Prime Number Waveform Coordinates Dataset - Midpoint Log Axis and Alternating Prime Gaps (Up to 1 Billion)

This dataset contains prime gap waveform coordinate values and corresponding plotted waveforms derived from the prime numbers upto 1 billion natural numbers.

Each CSV file contains:

• X-coordinates: log₁₀ of the midpoints between consecutive primes

• Y-coordinates: alternating prime gaps (positive/negative)

This representation yields a novel “prime waveform” that reveals visually interpretable oscillatory patterns in prime gaps when plotted.

The dataset includes both:

• CSV files for data reuse and reproducibility

• PNG and SVG waveform images for each scale

Included files:

• Prime gap coordinates and plots from 2 to 100

• Prime gap coordinates and plots from 2 to 1,000

• Prime gap coordinates and plots from 2 to 10,000

• Prime gap coordinates and plots from 2 to 100,000

• Prime gap coordinates and plots from 2 to 1,000,000

• Prime gap coordinates and plots from 2 to 10,000,000

• Prime gap coordinates and plots from 2 to 100,000,000

• Prime gap coordinates and plots from 2 to 250,000,000

• Prime gap coordinates and plots from 2 to 500,000,000

• Prime gap coordinates and plots from 2 to 750,000,000

• Prime gap coordinates and plots from 2 to 1,000,000,000 (1B)

This dataset supports ongoing research in prime visualizations, analytic number theory, and educational signal representations.

All figures and coordinate files are included in this versioned release.

To cite this dataset, please use the DOI provided.