According to Sheldon, the best number is 73

From a conversation in the series:

Sheldon: “The best number is 73. Why? 73 is the 21st prime number. Its mirror, 37, is the 12th and its mirror, 21, is the product of multiplying 7 and 3.”'

Leonard: “We get it, 73 is the Chuck Norris of numbers!”

Sheldon: “Chuck Norris wishes. In binary 73 is a palindrome, 1001001, which backwards is 1001001. All Chuck Norris backwards gets you is Sirron Kcuhc!”

Is 73 the only number with the properties Sheldon listed?

Before we look for other “Best numbers” we should review the criterias:

• Is must be a prime number
• Its reverse version must also be a prime number
• The positions of the number itself and the mirrored version in the prime number sequence must also be mirror versions of each other
• The prime number sequence position must have factors made up of the digits in the number
• The binary representation of the number must be palindrome

This is an impressive list of qualities. From the top of my head, not many numbers can fulfill those bullet points. To find out, I wrote some Python code to aid me.

Narrowing down the list with Python

There are lots of prime numbers, 1229 under 10000, but less where the digits reversed are one too. Not that many actually, just 256 under 10000.

Next, the position in the list of primes narrows down the numbers to three, 11, 37 and 73.

Not really necessary to go any further as the last to items in the list of criterias are only met by the number 73. I did check up to 100 000 as well, but no more luck finding one. As I’m writing this, I’m checking up to 1 million too, but nothing yet.

So to conclude, by those criterias, the number 73 really is truthfully special. If it is the best number can be discussed :-)