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Factoring 15 while using the fact that 15 = 5 x 3 to build the circuit.

(IIRC this is still the best; all the hype-y 2^xxx+1 PR ones aren't really using Shor's algorithm and also use some number theoretic short-cuts).

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Factoring 15 with quantum computers happened nearly 22 years ago[1]. The current record for factoring, with just Shor's and no minimization, is 21. Like you said, a lot of the hyped ones aren't practical. It's not that hard to pretend to factor large numbers on a quantum computer [2]. There have been a few newer algorithms can work with larger numbers, but they have scaling issues and so aren't useful for cryptography.

[1]https://research.ibm.com/blog/factor-15-shors-algorithm [2]https://arxiv.org/abs/1301.7007

Don’t forget 2x2=4

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