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> RSA works by raising numbers to a large power and then finding the remainder when divided by a big number.

Not necessarily. A common value for the exponent is 3. I don't think one would consider that a large exponent.

What a pointless article. Not only doesn't it get into the interesting side-effects of choosing Mersenne primes as your private key (which is actually interesting, as the bit pattern of a*b is very apparent when you multiple two Mersenne primes). The whole thing is just talking about "don't use this shiny new prime because people will notice that you have very long public keys". It glosses over how key generation actually works, and I really don't understand why the author felt like wasting people's time with such lack of content.
It's just a matter of time before using Shor's algorithm is feasable, and then encryption as we know it will be dead.
Quantum computing is an area where the hype is out of proportion to the certainty about time until its feasible. With self driving cars there are arguments about the number of decades until it is in use. With QC the uncertainty about building a quantum computer that can be used to break current RSA keys is about the order of magnitude of the number of years.
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