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(This was just going to be a comment but it got too long)

1. Maybe 1 is faster than 2 since that is running natively on the server, the VirtualBox overhead might slow things down.

2. On profiling programs:

   sage: %prun a=factorial(1000000)
            2 function calls in 0.286 seconds        
      Ordered by: internal time        
      ncalls  tottime  percall  cumtime  percall filename:lineno(function)
           1    0.286    0.286    0.286    0.286    0.286 <string>:1(<module>)
           1    0.000    0.000    0.000    0.000 {method 'disable' of  _lsprof.Profiler' objects}
   

   More details here.

3. Don't know.

4. Perhaps the naive answer is that running it on a "faster" computer would do the job. ;-) My experience back around sage-4.x was that compiling it resulted in faster runs, so my recommendation would be to compile sage on a linux machine.

   Just ran the factorial command and got

   sage: %time a=factorial(1000000)
   CPU times: user 0.27 s, sys: 0.01 s, total: 0.28 s
   Wall time: 0.28 s
   

   I'm running a compiled sage 5.10 on arch linux.

(This was just going to be a comment but it got too long)

1. Maybe 1 is faster than 2 since that is running natively on the server, the VirtualBox overhead might slow things down.

2. Don't know.

3. On profiling programs:

   sage: %prun a=factorial(1000000)
            2 function calls in 0.286 seconds        
      Ordered by: internal time        
      ncalls  tottime  percall  cumtime  percall filename:lineno(function)
           1    0.286    0.286    0.286    0.286    0.286 <string>:1(<module>)
           1    0.000    0.000    0.000    0.000 {method 'disable' of  _lsprof.Profiler' objects}
   

   More details here.

4. Don't know.

5. Perhaps the naive answer is that running it on a "faster" computer would do the job. ;-) My experience back around sage-4.x was that compiling it resulted in faster runs, so my recommendation would be to compile sage on a linux machine.

   Just ran the factorial command and got

   sage: %time a=factorial(1000000)
   CPU times: user 0.27 s, sys: 0.01 s, total: 0.28 s
   Wall time: 0.28 s
   

   I'm running a compiled sage 5.10 on arch linux.

Hi,

(This was just going to be a comment but it got too long)

1. Maybe 1 is faster than 2 since that is running natively on the server, the VirtualBox overhead might slow things down.

2. Don't know.You can create a worksheet and run the command

   %time a=factorial(1000000)
   

   Here is what I got.

3. On profiling programs:

   sage: %prun a=factorial(1000000)
            2 function calls in 0.286 seconds        
      Ordered by: internal time        
      ncalls  tottime  percall  cumtime  percall filename:lineno(function)
           1    0.286    0.286    0.286    0.286    0.286 <string>:1(<module>)
           1    0.000    0.000    0.000    0.000 {method 'disable' of  _lsprof.Profiler' objects}
   

   More details here.

4. Perhaps the naive answer is that running it on a "faster" computer would do the job. ;-) My experience back around sage-4.x was that compiling it resulted in faster runs, so my recommendation would be to compile sage on a linux machine.

   Just ran the factorial command and got

   sage: %time a=factorial(1000000)
   CPU times: user 0.27 s, sys: 0.01 s, total: 0.28 s
   Wall time: 0.28 s
   

   I'm running a compiled sage 5.10 on arch linux.

Hope it helps!