This is a really fascinating article by Randy Finch for codeproject – and is especially illuminating in helping to understand Ruth-Aaron pairs.

My story begins on February 6, 1895, in Baltimore, Maryland. On that day, a baby boy by the name of George Herman Ruth Jr. was born. At that time, no one could know the fame that would come his way. Later nicknamed “The Bambino” and “The Sultan of Swat” and “Babe”, he began to show proficiency in the game of baseball. On July 11, 1914, at the age of 19, he made his major league debut as a pitcher with the Boston Red Sox. But wanting to have more play time, he was allowed to convert to an outfielder. In 1919, he broke the MLB single-season home run record. In 1920, Ruth was sold to the New York Yankees where he continued to hit home runs. By the time he retired in 1935, he had 714 lifetime home runs, a record that seemingly could not be broken.

The next part of my story begins in Mobile, Alabama, on February 5, 1934, one day shy of 39 years after Babe Ruth was born, and the last year he played for the New York Yankees. (He played part of another year for the Boston Braves in 1935.) On that day, a baby boy by the name of Henry Louis “Hank” Aaron was born. Also known as “Hammer” or “Hammerin’ Hank”, he made his major league debut on April 13, 1954, at the age of 20. Over the next 22 years, he would play for the Milwaukee Braves (picking up with the Braves where Ruth left off), the Atlanta Braves, and the Milwaukee Brewers. Aaron was a home run hitter like Ruth. By the end of the 1973 season, he had hit 713 lifetime home runs, just one shy of the 38-year-old record set by Ruth.

You can imagine the fervor in Atlanta between the 1973 and 1974 seasons, with many fans anticipating Hank breaking Babe’s lifetime home run record. You could ask, “When’s 715 going to happen?” and everyone knew what you were talking about. It turned out that April 8, 1974, was the answer to that question as Aaron eclipsed Ruth’s record by hitting his 715^th home run for the major leagues.

One person that took notice of the excitement, and especially the numbers, was a young assistant professor of mathematics at the University of Georgia by the name of Carl Pomerance. He noticed that the product of 714 and 715 was also the product of the first seven prime numbers. Then a student of a colleague noticed that the sum of 714’s prime factors was equal to the sum of 715’s prime factors. A prime number is evenly divisible by only 1 and itself. Here’s the information in a nutshell.

2 x 3 x 5 x 7 x 11 x 13 x 17 = 714 x 715 = 510,510

714 = 2 x 3 x 7 x 17

715 = 5 x 11 x 13

Sum of 714’s prime factors = 2 + 3 + 7 + 17 = 29

Sum of 715’s prime factors = 5 + 11 + 13 = 29

Read more here.

(PS – Go Cardinals!)