterns. In some instances, you may even encounter a mysterious absence of primes. |
Science News
October 11, 2003
Ivars Peterson |
Goldbach Computations Goldbach's conjecture that every even number larger than 2 is the sum of two prime numbers remains unproven, but recent research may provide some insight. |
Science News
June 25, 2005
Ivars Peterson |
Magic Squares of Squares People have been toying with magic squares for more than 2,000 years--setting themselves increasingly difficult challenges to find arrays of numbers that fit given patterns. Here are some examples. |
Science News
January 18, 2003
Ivars Peterson |
A Perfect Collaboration Together, Euclid of Alexandria (c325-c265 BC) and Leonard Euler (1707-1783), born in Switzerland and at various times resident in St. Petersburg and Berlin, collaborated on proving an interesting result in number theory -- without the benefit of e-mail or time travel. |
Science News
July 29, 2006
Ivars Peterson |
Names for Numbers Recreational mathematics offers a vast playing field for amateur and professional mathematicians alike. Named numbers, such as Smiths, have all sorts of intriguing properties. |
Science News
August 19, 2000
Ivars Peterson |
Goldbach's Prime Pairs Evenly divisible only by themselves and one, primes are a rich source of speculative ideas that mathematicians often find simple to state but difficult to prove. The Goldbach conjecture is a prime example of such a conundrum. |
Science News
January 14, 2006
Ivars Peterson |
Team Mersenne A Central Missouri State University computer identified the 43rd Mersenne prime, setting the record for the largest known prime number. This behemoth, 2 30402457 - 1, runs to a whopping 9,152,052 decimal digits. |
Science News
June 5, 2004
Ivars Peterson |
Priming Upward The Great Internet Mersenne Prime Search (GIMPS) continues to unearth new Mersenne primes. |
InternetNews
December 28, 2005
Sharon Gaudin |
Grid Discovers Largest Known Prime Number Using an international grid of about 70,000 computers, researchers this month discovered the largest known prime number. |
Science News
March 5, 2005
Ivars Peterson |
Primal Surge Last month saw the discovery of the 42nd known Mersenne prime, the largest prime yet identified... Puzzle of the Week... |
Science News
April 6, 2002
Ivars Peterson |
The EKG Sequence Sequences of numbers have long fascinated both amateur and professional mathematicians. Here's a recently discovered example that has prompted some serious mathematical investigation... |
Science News
June 22, 2002
Ivars Peterson |
Conquering Catalan's Conjecture Preda Mihailescu of the University of Paderborn in Germany finally may have the key to a venerable problem known as Catalan's conjecture, which concerns the powers of whole numbers. |
Science News
December 6, 2003
Ivars Peterson |
Megaprime Champion The catalog of humongous prime numbers has a new entry -- the champion prime (2^20996011 - 1), which has 6,320,430 decimal digits. It's the largest known prime number and the 40th Mersenne prime ever found. |
Science News
December 2, 2000
Ivars Peterson |
Zeroing In on Catalan's Conjecture Preda Mihailescu of the Swiss Federal Institute of Technology in Zurich has proved a theorem that is likely to lead to a solution of Catalan's conjecture, a venerable problem involving relationships among whole numbers... |
National Defense
August 2007
Grace Jean |
Overlooked Business Model Could Benefit Small Firms Suppose a small business has produced a technology that will help troops fighting in Iraq, contract lawyers say it's better to sell off the business unit that developed the product. |
