This claim will pay 6*n cents (maximum of 100 cents) if a quantum computer has factored a number with n binary digits using the Shor algorithm, or any other essentially quantum algorithm, by July 1, 2006. n must be at least 4.Here an algorithm is "essentially quantum" if it is asymptotically much faster when executed by a quantum computer than when simulated by a standard (classical) computer.
If the conjectured gap between quantum and classical factoring algorithms disappears before the deadline, e.g. if someone finds a classical factoring algorithm whose complexity is comparable to that of the Shor algorithm, this claim will fail.
Note that a quantum computer is not the same as a standard computer that uses quantum devices such as silicon transistors. See the e-print archive quant-ph for both introductions to quantum computation and the state of the art.
I am in the process of judging this claim. Currently, I seek information on any publically released results after the IBM experiment which used a quantum computer to factor 15 (a 4 bit or binary digit number) using the Shor algorithm.
For results of a successful experiment to be accepted, the results must have been released publically by July 1. It is quite possible that larger numbers have been factored using a quantum computer in the time frame of the claim, but these results won't be accepted if the results were not publically announced by this time.