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I read that one reason why RSA is secure is because it uses a huge number that's called the modulus which is the product of two prime numbers.

For maths reasons the prime numbers being prime numbers allow only them to be multiply together and have that exact modulus as a result.

Getting both prime numbers from the modulus is hard. It would take years to do so and this is where the security comes from.

There seems to be an interest to find more and more prime numbers. A lot of prime numbers are known publicly and every once in a while they find another one. They become longer and longer, which helps with the algorithm.

If multiplying two primes is so much easier then the inverse task, why does nobody do this? Why does nobody multiply all known primes and build a table of results?

Would this be as impractical as solving factorisation problem? Or are the primes used for RSA secret?

I heard that people do this with hashing algorithms to build so called "rainbow tables" and am wondering why not the same is happening to RSA.

I'm not really into cryptography and would appreciate an answer in simple terms if possible.

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marked as duplicate by otus, SEJPM, Community Apr 18 '16 at 19:53

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