LOGGING IT OUT RAW (2)
Some cryptography protocols like RSA have their security based on a one-way function or trapdoor e.g, it's easy to multiply large prime numbers (e.g., 1024 bits), but factoring the result — a large semiprime is very hard. This is foundational to cryptographic security, and though there are algorithms that reduce the complexity, the problem remains hard when implemented well.
This is very interesting so I decided to explore this problem for fun more deeply. Maybe this is something I dare not look at ( trying out my way for prime factorization). Sure might fail woefully but the spark is just that I visualized the problem in my own way.
VISUALIZATION : A Color Metaphor:
Imagine a universe of infinite colors, beyond the limited color wheel we know.
- Each color represents an integer.
- Special colors represent prime numbers : pure & unmixed
- Blended colors represent composite numbers : mixtures of two or more special colors.
- Special blends made from exactly two special colors : these represent semiprimes.
- Rare refined blends symbolize safe primes, which are primes of the form 2q + 1, where q is also a prime (e.g., 23 = 2 × 11 + 1).
MY CORE QUESTIONS
Since these colors are spread arbitrarily through this infinite space, how can we:
- Find the gap between one special color and another also between one special blend (semiprime )and another?
- Determine the range or mix of special colors (primes ) that produced a given special blend (semiprime)?
- Since the colors are indefinite and we want to mix special colors at higher index, how can we easily detect and disintegrate them into their original state ( special blend state ).
Acknowledgments:
Yes, there are already methods for testing primes and for counting semiprimes in a range. There are also known results for analyzing prime gaps. But I’m approaching the problem by leading with intuition exploring patterns visually and structurally before relying heavily on existing resources.
Final Note:
My main purpose here is to learn to observe and work with my intuition at first then fall back to resources that are available to me when the fence is too high for me.
I would love to learn more about research and how to think like a researcher ❤️