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

This month's "Who's Counting" will be an assortment drawn from mathematically flavored stories in the news.

A 13-Million-Digit Prime Number

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.

Small Number Sense and Mathematical Ability

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.

A keen ability to discern the relative magnitudes of blue and yellow dots at a glance -- i.e., a good number sense -- correlated strongly with their past performance in math up to that time.

Whether this connection is causal, which direction it runs if it is, and whether number sense can be easily improved are unanswered questions.

In any case, this result is a little surprising because formal mathematics is abstract, whereas recognizing the relative magnitudes of small numbers seems much more intuitive and visceral, a skill that even some animals possess.

Another question occurs to me. In my classes, I often stress estimating and comparing large numbers -- the height of buildings, the number of coins in a jar, etc. -- and wonder whether there is a similar correlation between an ability to accurately estimate and compare large numbers and a facility with formal mathematics.

This latter skill is often useful in political discourse. A topical example: In an Oct. 24 speech in North Carolina on special needs children, vice presidential candidate Sarah Palin stated, "Sometimes these dollars, they go to projects having little or nothing to do with the public good, things like fruit fly research in Paris, France. I kid you not."

This, of course, is plain ignorant, because over the years research on fruit flies has played a seminal role in understanding human biology, particularly genetic disorders affecting children.

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