Prime number distribution and hit in a carrom game

In summary, the conversation discusses the unpredictability of the carrom game and the distribution of prime numbers. It is mentioned that there is no general formula to determine the exact position of the carrom piece after hitting the wall multiple times, similar to how there is no formula to determine the nth prime number. However, it is noted that the distribution of prime numbers has been extensively researched and it is possible to determine if a number is prime with enough time and resources.
  • #1
rajeshmarndi
319
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In carrom game, we have black/white small disc pieces, just imagine we have a single piece of it on the board.We hit that pieces with a striker on one side of the four wall. And the pieces goes on hitting side of the wall, number of times.

If I'm right, there cannot be a general formula, which can determine at what point of the wall, the pieces will hit after it goes hitting the wall nth times. We can have a formula, where the hit will be on the next wall but not where the hit will be after the pieces goes through hitting n wall.

What a computer does is, it calculates each hit position and goes on to the next hit position and finally arrive at the nth hit. This is how it can show the nth hit position.

Prime number distribution is similarly. If we take first primes number( for simplicity, ignoring 2 & 3 because we know all 2&3 multiples are not primes) 5,7 11,13 17,19 and 23. All the two combination of these numbers i.e multiply , they will generate composite number(25,35,49,55,65,77,...23^2) and between these composite number are new prime number. Again when these primes number multiply among themselves, they will again generate new composite number and prime number. And this go on.

So, just like we cannot have a formula of the point after nth hit in a carrom, similarly we cannot know nth prime number.
 

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  • #2
Not quite sure whether this is a legitimate comparison. The billiard balls are unpredictable because we do not know all parameters for a calculation, it's a lack of information. Prime number distribution was investigated in dozens of papers. Not knowing whether a number is prime or not means we haven't checked, yet. At least we can in principle, even if it takes too long for big primes.
 

1. What is a prime number?

A prime number is a positive integer that can only be divided evenly by 1 and itself. This means that prime numbers have exactly two factors.

2. How are prime numbers distributed?

The distribution of prime numbers is not completely understood, but they tend to become less frequent as numbers get larger. However, there are still an infinite number of prime numbers.

3. How are prime numbers related to carrom games?

In a carrom game, prime numbers are important because they determine the number of points a player can earn in a single turn. For example, if a player hits a single piece into a pocket, they earn the number of points equivalent to the prime number of that pocket.

4. How do prime numbers affect the strategy of a carrom game?

Since prime numbers are crucial in earning points in a carrom game, players often strategize to hit their pieces into pockets that correspond to prime numbers. They may also try to block their opponents from hitting their pieces into prime number pockets.

5. Is there a correlation between prime numbers and winning a carrom game?

There is no direct correlation between prime numbers and winning a carrom game. However, knowing how to strategically use prime numbers to earn points can certainly give players an advantage in the game.

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