量子物理學家稱73是「最好的數字」

大爆炸理論從卡爾波美蘭斯獲取數學筆記

教授對「謝爾頓猜想」的證明出現在熱門電視節目中。

榮譽退休數學教授Carl Pomerance解釋了他對「謝爾頓猜想」的證明，該證據指出數字73的不尋常屬性使它在素數中獨一無二。 

數學教授榮譽博士卡爾·波梅蘭斯的素數理論方程出現在「大爆炸理論」中，在熱門情景喜劇的背景下，它被潦草地寫在一塊白板上，講述了一群朋友和室友，他們是科學家，其中許多是加州理工學院物理學家。

在最近的一篇論文中，「Sheldon猜想的證明」，Pomerance，John G. Kemeny數學名譽家長教授，對虛構的量子物理學家Sheldon Cooper聲稱73是「最好的數字」，因為有幾個獨特的屬性。 Pomerance的證明表明，73確實是獨一無二的。

大爆炸理論以裝飾「復活節彩蛋」而聞名，以激發觀眾中自稱公開的科學書獃子。當大爆炸理論的技術顧問加州大學洛杉磯分校物理學教授David Saltzberg聽說Sheldon證據時，他聯繫Pomerance詢問他們是否可以在4月18日播出的節目中使用它。

「有趣的是，當你看到帶有技術資料的卡通片時，通常它沒有任何意義，但它們在電路板上的東西，我會說，哦，我認識到了，」Pomerance說。在做一些簡單的數學閱讀之前，他在遇到「謝爾頓素數問題」之前並不特別喜歡這個節目。

這張照片在「Sheldon猜想證明」一文中作為插圖出現，標題為「圖1. Sheldon總是知道73是最好的。」（攝影：Michael Yarish /©2019 Warner Bros. 

什麼是讓73對Sheldon如此具有吸引力的是什麼呢？Sheldon包括一件印有他常規襯衫輪換號碼的T恤？ Pomerance和合著者，晨興學院數學副教授Chris Spicer在證明的介紹中解釋，接受在American Mathematical Monthly上發表。上下文的一個註釋：素數的「索引」是按數字升序排列的位置。 （例如，連續的素數2,3,5,7被索引為1,2,3和4。）

「首先要注意的是，73不僅是素數，它在素數序列中的指數是其數字的乘積，即21;這是第21個素數。另外，扭轉73的數字，我們得到素數37，這是第12個素數，12是與21的相反，「他們寫道，列出了謝爾頓在節目中所做的點。

Pomerance和Spicer要解決的問題是這是否是具有這些屬性的唯一素數。由於理論上存在無數個素數，因此比證明更容易說。他們的論文提出了一系列方程式，他們說證明73事實上是獨一無二的。這是這個證明的一部分，它運行10頁，寫在節目集的白板上。

「這就像節目中的節目。它與情節毫無關係。它只是在後台。很難看到它。有時它有點模糊，它是一個角度，有一個字元阻止它。但如果你知道要找它 - 嘿，這是我的論文，「Pomerance說。

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.