Python Code for Prime Prediction
The following is a means I developed of zeroing in on more Prime numbers as relates:
import math
import numpy as np
# Constants
phi = (1 + math.sqrt(5)) / 2 # Golden ratio
r = 1 # Resistance term (this can be modulated later)
max_n = 100 # Limit for the number of candidates to check
# Known primes (first 100 primes for demonstration)
known_primes = [
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419,
421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503
]
# Function to calculate the predicted prime number using the combined model
def predicted_prime(n):
return (phi ** n * 2 ** n * n * math.log(n)) / r**3
# Calculate discrepancies and refine predictions
def refine_predictions():
discrepancies = []
adjusted_predictions = []
for n in range(2, max_n + 1):
predicted = predicted_prime(n)
if n <= len(known_primes): # Only compare for known primes in this range
actual_prime = known_primes[n - 2]
discrepancy = abs(predicted - actual_prime)
discrepancies.append(discrepancy)
adjusted_prediction = predicted + discrepancy # Adjust prediction based on discrepancy
adjusted_predictions.append(adjusted_prediction)
return discrepancies, adjusted_predictions
# Function to simulate the contraction and expansion behavior
def adjust_growth_patterns(discrepancies):
# This can be adjusted based on observed discrepancy patterns
# For example, we might adjust the scaling factors or resistance based on the average discrepancy
avg_discrepancy = np.mean(discrepancies)
contraction_factor = 1 / (1 + avg_discrepancy) # Example contraction based on error magnitude
expansion_factor = 1 + avg_discrepancy # Example expansion based on error magnitude
return contraction_factor, expansion_factor
# Main execution loop
discrepancies, adjusted_predictions = refine_predictions()
contraction_factor, expansion_factor = adjust_growth_patterns(discrepancies)
# Output the results
print("Discrepancies between predicted and actual primes:")
print(discrepancies)
print("\nAdjusted Predictions (after considering discrepancies):")
print(adjusted_predictions)
print("\nContraction Factor:", contraction_factor)
print("Expansion Factor:", expansion_factor)
Explanation of the Code:
- Predicted Prime Calculation: We compute predicted prime candidates using the growth model defined earlier.
- Discrepancy Calculation: For each prime candidate, we compare the predicted value with the actual prime from the
known_primes list and calculate the discrepancy.
- Refining Predictions: After computing discrepancies, we adjust our predictions by adding the discrepancy to the predicted value. This allows us to refine our model iteratively.
- Contraction and Expansion: Based on the observed discrepancies, we introduce contraction and expansion factors. These factors modulate how the growth patterns of our model should change to better match the actual prime numbers.
- The contraction factor is used to reduce the influence of errors.
- The expansion factor is used to amplify the influence of errors in areas where the model is off.
Step 4: Next Steps
You can now experiment with the following:
- Refining Contraction and Expansion: You can fine-tune the contraction and expansion factors to better fit the actual prime numbers.
- Analyzing Larger Primes: We are currently limiting the predictions to the first 100 primes. You can increase this range and explore how the model performs as it approaches larger prime numbers.
- Adjusting Scaling Factors: You might want to explore how changing the values of ϕ\phiϕ, 2n2^n2n, or r3r^3r3 affects the model’s predictions. Use the discrepancies to inform these adjustments.
Conclusion
This computational implementation provides a way to deterministically predict primes by refining the growth patterns using discrepancies between predicted and actual primes. The expansion and contraction help guide the model toward better predictions and could give us more insight into the fine-tuned relationships between different number sequences and prime numbers.
I intend to follow up looking closely at the shadows of our equations to determine not only the macro but the micro as it relates to the scale and precise locality of a given prime number. Yes, Base4096 and BaseZ play a role, as does analog computing (tertiary logic).
