Earthsky Interviews
Private: An unsolved math problem, worth ‘prime’ cash
01-28-2005 - Earth
_JB: The problem involves prime numbers. Prime numbers can only be evenly divided by themselves and one. For example, 3 is a prime number because you can only divide it evenly by 3 and 1. The first few prime numbers are:_ 2, 3, 5, 7, 11, 13 and so on.
_DB:_ Around 300 B.C., the Greek mathematician Euclid proved that there are an infinite number of prime numbers. Jim Carlson is president of the Clay Mathematics Institute in Cambridge, Massachusetts.
_Jim Carlson:_ Mathematicians, like children and like scientists, are curious, they want to explain things, so if you know there are infinitely many primes, you’d like to know how many there are less than a million, how many there are less than two million. If you’re really ambitious, you’d like to have a formula for it.
_JB:_ In 1859, a German mathematician named Georg Bernhard Riemann proposed a formula that would tell you exactly how many prime numbers there are below a certain number. There’s just one catch – the formula has an infinite number of parts to it. So it’s impossible to calculate an exact answer. Instead, mathematicians make approximations. The Riemann Hypothesis tells them how good their approximations are. The Clay Mathematics Institute is offering a prize of one million dollars for a proof of the Riemann Hypothesis. With thanks to the “National Science Foundation”:http://www.nsf.gov/ – where discoveries begin. We’re Block and Byrd for Earth and Sky.
For an English translation of the original 1859 paper that introduces the Riemann Hypothesis, go to: “On the Number of Primes Less Than a Given Magnitude”:http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Zeta/EZeta.pdf (University of Dublin Trinity College)
To find the largest prime number known, go to: “The Great Internet Mersenne Prime Search”:http://www.mersenne.org/prime.htm (GIMPS)
“The Prime Pages”:http://www.utm.edu/research/primes/ (University o Tennessee at Martin)
“Riemann Hypothesis”:http://www.claymath.org/millennium/Riemann_Hypothesis/ (Clay Mathematics University)
“Georg Friedrich Bernhard Riemann”:http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Riemann.html (University of St. Andrews)
Author’s Notes:
In mathematics, finding the largest known prime number has become a sort of sport. The largest known prime number today has over 7 million digits. [Note: A prime number with 7,235,733 digits was discovered on May 15, 2004 by Findley, Woltman, Kurowski, et. al.]
Thanks to:
Jim Carlson
Clay Mathematics Institute
Cambridge, MA