An Algorithm for Fame and Wealth!

There's a mathematical problem that, if solved, would bring you fame and glory, as well as completely disrupt the global landscape of cybersecurity.
Before we get to the problem, I recommend watching two significant videos:

From here, we're getting closer to the problem:

And here's the problem... read the text of the problem carefully several times...

Given a number N, which is the product of two prime numbers (a*b=N), is there a rule, outside of prime factorization, to identify a and b? If we imagine N to be large enough (e.g., a 100-digit number), the attempts to factorize it to find a and b cannot even be done by a computer!!!

Let's take an example: 1147 is a non-prime number that is the product of two prime numbers. With a bit of calculation, you might be able to determine its prime factors, which, when multiplied together, could have produced N (in this case, 1147).
You might have developed an algorithm that can factorize a number like 1147 into two prime factors. This is valid for a 4-digit decimal number, which is relatively small. If you were given a number with 8 digits, you might still be able to do it, but with a lot of calculations... with 16 digits, the algorithm you used would probably no longer return a solution... if you got a result, call me right away... ;-)

End of the first part.
Continues...