Prime Number Waveform • Visualizing Prime Gaps up to 1 Billion

This project provides Python scripts and datasets to generate prime gap waveforms — a novel visual representation of the gaps between consecutive prime numbers. Using the logarithmic midpoint between each prime pair and alternating the prime gaps in sign, the result is a striking, continuous waveform with both signal-like structure and emergent patterns.

📌 What This Project Does

• Generates coordinate pairs: x = log10(midpoint of prime pair), y = ±(prime gap)
• Produces smooth, high-resolution waveform plots (PNG + SVG)
• Supports waveform generation up to 1 billion natural numbers
• Optionally exports coordinate data to CSV files for further analysis

💡 Why It’s Useful

• Creates the first known visual archive of prime gap behavior at this scale
• Offers a reproducible framework for:
  • Mathematical pattern exploration
  • Educational demonstrations
  • Data-driven signal analysis (without traditional signal tools)
• Can support further research in number theory or AI pattern detection

📚 Dataset & Paper

• 📦 Full datasets up to 1 Billion numbers: Zenodo DOI [https://zenodo.org/records/15636895]
• 📝 Preprint (coming soon): [arXiv link]

🙋‍♂️ Who Maintains This

Created and maintained by Shashaank C D, independent researcher. This is part of an open-access contribution to mathematical exploration. Feel free to open issues or submit pull requests!

📬 Contact

🌐 ORCID: 0009-0006-0174-189X 🔗 LinkedIn: Shashaank CD

📄 License

This project is licensed under the MIT License — feel free to use, modify, and share with attribution.

🚀 Getting Started

Requirements

Make sure you have Python 3.8+ and the following libraries:

pip install sympy matplotlib pandas numpy scipy