Why haven't quantum computers factored 21 yet?

The article explains why quantum computers, despite factoring 15 in 2001, have not yet factored 21. It details that factoring 21 is over 100 times more computationally expensive than factoring 15, primarily due to the properties of modular multiplications in Shor's algorithm. The author elaborates on three key factors: the absence of multiplications by 1, a less effective 'first-one's-free' optimization, and the more complex implementation of certain modular multiplications for 21 compared to 15. The article also discusses other contributors to this gap, such as the inherent scaling issues of early NMR quantum computers, the significant overhead of quantum error correction, and the prevalence of misleading research claims regarding quantum factoring. It concludes that factoring numbers like 21 is not currently a good benchmark for assessing progress in quantum computing, suggesting focus should be on quantum error correction and scaling challenges instead.