Yankees and A’s considered Prime Number Suspects

Remember a few weeks ago, when the Mets beat the Tigers by the “perfect square” score of 16-9?  I promised at that point that I’d discuss “prime number” score games.  Well, we had one last Friday night.  The Yanks pummeled the A’s 17-7.

If you need a refresher on the concept of a prime number, it is:

A natural number is called a prime number (or a prime) if it is bigger than one and has no divisors other than 1 and itself. For example, 5 is prime, since no number except 1 and 5 divides it. On the other hand, 6 is not a prime (it is composite), since 6 = 2 · 3.

So, how common is that in baseball history?  We’re looking for both teams to score one of the following: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 43 or 47 runs (we stop there because 49 is the highest run total ever recorded).  Extra specialness will be bestowed if any of these games occur in March, May or July (the 3rd, 5th and 7th months).

Through the end of the 2010 season, there have been at least 38,002 instances of a game ending up with “perfect square” scores (that’s approximately one out of every five games in major league history).  Here is a table breaking out those scores by home/visitor:

As you can see, prior to the Yanks/A’s tilt, there had been only 42 17-7 games in history, with the home team winning 27 of them.  Now, we can extend the “prime numberness” of the game by including hits and errors for each team, giving us six possible attributes to shoot for.  Sadly, in the A’s/Yankees contest, the teams’ respective linescores (17 runs, 17 hits, 2 errors for the Yankees, 7 runs, 13 hits and . . . only 1 (!) error for the A’s) only satisfied five prime numbers.  But there have been MANY instances of the hits, runs and errors for both teams all being primes.

There are gaps in the recorded history of “linescores”, but the earliest “6 Prime Number” game on record just happened to occur on July 27th exactly 140 years ago.  The Troy Haymakers and Washington Olympics played to a 3-3 tie, with Washington tallying seven hits and two errors, and Troy notching three hits and five errors.  The 2010 season had only one such game, as Detroit bested Anaheim 3-2 on May 1st (Detroit’s 3-7-3 to Anaheim’s 2-11-2).

Prior to 2011, the highest total of runs, hits and errors for the sum of the six prime numbers was 58.  It happened only once, during the first game of a twinight doubleheader between the White Sox and Brewers on June 23, 1989.  Milwaukee’s 17-19-3 linescore, when added to Chicago’s 5-11-3 gives us the magic total.  The lowest sum for a six prime number game was 14, achieved by the Houston Colt .45s and the Milwaukee Braves on May 31, 1963.  These teams were seemingly going for the Yahtzee “full house”, as Houston’s 3-2-2 outlasted Milwaukee’s 2-3-2.

Taking our hunt for prime number nirvana even further, we could see if any of these “6 prime number” games occurred on a prime number date, making it a “9 prime number” game!  That is, the month, day and year are also prime numbers.

(And in case you are wondering, here are the “prime number years” within the timeframe of major league history: 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 1999 2003 . . . and 2011 is the newest one)

I’m happy to say, there have been two instances of  “9 prime number” games.  The first occurred during the first game of a doubleheader on 5/31/1931 between the Cardinals and Reds, as the host St. Louis squad beat Cincinnati, 7-5  (7-11-2 versus 5-11-3).  The other happened on 5/13/1951, in the first game of a twinbill at the Polo Grounds, as the New York Giants defeated the Philadelphia Phillies, 11-2 (11-11-2 versus 2-5-2).

OK . . . so that takes care of “perfect square” and “prime number” games. Anyone have suggestions for the next frontier to explore in a similar realm?

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3 Responses to Yankees and A’s considered Prime Number Suspects

  1. Ember Nickel says:

    I think the diagonal is my favorite part of this table. I would not have expected there to be a 19-19 game, but I guess by the time you score 38 runs, the sun has gone down…

  2. Pingback: What is Your Favorite Number? We All Have Them «

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