[pclmulqdq]

If you want a number accompanied by a scientific publication, the best you get is 21: https://www.nature.com/articles/s41598-021-95973-w

IBM has gone through 2 generations of chips since then.

[sgt101]

But have they factored anything bigger?

[pclmulqdq]

They have reportedly made it to proving that 31 is prime, as I said earlier, using their 1000-qubit chips.

[adgjlsfhk1]

proving primality is doable in polynomial time without a quantum computer, so that's hardly impressive.