Why Quantum Computers Haven't Factored 21 Yet (Despite Factoring 15 in 2001)
2025-08-31
In 2001, quantum computers factored 15. Now, in 2025, factoring 21 remains a challenge. This isn't due to a lack of progress, but rather a surprising complexity difference. Factoring 15 required 21 entangling gates, while factoring 21 needs a staggering 2405 – a 115x increase! This is because factoring 15 benefits from: 1. Most multiplications resulting in 1; 2. The first multiplication being cheap; 3. Modular multiplication simplifying to circular shifts. Factoring 21 lacks these advantages. Therefore, using number size alone to track quantum computing progress is misleading; focus should be on error correction and architectural advancements.