## The Pond Conjecture: Fishing For Patterns In Primes

2024-08-01 | tags : primes, videogame, conjectureA recent news about the distribution of prime numbers brings back the memory of a videogame that I started developing a while ago.

The game was inspired by an interesting pattern I've observed in prime numbers. There are few "islands" of prime numbers with a striking symmetric distribution.

The news about primes distribution is here. While the symmetric pattern of the primes is found on the post titled: Primes alignment

And here is the gist of the game titled **"The Pond Conjecture"**

### The story: a conjecture is born

Meet **Xander Pond**, a young Hungarian mathematician.

In 1965 Xander Pond presented his theory on the prime number distribution at the Budapest Mathematical Society conference.

**Xander claimed that given any prime number he could predict all the following ones**.

As recorded in the acts of the conference, the theory had no grounds, or better, it was based on the **absurd postulate that natural numbers are finite**.

Shocked and upset by the ludicrous postulate, the community derided Xander. Xander could do nothing but leave the conference. Back in his hometown, he was stripped of his academic title and rejected by his alma mater.

Disappointed and at his rock bottom, Xander left town and retired to a cottage in the woods of the Bukki National Park (Bukk Mountains of Northern Hungary) In his last years, **Xander devoted his last days to the relentless search for a confirmation of his theory** (relegated to the status of conjecture by the community, but only to make fun of Xander!).

In yet another counterintuitive move, **Xander turned to nature to find the ultimate proof of the veracity of his theory in abstract mathematics** (God gave us the natural numbers, after all!)

The videogame recounts the last days of Xander's life.

In a final twist, **Xander finally meets God (who looks awfully similar to Gauss...) on the shore of a small pond. God is throwing pebbles into the pond, creating small waves**. Xander humbly asks God: << What are you doing?>>.

**God replies:<< throwing pebbles in the pond...>>**

As Xander looks into the pond, he realizes that **the pond is nothing but the set of natural numbers. The pebbles generate wavy patterns in the natural numbers letting emerge prime numbers!**.

In his last breath of life, Xander sees that the **naturals are finite** and that the pattern he discovered in the primes is nothing but the point of contact of the pebbles with the water. It follows that **the wavy pattern of primes is degraded as it bounces back and forth against the shores of the pond of natural numbers**, leaving humanity pondering about the puzzling pseudo-random distribution of the primes.

So it is true, **this wavy-bouncing pattern in prime numbers is only observed because the Naturals are finite! He was right all along!**

As the story goes, Xander dies in the woods leaving humanity in the dark of why prime numbers have such an elusive distribution.