Factoring Massive Numbers: A Machine Learning Approach

Factoring Massive Numbers: A Machine Learning Approach

We are interested here in factoring numbers that are a product of two very large primes. Such numbers are used by encryption algorithms such as RSA, and the prime factors represent the keys (public and private) of the encryption code. Here you will also learn how data science techniques are applied to big data, including visualization, to derive insights. This article is good reading for the data scientist in training, who might not necessarily have easy access to interesting data: here the dataset is the set of all real numbers -- not just the integers -- and it is readily available to anyone. Much of the analysis performed here is statistical in nature, and thus, of particular interest to data scientists. 

Factoring numbers that are a product of two large primes allows you to test the strength (or weakness) of these encryption keys. It is believed that if the prime numbers in question are a few hundred binary digits long, factoring is nearly impossible: it would require years of computing power on distributed systems, to factor just one of these numbers.

While the vast majority of big numbers have some small factors and are thus easier to break, the integers that we are dealing ...


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Great Mathematical API by Wolfram

Great Mathematical API by Wolfram

I was in the process of computing some definite integrals involving special mathematical constants, when I discovered WolframAlpha. It solves tons of mathematical problems, for free, online, offering exact solutions whenever possible. Not just integrals, but matrix computations and much more.

In my case, I was trying to see, if by computing an integral in two different ways, one using the original function on the original domain, and the other one using the inverse function on the image domain, I would be able to find a mathematical equality involving one special mathematical constant for the first integral (say e or Pi) and one involving some other special mathematical constants (say log 2) for the second integral. The idea being that, if I manage to find such a relationship, then it means that the two mathematical constants (say e and log 2) are a simple function of each other, and thus we only need one. 

Needless to say, I was not able to find such relationships. I did find some interesting stuff though. First, the WolframAlpha API, and then, I rediscovered an obscure but fundamental theorem, not mentioned in math textbooks -- a theorem linking the integral of a function to the integral ...


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