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Nike Dattani
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New largest number factored on a quantum device is 56,153

'(Phys.org)—Researchers have set a new record for the quantum factorization of the largest number to date, 56,153, smashing the previous record of 143 that was set in 2012. They have shown that the exact same room-temperature nuclear magnetic resonance (NMR) experiment used to factor 143 can actually factor an entire class of numbers, although this was not known until now. Because this computation, which is based on a minimization algorithm involving 4 qubits, does not require prior knowledge of the answer, it outperforms all implementations of Shor's algorithm to date, which do require prior knowledge of the answer. Expanding on this method, the researchers also theoretically show how the same minimization algorithm can be used to factor even larger numbers, such as 291,311, with only 6 qubits. '

http://phys.org/news/2014-11-largest-factored-quantum-device.html

[1411.6758] Quantum factorization of 44929 with only 4 qubits

'The largest number factored on a quantum device reported until now was 143. That quantum computation, which used only 4 qubits, actually also factored much larger numbers such as 3599, 13081, and 44929, without the awareness of the authors of that work. Furthermore, unlike the implementations of Shor's algorithm performed thus far, these 4-qubit factorizations do not need to use prior knowledge of the answer. However, because they only use 4 qubits, these factorizations can also be performed trivially on classical computers. We discover a class of numbers for which the power of quantum information actually comes into play. We then demonstrate a 3-qubit factorization of 175, which would be the first quantum factorization of a triprime. '

http://arxiv.org/abs/1411.6758
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