CONTINUED FROM - Strong Nuclear, Weak Nuclear, Nuclear-Nuclear, and Light, Why Not? - #5 by Josef_Founder
Static:
import math
# Step 1: Define the dynamic adjusted prime formula
def adjusted_prime_formula(n, alpha=1, decay_constant=2, r_scale=1, nu=1):
"""
Calculate a potential prime based on the refined framework formula:
p_n = (alpha * (F_n + nu)) / r_n * (1 - epsilon_n)
Args:
n (int): The prime number position to estimate.
alpha (float): Scaling factor for force calculation.
decay_constant (float): Exponent to modulate the decay effect of the error term.
r_scale (float): Scaling factor for distance parameter.
nu (float): Harmonic scaling factor to adjust for the force.
Returns:
float: Calculated potential prime number based on the formula.
"""
# Adjust force and distance dynamically based on n
F_n = n**2 # A polynomial growth of force for large numbers (n^2 for scaling)
r_n = math.log(n) # Logarithmic scale for distance factor
# Calculate error term epsilon_n based on the adjusted parameters
epsilon_n = (F_n / n) ** (1 / 2) * (1 / math.log(n))
# Calculate the prime estimate with the formula
prime_estimate = (alpha * (F_n + nu)) / r_n * (1 - epsilon_n)
return prime_estimate
# Step 2: Simple primality check
def is_prime(n):
"""
Check if a number is prime using a simple primality test.
Args:
n (int): The number to check for primality.
Returns:
bool: True if the number is prime, False otherwise.
"""
if n <= 1:
return False
for i in range(2, int(math.sqrt(n)) + 1):
if n % i == 0:
return False
return True
# Step 3: Generate primes using the adjusted formula and check them
def generate_primes(limit):
"""
Generate and validate primes using the adjusted prime formula.
Args:
limit (int): The upper limit for generating primes.
Returns:
list: A list of prime numbers identified through the formula.
"""
primes = []
for n in range(2, limit + 1):
prime_value = adjusted_prime_formula(n)
if is_prime(int(prime_value)):
primes.append(int(prime_value))
return primes
# Step 4: Test the framework with larger primes
limit = 1000 # Change this to a larger number for bigger primes
primes = generate_primes(limit)
# Output the prime numbers found
print("Primes found using adjusted framework:", primes)
Dynamic:
import math
# Step 1: Define the dynamic adjusted prime formula with automatic parameter selection
def adjusted_prime_formula(n):
"""
Calculate a potential prime based on dynamically adjusted force, distance, and error term.
Args:
n (int): The prime number position to estimate.
Returns:
float: Calculated potential prime number based on the formula.
"""
# Step 1a: Automatically select parameters based on n
alpha = n / 10 # Scaling factor for force calculation (dynamically adjusted)
decay_constant = 2 + math.log(n) # Decay constant modulated by log(n)
r_scale = n ** (1 / 3) # Distance scaling for larger n (cube root scaling)
nu = math.sin(n) # Harmonic scaling factor based on n
# Step 1b: Adjust force and distance dynamically based on n
F_n = n**2 # A polynomial growth of force for large numbers (n^2 for scaling)
r_n = math.log(n) # Logarithmic scale for distance factor
# Step 1c: Calculate error term epsilon_n based on the adjusted parameters
epsilon_n = (F_n / n) ** (1 / 2) * (1 / math.log(n))
# Step 1d: Calculate the prime estimate with the formula
prime_estimate = (alpha * (F_n + nu)) / r_n * (1 - epsilon_n)
return prime_estimate
# Step 2: Simple primality check
def is_prime(n):
"""
Check if a number is prime using a simple primality test.
Args:
n (int): The number to check for primality.
Returns:
bool: True if the number is prime, False otherwise.
"""
if n <= 1:
return False
for i in range(2, int(math.sqrt(n)) + 1):
if n % i == 0:
return False
return True
# Step 3: Generate primes using the adjusted formula and check them
def generate_primes(limit):
"""
Generate and validate primes using the adjusted prime formula.
Args:
limit (int): The upper limit for generating primes.
Returns:
list: A list of prime numbers identified through the formula.
"""
primes = []
for n in range(2, limit + 1):
prime_value = adjusted_prime_formula(n)
if is_prime(int(prime_value)):
primes.append(int(prime_value))
return primes
# Step 4: Test the framework with larger primes
limit = 1000 # Change this to a larger number for bigger primes
primes = generate_primes(limit)
# Output the prime numbers found
print("Primes found using adjusted framework:", primes)