Above Prime

Binary Carpeting from the Museum of Science and Industry

Binary Carpeting from the Museum of Science and Industry

Enter any 11-digit prime number to continue:

A prime number is a positive integer not divisible without a remainder by any positive integer other than itself and one. The preceding reference to an 11-digit prime number is a gag that has been around almost as long as computers have been. The idea behind it is that any such number would be so absurdly arcane as to prevent any further continuation thereby stymieing any user.

The genesis of this post came when Anne was telling me today about how one day in Goals (new-speak for detention), when she was tasked to watch over a couple of miscreants. She had no knitting with her to while away the time. So she tried to divine an 11-digit prime number. I asked her why she didn’t just use Google, which would have defeated the time-wasting aspect of this exercise. She gave me a look and said that would have been cheating.

Here are an interesting sequence of prime numbers:

31
331
3331
33331
333331
3333331
33333331

The next one, 333333331, is not a prime, it is the product of 17 and 19607843.

Anne’s predilection for prime numbers dates back to a high school science project. I knew her then, but was unaware of until later about this project. She must have been deeply absorbed with it, because I later heard of it, when she was teased about it by her cousin. Anne was taking calculus and advanced placement math in high school, while I was not. She is not just a pretty face.

As an aside, 47 is the fifteenth prime number, a safe prime, the thirteenth super-singular prime, and the sixth Lucas prime. 47 is a highly cototient number. I just liked the sound of these two sentences, but couldn’t explain moonshine theory for the life of me. While not the answer to the question about life, the universe and everything (42), 47 is not without its own science fiction chops.

47 is purposely popularized in the various TV shows and movies of the Star Trek franchise. Originally, it was just one writer’s inside joke that now has become institutionalized. In the 2009 J.J. Abrams reboot, the Enterprise was built in Sector 47 of the Riverside Shipyards, and 47 Klingon ships are said to have been destroyed by Nero. With Abrams’ planned jump to Star Wars, look for this prime number to surface there too.

I cheated and Googled any 11-digit prime number and found, 99999999977, the largest such number. When I told Anne about it, she said, “I guess I started at the wrong end.” Composed of nine nines, followed by two sevens, it is an easy 11-digit prime number to remember, just in case you ever need one to continue.

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