In 2001, quantum computers factored 15, but by 2025 they have yet to factor 21. This gap is not due to a lack of progress but rather the vastly increased complexity of factoring 21 compared to 15. The critical factor is the quantum circuit cost, measured mainly by the number of two-qubit entangling gates. The factoring-15 circuit uses 21 entangling gates, while the factoring-21 circuit requires about 2405 entangling gates, making it over 100 times more expensive. This huge increase arises because, in Shor’s algorithm, factoring an n-bit number N involves conditional modular multiplications by constants m_k = g^(2^k) mod N. For 15, most of these multiplications are by 1, which costs nothing to implement, and the nontrivial multiplications can be simplified using rare properties of modulo 15 (close to a power of two). Specifically, - Most multiplications in factoring 15 are by 1 and require no operation. - The first multiplication is simple since its input is always 1. - Multiplication by 4 mod 15 can be implemented by simple circular shifts (conditional swaps), a special and rare property. In contrast, for factoring 21, using g=2 as an example, all multiplications are nontrivial (none equal 1), so every step must be performed explicitly, contributing about 4x cost increase. The first-one-free trick only reduces a small fraction, giving another 1.8x increase, and the multiplications by 4 and 16 mod 21 cannot be simplified and require many Toffoli gates, contributing about a 20x increase. These multiplicative effects compound to roughly a 100x increase in circuit cost from 15 to 21. Additional factors slowing progress include the nature of early quantum computers used for factoring 15 (NMR quantum computers with scaling issues), and the overhead of quantum error correction needed to reduce errors for the much longer circuits. Factoring 21 thus requires error rates roughly 100 times lower or correspondingly larger overhead, possibly putting actual resource needs up to 10,000x that of factoring 15. Claims of factoring 21 on quantum computers often rely on circuit optimizations that implicitly use prior knowledge of the factors, not genuine quantum factoring, so those results are not considered true celebrations of progress. Thus, factoring beyond 15 remains an open and challenging benchmark, and near-term progress is better tracked by advances in quantum error correction and scalable quantum architectures rather than factoring itself.