Prime Vowel Mapping Project

A Python program that maps prime numbers to vowels, generates composites through mathematical operations, and visualizes the relationships using graphs. It also includes utilities for prime factorization.

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Features

• Prime-to-Vowel Mapping: Assigns vowels to prime numbers and dynamically maps higher primes using fallback vowels.
• Composite Generation: Creates composite numbers through addition, multiplication, and exponentiation of prime pairs.
• Visualization:
  • Static graphs using Matplotlib.
  • Interactive graphs using Plotly.
• Prime Factorization: Identifies the prime factors of a given number.

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Requirements

The program requires the following Python packages:

sympy==1.13.3
matplotlib==3.9.2
networkx==3.4.2
plotly==5.24.1

To install dependencies, run:

pip install -r requirements.txt

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How to Run

1. Clone the repository:

   git clone <repository_url>
   cd PrimeVowelMap

2. Run the program:

   python prime_vowel_map.py

3. Follow the on-screen prompts:

   • Enter an upper limit for generating primes.
   • Enter a number to factorize.
   • Choose a visualization method (static or interactive).

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Example Usage

Input:

• Upper limit for primes: 20
• Number to factorize: 30
• Visualization: static

Output:

• A list of primes and their vowel mappings.
• Composite mappings based on mathematical operations.
• Prime factors of the input number.
• A graph visualizing relationships (static or interactive).

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Functions

1. generate_vowel_mappings(limit):

   • Generates prime numbers up to the specified limit and maps them to vowels.

2. generate_composite_vowel_mappings(primes, vowel_mappings):

   • Creates composites using addition, multiplication, and exponentiation.

3. plot_static_graph(primes, vowel_mappings, composites, composite_mappings):

   • Visualizes relationships using Matplotlib.

4. plot_vowel_graph(primes, vowel_mappings, composites, composite_mappings):

   • Visualizes relationships interactively using Plotly.

5. find_prime_factors(number):

   • Finds the prime factors of a given number.

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Limitations

• Large values for prime generation or exponentiation may cause performance issues.
• Requires Python 3.8+ for compatibility.

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Future Enhancements

• Optimize composite generation for larger numbers.
• Add support for distributed computation of primes and composites.
• Improve graph aesthetics for better clarity with large datasets.