Why is 73 such a special number?

If you have seen the series The Big Bang Theory you will have noticed Sheldon Cooper's obsession with the number 73, to which he attributes many unique properties.

But is it really that special?

Yes. Luckily, The Big Bang Theory series had magnificent scientific rigor despite being a comedy, so almost all of its scientific statements are correct.

73 is really special and bases almost all of its properties on prime numbers. Prime numbers are those that are only divisible integer by themselves or by 1. At the end of the article you can find some extra curiosities about prime numbers.

Below are the magical properties of 73:

• The number 73 is a prime number. We're off to a good start, since prime numbers are the basis of mathematics and many scientific and technological principles. For example, prime numbers are the basis of digital certificates, mobile communications, cryptographic hashes that mean that even if Google has your password, it cannot know which one it is, and even the pseudo-random numbers that computers calculate (yes, a computer It can't calculate real random numbers, but that's for another article.)

• 73 is a mirror prime, also called emirp prime, which means that 37 is also a mirror prime.

• 73 is the 21st prime number that exists (and 21 is 7x3), but the number 37 (73 backwards) as mentioned before, is also prime and is also the 12th (21 backwards) prime number.

• If we convert 73 to binary, this turns out to be 1001001, which is seven digits (7) with three (3) ones and curiously, it is a palindrome, since it reads the same to the right as to the left. This makes it one of the few palindromous binary primes.

• To complete this, if we obtain the positions of the "1" of 73 in binary (1001001), we have that these are position 0, position 3 and position 6. The binary code is base 2, and if the 2 to each of the positions we have:
• 2^0 = 1
• 2^3 = 8
• 2^6 = 64
• And what is 64+8+1? Exactly, 73!!
• In the octal system (base 8) 73 is represented as 111, which is also a palindrome :)

These characteristics make this number truly unique, so unique that some scientists who are fans of the series made a mathematical demonstration that no matter how many prime numbers are calculated, only 73 will meet this series of characteristics.

It is a formal investigation, it is called "the Sheldon conjecture" and you can read it here -> https://math.dartmouth.edu/~carlp/sheldon02132019.pdf

Curiosities

Finally, more curiosities:

• The episode of The Big Bang Theory (called The Alien Parasite Hypothesis) in which this aired is the 73rd episode of the series. In addition to this, the actor Jim Parsons, who plays Sheldon Cooper, was born in 1973 and when the episode aired he was 37 years old!! Marvelous.

• Prime numbers, like the set of all numbers, are infinite, but the larger they are, the more difficult it is to calculate the next prime number. As happens when mining cryptocurrencies (whose base is prime numbers), the more cryptocurrencies are calculated, the more complex it is to calculate the next one.

• The largest prime number discovered has more than 23 million digits and is the result of -1 + 2^77232917. Which also makes it a member of the select club of "Mersenne Primes", which are those prime numbers that comply with the formula (-1 + 2^x), with x also being a prime number. There are currently only about 50 Mersenne primes ​​discovered.

• The number 2 is the only prime number that is even.

• In 1963, mathematician Stanislaw Ulam created a visual method to look for patterns among prime numbers. By writing consecutive numbers in a square spiral and marking the primes, Ulam discovered surprisingly dense diagonal lines of prime numbers, suggesting underlying patterns in their distribution. This is known as The Spiral of Ulam .

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