Shor's algorithm is possible with as few as 10k reconfigurable atomic qubits (arxiv.org)

The paper argues that Shor’s algorithm could be run for cryptographically relevant problems using as few as 10,000 reconfigurable neutral-atom qubits by combining recent advances in fault-tolerant quantum error correction, efficient logical operations, and circuit design. The authors estimate that more qubits would improve runtime, giving example timelines such as a few days for discrete logarithms on P-256 with about 26,000 physical qubits, while RSA-2048 factoring remains significantly longer. They conclude that, while engineering challenges are substantial, a neutral-atom platform could plausibly reach the required scale.