What a name for what a man. He played football and baseball, not just in high school but in the majors. He also played both sides of the ball for the Cowboys, and I can remember one occasion when the color commentary during a lull in the football game drifted to explaining the differences between the two helmets that Deion sported.
But I'm not talking about this amazing star of the Atlanta Braves outfield. I'm also not talking about the not referring to χαιρος - the concept of the time being the right time.
No, I'm talking about prime in the mathematical sense. Recently, I was bothering my wife with undesirable behavior, and when chastised, I quickly noted that I only do it when the time is prime, pointing to the clock which displayed a time whose digits summed to a prime number. When I repeated the mistake I simply pointed to the clock in helpless submission to prime time.
After this going on for a few days and happening much more frequently than socially acceptable, we began to question how common these prime numbers really were.
In the first example, the sum is clearly 19, which is prime. In the second example, however, just 20 minutes later, the sum is 16 which is decidedly composite.
So how common are the times of the first kind? How much of our time is actually prime?
Acknowledging that neither 0 or 1 are considered prime, we then have a simple computational task of determining which of the 1,440 minute sums are prime. If we use military time, then the possible range of sums spans 0 to 24, which occur at midnight and 19:59 respectively. So, our questions is really how does base 60 for the minutes, and the limitation of the hours to 0 through 23 affect the distribution of sums on the range of 0 to 24. Below is a histogram with an approximated normal distribution on top of it.
I probably shouldn't have been, but I was stunned to see the distribution so closely follow a normal curve. But to our real question, how many of these are prime? It turns out that 505 minutes of our day sum to prime numbers in military time. This corresponds to 35% of the time being prime. Likely not a coincidence is that between of the 25 numbers in our range 9 of them are prime leading to a 35% prime rate in our range. Again, being a Math major, I shouldn't be surprised by this fact, but it surprises me that the rate of primes in the time in our day corresponds to the rate of primes in the range of the possible sums. Further more that the possible sums corresponds to the hours in the day begins to border on numerology instead of mathematical observation.
Going further with this question, I began to ask questions like what percentage of the time are all of the numbers displayed primes individually (2% - e.g. 22:22, 23:25, 23:57, etc.), what percentage of the time are any of the numbers display primes (85% - e.g. 0:02, 11:16, 22:24, etc.), and what percentage of the time are there any 1, 2, 3, or 4 digit primes displayed on the clock face (92%).
For those of you considering the differences presented by limiting our attention to the laymen's watches, you might be surprised that the percentage of primes is only slightly higher at 36%. The notable fact when we begin to consider the other questions is that there are no examples where all the numbers are prime since the tens digit of the hour is always either 0 or 1.
All of this to say, I wonder if Deion ever felt like his swings were actually on prime time...television.
