Divisible only by itself and one. Remarkably simple, but simply amazing.

“Prime, any positive integer greater than 1 that is divisible only by itself and 1” []. For years I've associated primes with this definition and didn't think much of it. Primes were a mere abstraction; their profundity obscured up until some recent idle thoughts.

“A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers.” []. This definition better conveys their extraordinary nature, but it's still no match for actually visualizing what “indivisible” or “not a product” means.

996 = 1 × 996 = 2 × 498 = 3 × 332 = 4 × 249 = 6 × 166 = 12 × 83 = 2 × 2 × 3 × 83. Simply put, it is possible to represent a collection of 996 things as multiple equal collections of a smaller size. For instance, below is 996 represented as 3 collections of 332 letters “i”.

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Okay, so what?

997 = 1 × 997. That's it. Merely adding 1 to 996 makes a collection of 997 things, a collection that is *impossible* to represent as any other amount of equal collections of a smaller size—“impossible”!

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What the heck? It goes to show how some *one* can make a difference—how *you* can change the world.

Remarkable. But now consider the prime 67 280 421 310 721, which reads “67 trillion 280 billion 421 million 310 thousand 721”, yes, also indivisible. Let's go even bigger. The current largest known (Mersenne) prime is:

2^{82589933} - 1 = 148894445742041325547…(24 862 006 digits omitted)…037951210325217902591.

So, primes can be unfathomably large, are infinite in supply [], yet remain indivisible. Seriously, how?

—Angelino Desmet; 21 January 2022.

Edited: 23 January 2022.

♔

- Britannica: prime.
- Wikipedia: prime number.
- The University of Utah: Why are there infinitely many prime numbers?

- Wikipedia: Mersenne prime.
- Great Internet Mersenne Prime Search: Why join GIMPS?
- Vicky Neale: Closing the Gap: The Quest to Understand Prime Numbers.

Reply on Telegram.