ITinfo: Your Prime Goal: Win A Million Bucks

Two Plus Two Equals Four

Prime numbers yield big rewards

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Your Prime Goal: Win A Million Bucks

by Dave Murphy
ISSN 1535-3613

"Some numbers have the special property that they cannot be expressed as the product of two smaller numbers, e.g., 2, 3, 5, 7, etc. Such numbers are called prime numbers, and they play an important role, both in pure mathematics and its applications. The distribution of such prime numbers among all natural numbers does not follow any regular pattern, however the German mathematician G.F.B. Riemann (1826 – 1866) observed that the frequency of prime numbers is very closely related to the behavior of an elaborate function “z(s)” called the Riemann Zeta function. The Riemann hypothesis asserts that all interesting solutions of the equation z(s) = 0 lie on a straight line. This has been checked for the first 1,500,000,000 solutions. A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers," begins a page on the Clay Mathematics Institute Web site.

So what's this mean? It could mean a million dollars if you're the first to solve the mathematical problem related to the Riemann Zeta function posed by the Clay Mathematics Institute, a Massachusetts-based think tank dedicated to increasing and disseminating mathematical knowledge.

Considered to be one of the most difficult unsolved mathematics problems, the Riemann hypothesis was posed in an 1859 paper written by Bernhard Riemann, the only paper on number theory Riemann wrote.

Prime numbers can be divided only by one and themselves, for example, 2, 3, 5, 7, 11, 13 are each prime numbers. However, no one yet has calculated a formula that will accurately and quickly determine if any given number is prime, nor is there a simple way to determine the next prime number in a line of numbers. Prime numbers seem to be randomly dispersed throughout the integer number line.

Dave's Opinion

Most digital encryption programs use prime numbers to create keys for the encryption cipher because the factoring process is currently so difficult. The math whiz who solves the Riemann hypothesis problem stands to not only earn a million dollars and global acclaim, but also to stand the information security industry on its ear. If it becomes simple to factor the product of prime numbers, current digital encryption software will be worthless.

If prime numbers aren't your thing, the Clay Mathematics Institute has six other million dollar prizes waiting for your stubby pencil and calculator types to tackle. If you like a good number challenge, the CMI site is worth visiting.

Call for Comments

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References

Clay Mathematics Institute
Description of CMI's Problem
Message Center

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updated July 3, 2002
http://dgl.com/itinfo/2002/it020703.html