Big Primes, Small Numbers, Sarah Palin and the Financial Crisis

Nov. 2, 2008 — -- This month's "Who's Counting" will be an assortment drawn from mathematically flavored stories in the news.

The first concerns a number that easily swamps even the billions and trillions cited in recent financial stories. We know a lot about the existence of millions of subprime mortgages, but little media attention has been devoted to the existence of a just-discovered 13-million digit prime number. (A prime number, recall, is one divisible only by itself and 1. The numbers 3, 19 and 37 are prime, whereas 6, 33 and 49 are not.)

Mathematicians at UCLA won the $100,000 prize offered by the Electronic Frontier Foundation for discovering this humongously large prime number. It is a Mersenne prime number, a prime number of the form 2^P-1, where P is also prime. In this case P = 43,112,609, and the 13-million digit number is 2^43,112,609 - 1.

To find a Mersenne prime having more than 10 million digits and thus win the prize, people from around the world contributed the power of their underused computers in order to perform the complex and repetitive calculations required.

Such an accomplishment may strike many as pointless, but prime numbers and the difficulty of factoring nonprime numbers into primes is part of what allows the secure transfer via numerical code of trillions of dollars around the world.

Another story that appeared recently concerns a study at Johns Hopkins University that established a connection between students' intuitive "number sense" and how well they performed in mathematics class.

Specifically, the researchers looked at the ability of 14-year-olds to look at collections of flashing blue and yellow dots on a computer screen and quickly determine which color dot was more numerous. If the difference is great -- say eight yellow and 20 blue dots -- this is easy, but if the numbers are closer, the task is more difficult.