MRob> I discovered a calculation error problem in Wolfram Alpha. When given "20000!" (the factorial of 20000) it gives the answer in two forms: * a "Decimal approximation", 1.8192063202303451348276... x 10^77337 * a "Power of 10 representation", 10^(10^4.888364627124846). My own calculations (using the Stirling series for the log Gamma function) indicate that the first answer is correct. One can see that the second answer disagrees with the first, by computing log(77337+log(1.81920632023)) using base-10 logarithms. The exponent should be 4.888388... not 4.888364... For "LogGamma[20001]", Wolfram Alpha gives 178075.621737198700312867928177..., which agrees with its first 20000! answer and with my calculations. I also checked this in GP/PARI, which of course gives all the digits of 20000!, but you can multiply by 1.0 to put it in the more familiar scientific notation, and it agrees with Wolfram Alpha's first answer. I'd be curious to find out what Mathematica gives (I suspect it will be the correct first answer). I sent feedback to WoldramAlpha to report the problem. -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 -mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com In[487]:= N[20000!, 22] Out[487]= 1.819206320230345134828*10^77337 In[488]:= Log[10, Log[10, %]] Out[488]= 4.888388780625234145206724465 In[489]:= N[Log[10, Log[10, 20000!]], 23] Out[489]= 4.8883887806252341452067 --rwg