prime_pair_constellations.py

# prime_pair_constellations.py

import plotly.graph_objects as go
from core.primes import generate_primes

def run_visualization(limit, primes_list=None):
    """
    Visualizes the Goldbach Conjecture as an interactive heatmap constellations of
    prime pairs using Plotly. 
    Hover over any point to see the prime pair and their even sum.
    """
    print("Generating interactive Prime Pair Constellation...")

    if primes_list is None:
        primes_list = generate_primes(limit)

    x_coords = []
    y_coords = []
    text_labels = []

    # Iterate through all prime pairs (p1,p2)
    for i in range(len(primes_list)):
        p1 = primes_list[i]
        for j in range(i, len(primes_list)):
            p2 = primes_list[j]
            even_sum = p1 + p2

            x_coords.append(p1)
            y_coords.append(p2)
            text_labels.append(f'{p1} + {p2} = {even_sum}')

    # Plotly scatter plot
    fig = go.Figure(data=go.Scatter(
        x=x_coords,
        y=y_coords,
        mode='markers',
        marker=dict(
            size=5,
            color=[val for val in x_coords],  
            colorscale='Viridis',
            showscale=True,
            colorbar_title="Prime Number"
        ),
        text=text_labels, # This is the text that appears on hover
        hoverinfo='text'
    ))

    # Update plot layout for a cleaner look
    fig.update_layout(
        title=f'Goldbach Prime Pair Constellations (up to {limit})',
        xaxis_title='Prime Number p1',
        yaxis_title='Prime Number p2',
        width=800,
        height=800,
        plot_bgcolor='black'
    )

    # Show the plot ( in browser window)
    fig.show()
    print("Interactive Prime Pair Constellation Visualization complete.")