wwp 1.1.1
Python module for working with prime numbers
License: MIT
Requires Python: >=3.10
Keywords: Prime,Numbers,Mathematics,Math

# Working With Primes

This Python module provides a collection of functions for visualizing and performing operations with prime numbers. It is a simple tool for mathematical analysis and educational purposes.

## Usage

To use this module, import it in your Python script:

to import all functions

```
from wwp import *
```

or to import specific functions,

```
from wwp import _function_name_
```

Then you can use the functions provided in the module, For example:<br>


Getting the first 5 known prime numbers:

```
from wwp import firstNPrimes

firstFivePrimes = firstNPrimes(5)

print(firstTwelvePrimes)

#Output: [2, 3, 5, 7, 11] 
```

## Functions

### firstNPrimes(n): 
Returns an array containing the first 'n' prime numbers along the number line.<br><br>
**Arguments**:<br>
n (int): The number of prime numbers to generate.<br><br>
**Returns**:<br>
list: A list of the first 'n' prime numbers. <br>
None: If 'n' is equal to 0.

### isPrime(n):
Returns True if 'n' is prime and False if it is not.<br><br>
**Arguments**:<br>
n (int): The number to check for primality.<br><br>
**Returns**:<br>
Boolean: True if 'n' is prime and False if it is not.<br>
None: If 'n' is equal to 0.

### differences(n):
Returns an array containing the differences between successive prime numbers up to the 'n'-th prime.<br><br>
**Arguments**:<br>
n (int): The number of prime numbers to consider for difference calculation.<br><br>
**Returns**:<br>
list: A list of the differences between successive prime numbers.<br>
None: If 'n' is equal to 0.

### sumOfPrimes(n):
Calculates the sum of the first 'n' prime numbers.<br><br>
**Arguments**:<br>
n (int): The first 'n' prime numbers to add up.<br><br>
**Returns**:<br>
int: The sum of the first n prime numbers.<br>
None: If 'n' is equal to 0.

### theNthPrime(n):
Returns the 'n'-th prime number.<br><br>
**Arguments**:<br>
n (int): The position of the prime number.<br><br>
**Returns**:<br>
int: The 'n'-th prime number.<br>
None: If 'n' is equal to 0.

### sumOfDifferences(n):
Calculates the sum of differences between the first 'n' prime numbers.<br><br>
**Arguments**:<br>
n (int): The first 'n' prime numbers to consider.<br><br>
**Returns**:<br>
int: The sum of the differences between the first 'n' prime numbers.<br>
None: If 'n' is equal to 0.

### primeCounting(n):
Returns the number of primes less than 'n'.<br><br>
**Arguments**:<br>
n (int): The positive integer for which you want to count the prime numbers less than it.<br><br>
**Returns**:<br>
int: The number of prime numbers less than 'n'.<br>
None: If 'n' is equal to 0.

### lcm(n):
Calculates the lowest common multiple of the first 'n' primes.<br><br>
**Arguments**:<br>
n (int): The first 'n' prime numbers to consider.<br><br>
**Returns**:<br>
int: The lowest common multiple of the first 'n' prime numbers<br>
None: If 'n' is equal to 0.

### primeSlice(start, stop):
Returns an array of prime numbers between 'start' and 'stop' (inclusive).<br><br>
**Arguments**:<br>
start (int): The starting integer for the range.<br>
stop (int): The ending integer for the range.<br><br>
**Returns**:<br>
list: A list of prime numbers within the inclusive range from 'start' to 'stop'.

### primeDifferenceSlice(start, stop):
Returns an array of the differences between successive prime numbers between 'start' and 'stop' (inclusive).<br><br>
**Arguments**:<br>
start (int): The starting integer for the range.<br>
stop (int): The ending integer for the range.<br><br>
**Returns**:<br>
list: A list of the differences between the prime numbers within the inclusive range from 'start' to 'stop'.

### modifyValues(array, operation, operand):
Modifies an array using the specified 'operation' and 'operand' values.<br><br>
**Arguments**:<br>
array (arr): An array of integer values.<br>
operation (str): The operation to perform on the prime numbers within the range. Valid values are "multiply" or "*", "divide" or "/", "subtract" or "-", "add" or "+", and "exponent" or "^".<br>
operand (int, float or expression): The value to use as the operand for the specified operation.<br><br>
**Returns**:<br>
list: A list of integers after applying the specified 'operation' and 'operand'.

### randomPrimeSlice(start, stop, length):
Generates a random selection of prime numbers within the inclusive range from 'start' to 'stop'.<br><br>
**Arguments**:<br>
start (int): The starting integer for the range.<br>
stop (int): The ending integer for the range.<br>
length (int): The number of prime numbers to include in the random selection.<br><br>
**Returns**:<br>
list: A list of prime numbers randomly selected from within the inclusive range between 'start' and 'stop'.<br>
None: 'length' is equal to 0.

### randomDifferencesSlice(start, stop, length): 
Generates a random selection of differences between successive prime numbers within the inclusive range from 'start' to 'stop'.<br><br>
**Arguments**:<br>
start (int): The starting integer for the range.<br>
stop (int): The ending integer for the range.<br>
length (int): The number of differences to include in the random range.<br><br>
**Returns**:<br>
list: A list of the differences between prime numbers randomly selected from within the inclusive range between 'start' and 'stop'.<br>
None: 'length' is equal to 0.  

### graphDifferences(n):
Graphs the differences between the first 'n' successive prime numbers.<br><br>
**Arguments**:<br>
n (int): The number of successive prime numbers to consider for generating the graph.<br><br>
**Returns**:<br>
This function doesn't return any value; it generates and displays a graph.<br>
None: if 'n' is equal to 0.

### graphPrimes(stop, operation, operand, start):
Plots and displays a graph comparing a set of regular and modified prime numbers.<br><br>
**Arguments**:<br>
stop (int): The ending integer for the range of primes.<br>
operation (str, optional): The mathematical operation to apply to the prime numbers. Valid values are "multiply" or "*", "divide" or "/", "subtract" or "-", "add" or "+", and "exponent" or "^". Defaults to addition ("+").<br>
operand (int, float, or expression, optional): The value to use as the operand for the specified operation. Defaults to 0.<br>
start (int, optional): The starting integer for the range. Defaults to 1.<br><br>
**Returns**:<br>
This function doesn't return any value; it generates and displays a graph.

### sacksSpiral(n, coordinateRange, dotSize):
Draws a Sacks Spiral representation of the first 'n' prime numbers.<br><br>
**Arguments**:<br>
n (int): The first 'n' prime numbers to consider for drawing the Sacks Spiral.<br>
coordinateRange (int, optional): The coordinate system's range for both axis. Defaults to 100.<br>
dotSize (int, optional): The size of dots representing the prime numbers. Defaults to 5.<br><br>
**Returns**:<br>
This function doesn't return any value; it generates and displays a drawing.

### differenceSpiral(n, coordinateRange, dotSize):
Draws a spiral using the same rules of the Sacks Spiral using non-repeating differences
between the primes instead of the primes themselves. Uses turtle graphics library.<br><br>
**Arguments**:<br>
n (int): The limit of differences to consider for drawing the spiral.<br>
coordinateRange (int, optional): The coordinate system's range for both axis. Defaults to 15.<br>
dotSize (int, optional): The size of dots representing the differences. Defaults to 10.<br><br>
**Returns**:<br>
 This function doesn't return any value; it generates and displays a graph.

## License

This project is licensed under the MIT License - see the [LICENSE](https://mit-license.org/) for more details.