Mathematics: Big Bang Theory inspires proof

The character of Sheldon Cooper in the US series “The Big Bang Theory”, played by Jim Parsons, may be an ultra-nerd and an insufferable know-it-all, but there’s one thing you have to give him credit for: His glorious work on the series has led to a mathematical advance in the real world. In episode 73, “The Alien Parasite Hypothesis” – aired in the year Sheldon explains why 73 is the best number. Clearly, it’s the 21st prime number, if you mirror its digits, 37 emerges, which is prime number 12, i.e. the reflection of 21, and the product of 7 and 3 is also 21.

Now you can play such mind games with many numbers, but now two mathematicians have shown that Sheldon is right: 73 is really the only number with these properties. In their article “Proof of the Sheldon Conjecture” (American Mathematical Monthly), Carl Pomerance of Dartmouth College and Chris Spicer of Morningside College define a Sheldon prime number y as the nth prime number y, where the product of the digits of y is n and the reflection of the digits of y is the mth prime number. And m is then also supposed to be the reflection of n-pooh.

For very large prime numbers, Sheldon’s conditions cannot be satisfied

Spicer had already dealt with such Sheldon numbers in an earlier work. Only now, together with Pomerance, he was able to show that the Sheldon conditions for prime numbers greater than 10 to the power of 45 cannot be fulfilled. Afterwards, the two mathematicians were able to use all kinds of restrictions and tricks to graze the number space up to this huge number by means of an algorithm, and thus prove it: 73 is the only Sheldon prime number in existence.

This is where the story could end, it would be a nice example of how an episode from television gets into the world of science. But in fact, the story went back again, and the nerd circle closed: In the April 18th episode of “The Big Bang Theory,” the evidence of Pomerance and Spicer appears in the background on a whiteboard.

Pomerance and Spicer wanted to use an image from the series to illustrate their article and were in contact with the makers of “The Big Bang Theory” to do so. That’s how the scientific advisor of the series found out about the work – David Saltzberg, physicist at the University of California, Los Angeles. He, in turn, asked for permission to use the evidence for the series and gave the documents to the series authors. This is how the whiteboard scribbling came about, which was not otherwise discussed in detail in the following.

According to the Dartmouth college newspaper, the mathematicians were impressed by this indirect TV appearance. “I didn’t get much out of the episode at first viewing because I kept stopping and zooming in to see what was on the boards,” Spicer said. “The next day my wife and I watched it again, just for fun.”