# Who's Counting: Jesus' Descendants

In any case, this is another instance of a common phenomenon: A number gains a certain currency when commentator A pulls it out of ... the air and is then cited by B as the number's source; B is cited by C as the number's source; C is cited by D; and so on, until someone in the loop is cited by A, and few ever check to see if the number has any validity. Still, for a while at least, "everyone knows" it's true.

#### Home Run Records and Prime Numbers

Thirty-two years ago, Hank Aaron hit his 715th home run and surpassed Babe Ruth's record of 714, a feat that Barry Bonds accomplished just last month. Reams of newsprint have been devoted to various aspects of these record-breakings but not well known is that Aaron's breaking of the record stimulated a spate of mathematical papers about what has come to be known as Ruth-Aaron pairs.

If we break 714 into its prime number factors, we find that 714 = 2 x 3 x 7 x 17. Likewise 715 = 5 x 11 x 13. Adding the prime factors of 714 and 715, we find that they have the same sum. That is, 2 + 3 + 5 + 17 = 29, and 5 + 11 + 13 = 29. Consecutive numbers like 714 and 715 whose prime factors add up to the same number have come to be called Ruth-Aaron pairs.

Interestingly, if we multiply 714 (which equals 2 x 3 x 7 x 17) by 715 (which equals = 5 x 11 x 13), we find that 714 x 715 = 2 x 3 x 5 x 7 x 11 x 13 x 17. So we have the product of the two consecutive whole numbers, 714 and 715, that is equal to the product of the first seven prime numbers: 2 x 3 x 5 x 7 x 11 x 13 x 17.

In any case, as is their wont, mathematicians tried to find out how common these properties were among pairs of consecutive numbers and whether there were arbitrarily large examples of such pairs. (No one knows yet.) Even Paul Erdos, the famous peripatetic mathematician wrote about Ruth-Aaron pairs (or Ruth-Aaron-Bonds pairs) and proved a crucial theorem about them.

Having grown up in Milwaukee, where Aaron played for years for the Braves (before the team moved to Atlanta), I can't help but hope that "Hammering Hank's" record of 755 home runs stands, even though the latter number (755 = 5 x 151) seems to be rather mathematically undistinguished.

Professor of mathematics at Temple University, John Allen Paulos is the author of best-selling books including "Innumeracy" and "A Mathematician Plays the Stock Market." His "Who's Counting?" column on ABCNews.com appears the first weekend of every month.

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