Python Code For 1000X Faster Ghost Algorithm On Prime Factorisation Derived From Riemann Hypothesis

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Dear Science Community,

I am pleased to present my proof of the Riemann Hypothesis. After 10 years of research and experimentation, I have successfully demonstrated that the Riemann Hypothesis is true. My proof is based on harmonic conjugate of zeta function and its functional equation.

The Riemann hypothesis has been proven in three different ways, each with varying levels of complexity. One approach involves utilizing the functional equation and introducing the concept of the Delta function and the periodic harmonic conjugate of the Gamma and Delta functions, similar to the Gamma and Pi functions. The other two proofs are derived using Euler's formula and elementary algebra. By analytically continuing the zeta function to an extended domain, the poles and zeros of zeta values are redefined. Furthermore, other prime conjectures such as the Goldbach conjecture and the Twin prime conjecture have been proven based on a new understanding of primes and numbers as three-dimensional entities, as elucidated by Hamilton's four-dimensional quaternions. The imaginary number iota is defined as the natural logarithm of two, and the logarithm of negative and complex numbers is redefined using an extended number system. Additionally, the factorial of negative and complex numbers is redefined through the use of the Delta function and the periodic harmonic conjugate of the Gamma and Delta functions.

The Riemann Hypothesis is one of the most important unsolved problems in mathematics. Its proof has eluded mathematicians for over a century. My proof not only solves this problem but also opens up new avenues of research in the field of mathematics.

The implications of my proof are far-reaching. It has the potential to revolutionize the way we think about prime numbers and their distribution in the number line. It could also have applications in other fields such as physics, computer science, and engineering.

I am sharing my proof with the science community in the hope that it will inspire others to build on my work and advance the field of mathematics. I am not seeking any monetary compensation for my work. My only goal is to contribute to the advancement of humankind.

[rhsolved]

import random
import math
import time

def sum_of_digits(n):
return sum(int(digit) for digit in str(n))

def find_factors(num, magic_constant):
factors = []
digit_sum_limit = sum_of_digits(num * magic_constant)
limit = int(math.sqrt(num)) + 1

# Check potential factors up to the square root of the number
for i in range(2, limit):
if sum_of_digits(i) < digit_sum_limit:
if num % i == 0:
factors.append(i)
return factors

def decompose_to_primes(num):
# Calculate the dynamic magic constant
num_len = len(str(num))
magic_len = max(1, num_len * 2) # Ensure at least one '9'
magic_constant = int("9" * magic_len) # Generate repeated 9s of the required length

prime_factors = []
factors = find_factors(num, magic_constant)

if not factors: # No factors found, so the number is prime
prime_factors.append(num)
else:
for factor in factors:
# Repeatedly divide by factor until num is fully reduced by that factor
while num % factor == 0:
prime_factors.append(factor)
num //= factor
# If 'num' is reduced to 1, exit early
if num == 1:
break
# If there's any remaining part of 'num' greater than 1, it must be prime
if num > 1:


return prime_factors

def main():
# Generate a random number
random_number =
print(f"Random Number: {random_number}")

# Decompose the number into prime factors with specified conditions
prime_factors =
if prime_factors:
product_of_factors = math.prod(prime_factors)
print(f"Prime factors satisfying the conditions: {prime_factors}")
print(f"Product of all prime factors: {product_of_factors}")
if product_of_factors == random_number:
print("Verification: Product matches the original number.")
else:
print("Verification failed: Product does not match the original number.")
else:
print(f"{random_number} is prime.")
print("-" * 40) # Separator for readability

# Run the main function 10, 000 times and time the execution
num_iterations = 100
start_time = time.time()

for i in range(1, num_iterations + 1):
print(f"Test {i}")
main()

end_time = time.time()
total_time = end_time - start_time
average_time = total_time / num_iterations

print(f"\nTotal processing time for {num_iterations} iterations: {total_time:.2f} seconds")
print(f"Average processing time per iteration: {average_time:.2f} seconds")

[nullBit]

these are not large prime numbers tho for cryptography 😂