量子物理学家称73是“最好的数字”

大爆炸理论从卡尔波美兰斯获取数学笔记

教授对“谢尔顿猜想”的证明出现在热门电视节目中。

荣誉退休数学教授Carl Pomerance解释了他对“谢尔顿猜想”的证明，该证据指出数字73的不寻常属性使它在素数中独一无二。 

数学教授荣誉博士卡尔·波梅兰斯的素数理论方程出现在“大爆炸理论”中，在热门情景喜剧的背景下，它被潦草地写在一块白板上，讲述了一群朋友和室友，他们是科学家，其中许多是加州理工学院物理学家。

在最近的一篇论文中，“Sheldon猜想的证明”，Pomerance，John G. Kemeny数学名誉家长教授，对虚构的量子物理学家Sheldon Cooper声称73是“最好的数字”，因为有几个独特的属性。 Pomerance的证明表明，73确实是独一无二的。

大爆炸理论以装饰“复活节彩蛋”而闻名，以激发观众中自称公开的科学书呆子。当大爆炸理论的技术顾问加州大学洛杉矶分校物理学教授David Saltzberg听说Sheldon证据时，他联系Pomerance询问他们是否可以在4月18日播出的节目中使用它。

“有趣的是，当你看到带有技术资料的卡通片时，通常它没有任何意义，但它们在电路板上的东西，我会说，哦，我认识到了，”Pomerance说。在做一些简单的数学阅读之前，他在遇到“谢尔顿素数问题”之前并不特别喜欢这个节目。

这张照片在“Sheldon猜想证明”一文中作为插图出现，标题为“图1. Sheldon总是知道73是最好的。”（摄影：Michael Yarish /©2019 Warner Bros. 

什么是让73对Sheldon如此具有吸引力的是什么呢？Sheldon包括一件印有他常规衬衫轮换号码的T恤？ Pomerance和合着者，晨兴学院数学副教授Chris Spicer在证明的介绍中解释，接受在American Mathematical Monthly上发表。上下文的一个注释：素数的“索引”是按数字升序排列的位置。 （例如，连续的素数2,3,5,7被索引为1,2,3和4。）

“首先要注意的是，73不仅是素数，它在素数序列中的指数是其数字的乘积，即21;这是第21个素数。另外，扭转73的数字，我们得到素数37，这是第12个素数，12是与21的相反，“他们写道，列出了谢尔顿在节目中所做的点。

Pomerance和Spicer要解决的问题是这是否是具有这些属性的唯一素数。由于理论上存在无数个素数，因此比证明更容易说。他们的论文提出了一系列方程式，他们说证明73事实上是独一无二的。这是这个证明的一部分，它运行10页，写在节目集的白板上。

“这就像节目中的节目。它与情节毫无关系。它只是在后台。很难看到它。有时它有点模糊，它是一个角度，有一个字符阻止它。但如果你知道要找它 - 嘿，这是我的论文，“Pomerance说。

The professor’s proof of the “Sheldon conjecture” turns up on the popular TV show.

Mathematics professor emeritus Carl Pomerance points to a whiteboard

Mathematics professor emeritus Carl Pomerance explains his proof of the “Sheldon conjecture” that states that the number 73’s unusual properties make it unique among prime numbers. (Photo by Eli Burakian)

A prime number theory equation by mathematics professor emeritus Carl Pomerance turned up on The Big Bang Theory, where it was scrawled on a white board in the background of the hit sitcom about a group of friends and roommates who are scientists, many of them physicists at the California Institute of Technology.

In a recent paper, “Proof of the Sheldon Conjecture,” Pomerance, the John G. Kemeny Parents Professor of Mathematics Emeritus, does the math on a claim by fictional quantum physicist Sheldon Cooper that 73 is “the best number” because of several unique properties. Pomerance’s proof shows that 73 is indeed unique.

The Big Bang Theory is known for dressing the set with “Easter eggs” to delight the self-avowed science nerds in the audience. When UCLA physics professor David Saltzberg, technical consultant for The Big Bang Theory, heard about the Sheldon proof, he contacted Pomerance to ask if they could use it in the show, which was broadcast April 18.

“What’s interesting is, when you see cartoons with technical stuff on boards, usually it doesn’t make any sense, but the stuff that they have on the boards, I’ll usually say, oh, I recognize that,” says Pomerance, who wasn’t particularly a fan of the show before he came across the “Sheldon prime number problem” while doing some light math reading.

sheldon73_590.jpg

A character from The Big Bang Theory sits on a couch

This picture appears as an illustration in the paper “Proof of the Sheldon Conjecture,” with the caption, “Figure 1. Sheldon always knew 73 was the best.” (Photo by Michael Yarish/©2019 Warner Bros. Entertainment Inc.)

What is it about the number 73 that makes it so attractive to Sheldon, who includes a T-shirt emblazoned with the number in his regular shirt rotation? Pomerance and co-author Chris Spicer, associate professor of mathematics at Morningside College, explain in the introduction to the proof, accepted for publication in American Mathematical Monthly. One note of context: The “index” of a prime number is its place in ascending numerical order. (For example, the consecutive prime numbers 2, 3, 5, 7 are indexed 1, 2, 3, and 4.)

“First note that not only is 73 a prime number, its index in the sequence of primes is the product of its digits, namely 21; it is the 21st prime. In addition, reversing the digits of 73, we obtain the prime 37, which is the 12th prime, and 12 is the reverse of 21,” they write, laying out the points Sheldon makes on the show.

The question Pomerance and Spicer set out to solve is whether this is the only prime number with these properties. Since there is, theoretically, an infinite number of prime numbers, that is easier said than proved. Their paper proposes a series of equations that they say proves 73 is, in fact, unique. It is a portion of this proof, which runs 10 pages, that is written on a whiteboard on the show’s set.

“It’s like the show within the show. It has nothing at all to do with the plot. It’s just in the background. It’s difficult to see it. Sometimes it’s a little fuzzy, it’s at an angle, there’s a character blocking it. But if you know to look for it—hey, that’s my paper,” Pomerance says.