**[update (09/03/14): Vladica Andrejic and I wrote a paper regarding this problem and extended the search to 2^34 »]**

Kurepa’s left factorial hypothesis states that , for all , where . This conjecture is also listed as a problem B44 in Guy’s “Unsolved problems in number theory”.

Official proof was published in 2004 by D. Barsky and B. Benzaghou “Nombres de Bell et somme de factorielles”. **[update (12/12/12): This ‘proof’ turned out to be false »]**

Vladica Andrejic (University of Belgrade) was suspicious that proof isn’t valid and conjectured that there are good chances that counterexample lies in the interval . Using the existing hardware, it isn’t possible to check all values from this interval, so I decided to extend the search beyond , which was covered in the latest attempt by P. Jobling.

Unfortunately, I didn’t find any counterexamples, but new values for were found.

Some previous searches:

– Miodrag Zivkovic, 1999,

– Yves Gallot, 2000,

– Paul Jobling, 2004,

My results for and