Sheldon Conjecture

Theorem

There is only $1$ Sheldon prime, and that is $73$.


Proof


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Historical Note

The was expounded by the fictional physicist Sheldon Cooper, who expounded upon the properties of the number $73$ in (fittingly) episode $73$ of The Big Bang Theory, by Lee Aronsohn, Jim Reynolds and Maria Ferrari:


Sheldon Cooper:

$73$ is the best number:
$73$ is the $21$st prime number.
Its mirror $37$ is the $12$th prime number.
Its mirror $21$ is the product of multiplying, hang on to your hats, $7$ by $3$.
Eh? Eh? Did I lie?


Leonard Hofstadter:

We get it. $73$ is the Chuck Norris of numbers.


Sheldon Cooper:

Chuck Norris wishes.
In binary, $73$ is a palindrome: $1,001,001$, which backwards is $1,001,001$, exactly the same.
All Chuck Norris backwards gets you is Sirron Kcuhc!


The unspoken implication of this statement was that $73$ was the only (prime) number to have this property.


The question was settled by Carl Pomerance and Chris Spicer in $2019$, who proved that the is indeed true, thereby turning it into a theorem.

However, as of time of writing (May $2019$), this result is still referred to as the .


Sources

  • Jan. 2019: Carl Pomerance and Chris Spicer: Proof of the Sheldon Conjecture (Amer. Math. Monthly Vol. 121, no. 1: pp. 1 – 10)
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